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Line and continuum studies of some star forming regions Sato, Takashi 1995

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LINE AND CONTINUUM STUDIES OF SOME STAR FORMING REGIONS By Takashi Sato B. Sc. (Physics & Astronomy) University of British Columbia, M. Sc. (Astronomy) University of British Columbia  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA  March 1995  ©  Takashi Sato, 1995  ,  1989  1986  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of Physics The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1Z1  D ate:  23  Abstract  Two sets of protostellar objects have been studied using the James Clerk Maxwell Tele scope as the main observational facility. The first set is a selection of sources from the IRAS Point Source Catalog, originally observed as part of a survey of protostellar candidates. In this present work, the ob servational database has been extended to include the (sub)millimetre continuum and J  =  3  —*  2 and 2  —*  1 lines of CO, ‘ C0 and 7 3 C’ 0 , and J  =  7  —  6 and 5  —‘  4 lines  of CS and C 5. 3 4 The continuum mapping was able to resolve each source in addition to making flux measurements. The analysis of these flux values using dust emission models is reported in a separate paper. The molecular lines have been analysed using radiative transfer models in the Large Velocity Gradient (LVG) approximation. Molecular hydro gen densities have been derived for most of the sources studied and have been found to cluster around n  3 c 5 10 . m No apparent correlations are seen among the observed and  derived parameters. NGC 6334 I and NGC 6334 I(North) comprise the second set of objects and are located at the northern end of the molecular cloud complex NGC 6334. This region has been observed using the same lines, and in particular, mapped in CO (J (J  =  7  —  6). “Extreme High Velocity” (V  ‘-s  =  3  —*  2) and CS  kmr’) wings of CO are seen around  NGC 6334 I and the outflow is found to be bipolar. The outfiowing material has been shown using radiative transfer models to contain gas at a density of ii  “-‘  x 10 cm for a 3  total mass of 2.5M 0 in the wings. This corresponds to a mass flow rate of 8 x 10 M® yr’ 4 and a mechanical luminosity of 89 L . A neutral H 0  I  wind ejected at high velocity from  the star is inferred to be driving this molecular flow. The implied stellar mass loss rate 11  is 4 x 4 10 M ® yr . The CO line wings at peak I(North) are much less prominent, with 1 20 km  5—1,  although significant wings are present. They are not, however, in the  form of bipolar lobes. Another feature, an extension 30 arcseconds to the northwest of I, has been newly identified. LVG model analysis has been used to derive H 2 densities at a large number of beam positions. This yields n for I(North) the gas density is only  n-I  ‘—s  1.3 x l0 3 c 7 m for peak I while  4.5 x . 3 c 5 10 m This contrast in gas density,  combined with the lack of a luminous thermonuclear source detected around I, supports the suggestion that NOC 6334 is a very young stellar object bnt that I(North) is an even younger one. A lower limit of  n.  3000 yr for the age difference between the two systems  is inferred from the time scales of the bipolar outflow at NOC 6334 I.  111  Table of Contents  Abstract  ii  Table of Contents  iv  List of Tables  ix  List of Figures  x  Acknowledgement 1  2  xii  Introduction  1  1.1  The Star Forming Environment  2  1.2  Current Issues in Star Formation Research  5  1.3  Objects Studied in This Work; Background and Review  6  1.3.1  IRAS Selected Protostellar Candidates  7  1.3.2  NOC 6334  10  1.4  Radiative Transfer Model/Code and Applications of its Results  14  1.5  The Objectives  16  The Radiative Line E&ansfer Model: The Physics and The Computing 17 2.1  Introduction  17  2.2  The Model Basics  18  2.3  The Detailed Picture  22  2.3.1  22  Optical Depth  iv  2.3.2  Transition Probabilities.  2.4  The Algorithm: An Outline  24  2.5  Structure of the Code  25  2.5.1  Array Structure  25  2.5.2  Initial Conditions  28  2.5.3  Iteration and Convergence  29  2.6  Sample Output  31  2.7  Validity of the Models  34  2.7.1  Is the Code OK?  34  2.7.2  Is the Model Representativ 2 e  37  2.8  2.9  Internal Checks  38  2.8.1  Grid Resolution  38  2.8.2  Initial Values  39  External Checks 2.9.1  2.9.2  .  .  40  Tests Against Expected Behaviour or Analytical Solutions in Lim iting Cases  3  22  .  40  .  Tests Against LVG Solutions  41  Observations  44  3.1  The James Clerk Maxwell Telescope  44  3.1.1  Physical Description of the JCMT  44  3.1.2  Signal Paths and Receivers for the JCMT  45  3.2  Observations of IRAS Selected Protostellar Sources with the JCMT  3.3  Observations of NGC 6334 with the JCMT  52  3.4  Calibration  53  3.4.1  53  Calibration of Continuum Data  v  .  48  3.4.2  4  55  3.5  Telescope Pointing  56  3.6  Transport of Observed Data  57  The IRAS Selected Protostellar Candidates 4.1  4.2  5  Calibration of Line Data  58  Continuum Data 4.1.1  Results from Continuum Data  4.1.2  Dust Models  Line Data 4.2.1  Results from Line Data  4.2.2  Column Densities  4.3  Possible Trends and Patterns  4.4  Future Work  4.5  Individual Sources  NGC 6334 I & I(North)  78  5.1  Observed Data; Overview  78  5.2  CO Spectra at I and I(North)  78  5.3  Molecular Line Maps  82  5.4  The Mystery of NGC 6334 I(North)  91  5.5  LVG Models  92  5.5.1  Model Results  93  5.5.2  S 3 C 4 J  =  7  —  6 Anomaly at Peak I  97  5.6  Derived Parameters: The Bipolar Outflow at NGC 6334 I  5.7  Discussion  104  5.7.1  Relative Ages  104  5.7.2  Are EHV Outflows a Common Phenomenon 7  104  vi  99  Neutral Hydrogen Wind in NGC 6334 J?  5.7.3 6  Conclusions  107 108  6.1  The IRAS Selected Protostellar Candidates  108  6.2  Northern End of the NGC 6334 Complex  109  6.3  General Conclusions  110  6.4  Summary of Suggested New Observations  110  Bibliography  112  Appendices  117  A Other Discussion  117  A.1 IRAS Protostellar Candidates Revisited  117  A.1.1  Artifacts in the LVG Model 7  117  A.1.2  FutureWork  118  A.2 In general  118  A.2.1  Potential for Problems with the LVG Analysis  118  A.2.2  Line Transfer Model  120  A.2.3  Additional Lines for Observation/Modelling  121  B Data Transport  123  B.1 Spectra  123  B.2 Continuum Maps  126  C Figures in Series: IRAS Protostellar Candidates  128  D Figures in Series: NGC 6334 I & I(North)  160  vii  E Astronomical Units and Constants  167  F Abbreviations and Symbols; A Glossary  168  viii  List of Tables  1.1  Protostellar Cloud Conditions  2  1.2  Protostellar Candidates from IRAS PSC  9  2.1  Models in the High Density Limit  2.2  Models in the Low Density Limit  2.3  IViodels in the LVG Limit  42  3.1  Spectral Lines Observed  48  3.2  Log of Observations for the MDPS IRAS Sources  49  3.3  TJKT14 On-The-Fly Mapping Parameters  3.4  Log of Observations for NGC 6334 I  3.5  JCMT Calibration for Continuum Mapping  55  4.1  Integrated Continuum Fluxes  60  4.2  Source Angular Size and Position Angle  61  4.3  Molecular Abundances  64  4.4  LVG Model Results  66  4.5  Masses of the Molecular Component  67  4.6  0 Column Densities 7 C’  68  5.1  LVG Model Results over NGC 6334  94  5.2  Physical Parameters for the Outflow in NGC 6334 I  ix  .  40  .  41  a I(North)  .  51 52  100  List of Figures  2.1  Model Geometry  2.2  Iterating Towards Convergence  2.3  Sample Output Spectra  2.4  Self Absorbed Profile  2.5  Exploring the Effects of a Temperature Gradient  3.1  Signal Path to the JCMT Spectrometer  47  4.1  Example of LVG solutions  65  4.2  Patterns in our Sample  70  5.1  Sample CO J  79  5.2  Spectra Centred on NGC 6334 I  81  5.3  Map of Velocity Integrated CO Emission  83  5.4  Map of Velocity Integrated CS Emission  84  5.5  Overlay of Near IR and Other Compact Objects  86  5.6  CO 3  89  5.7  R.A.  5.8  Derived Gas Densities over NGC 6334  —*  —  =  3  —f  2 Spectra  2 Wing Emission  Velocity Diagram for Peak I  90 96  B.1 Data flow for Line Observations  124  B.2 Data flow for Continuum Observations  127  C.1 Continuum Data on the MDPS IRAS Objects  x  .  .  .  129  C.2 Molecular Line Data for the MDP•S IRAS Objects  139  D.1 Beam Positions for Each Line Observed  161  D.2 Velocity Slices of CO Emission  162  D.3 Velocity Slices of CS Emission  165  xi  Acknowledgement  This thesis represents much of my contributions towards two ongoing projects. I thank my collaborators, Drs. W.H. McCutcheon, P.E. Dewdney and C.R. Pnrton, for the IRAS selected protostellar candidates programme, and Drs. W.H. McCutcheon, T.B.H. Kuiper and H.E. Matthews, for the NOC 6334 programme, for many enlightening discussions. The special role of my supervisor cannot go unnoticed. In addition, the superb receiver constructed and made available to the JCMT community by the group led by Dr. E.C. Sutton has been instrumental in both projects. Also, I wish to thank the observatory staffs of both DRAO and JCMT for ‘showing me the ropes’ during my countless visits, both personal and electronic. The export software package from DRAO was used to perform some of the analysis and to prepare most of the figures presented in this work. I wish to thank Dr. L.A. Higgs for making the software available and for his unending guidance during the installation process. Finally, I hope all readers appreciate my gratitude to Dr. L.W. Avery who kindly provided the LVG code used in this study although I may appear to criticise it at certain points in the text.  xii  Chapter 1  Introduction  Astrophysics, if we take the literal meaning of the word, is the branch of physics con cerned with the study of stars. In a discipline supposedly concerned primarily with stars, one logical starting place may appear to be the investigation into the origins of stars. Yet, our understanding in the field of star formation has been surprisingly superficial. In our century, great advances have been made in our understanding of already formed stars, from the quiescent main sequence stage of hydrogen burning in the core through the shorter lived but more dramatic stages of evolution, all the way to their end states. Theoretical predictions are now of such precision that detailed comparison with observed data can he used to determine composition, age, temperature, luminosity, etc. for indi vidual stars or groups (e.g. Sato et al. 3 1989). By comparison, the formation process of stars is very poorly understood. Observational evidence tells us that stars must somehow form inside dense molecular clouds by the gravitational collapse of interstellar gas and dust, and that the remaining material is blown away once the star becomes sufficiently luminous. The quantitative details of the exact physical processes, however, are poorly known (but see the list of review articles at the end of Section 1.2 for current state of the art.). This lag in development in star formation research compared to other areas of astrophysics can be attributed to the historical weakness in observational accessibility. With new instruments in operation today, it is the intent of this thesis to attempt to make a contribution to this field of research.  1  Chapter 1. Introduction  Property Gas Density H + H ) 3 2 (cm Size (pc) Gas Temp., TkI (K) Visual Extinction, Av (mag) Mass (Me) Free Fall Time (yr)  2  “Standard” Cloud 10 10 70 0.1 300 not bound  Protostellar & Circumstellar 1010  iO  10_i (or 1 a.u.) 4 10 1000 10 opaque 0.01 100 io  Table 1.1: Protostellar cloud conditions. Some parameters describing protostellar clouds are compared with “typical” conditions found in interstellar clouds. [Taken from Table 2 of the review article by Zuckermann and Palmer (1974).] These numbers are here to serve only as rough guides to help develop an intuition for the star forming environment. 1.1  The Star Forming Environment  Iviolecular clouds, which have been identified as sites of star formation, are simply clouds in interstellar space consisting of dust and molecular gas. Normally, in the interstellar medium, gas is found in atomic or ionised form. However, in dense clouds such as these, the gas has an opportunity to form molecules on dust grain surfaces. Furthermore, the outer (or circumstellar) regions, which still consist of atomic and ionised gas, can be effective in shielding the central material. Thus, the ambient radiation field or radiation from stars nearby (or within) is prevented from dissociating the molecules. The range of typical gas densities found in such clouds are n  =  (10  1010)  . The gas kinetic 3 cm  temperatures can be few tens to lOOK but as high as 1000K near the protostar (See also Table 1.1). The most abundant molecular species is H , followed by CO. The primary 2 reason molecular clouds are identified as regions of star formation is that we see luminous  Chapter 1. Introduction  3  OB stars’ and H II regions 2 associated with them (e.g. see Lada 1980). Triggered by external influence (e.g. galactic density waves or supernova winds, the exact choice is a subject for cnrrent and future study) or in isolation (e.g. Bok Globules, where internal instabilities, snch as thermal, may play a key role), small clumps of gas and dust start to collect within the molecular clouds aided by self gravitation and perhaps the local magnetic field. Eventually, these grow into star forming regions which are thought to be in states of general collapse. Such a cloud then releases energy by radiative means. This “cooling” permits further contraction. Thus the system is gravitationally unstable and is on its  way  to  becoming a protostar. As the density increases, the free-  fall is retarded by thermal, radiation, and perhaps magnetic pressures from within. The infalling material is heated by release of gravitational energy and also by such processes as molecule formation. It cools by radiating in the infrared continuum as well as in spectral lines of constituent molecules. The infrared radiation is due to the dust component and this can be used to study not only the properties of the dust itself but also the coupling between the dust and the molecular component. The radiative transfer of line radiation depends very much on the spatial velocity structure since the large optical depths of CO (the dominant molecular species of interest, as we shall see below) and some of the other high abundance molecules imply that, in order to evade reabsorption and thus be available to be observed by us here on Earth, a photon from one region within a cloud must be Doppler-shifted out of the line in an adjacent region. This requires a significant velocity gradient within the cloud. A comprehensive modelling of a star forming cloud must therefore solve simultaneously equations describing the radiative processes locally Stars of spectral types 0 and B are those with the greatest masses. They are also the most short-lived. 1 This combined with their observed kinematics imply that OB stars could not have formed elsewhere and then travelled to their present locations for they would have evolved past the main sequence during the journey. Thus, if one sees OB stars in association with molecular clouds, it is reasonable to suppose they were formed there. ii regions are those regions of interstellar clouds in which the gas is ionised by the high energy radiation from the stars within.  Chapter 1. Introduction  4  as well as those describing the coupling between the regions. Owing to the cosmic elemental abundances, the most abundant molecule by far in the interstellar medium is H . Due to its symmetry, however, this molecule lacks a permanent 2 electric dipole moment. This attribute makes the H 2 molecule unobservable by means of its rotational transitions, in contrast to other molecules such as CO. The CO molecule, being the second most abundant, is a good, readily observed tracer of molecular material. In addition to its high abundance, it requires only relatively low energies to excite the higher J levels. Thus, in this study, the observational and modelling efforts begin with the lines of CO. The rotational transition lines of CO have proven to be the primary workhorse in delineating molecular structures in our galaxy (see, for example, Williams 1985, Polk et al. 1988 or Liszt 1982). It is particularly useful in the study of dense clouds and regions of forming stars where, traditionally, observations consisted only of optical work. By their dusty and nebulous nature and associated high extinction, these regions could not be penetrated beyond the outer skin by optical observations. Thus, the description of their interiors was left to the astronomer’s imagination. With molecular observations, we are now able not only to see into the cloud cores but also to observe that major component of the cloud directly, rather than relying on some starlight to illuminate (and interact with) it. Although some difficulties arise with 12 O observations due to the 6 C often excessively high optical depth caused by its high abundance, this effect can be modelled in the manner outlined below. In addition, we have used observations of less abundant isotopic species of CO as well as CS in order to minimise or avoid problems associated with high optical depths.  Chapter 1. Introduction  1.2  5  Current Issues in Star Formation Research  On the observational side, the accessibility of a great deal of data on the molecular gas component has now been established for some time, in the form of molecular rotational transitions observable using millimetre-wave and, more recently, submillimetre-wave tele scopes. However, while we have been able to measure global characteristics of the cir cumstellar matter, these do relatively little to probe the stellar component directly. With the emergence of far infrared and submillimetre technology, we are now gaining access to this component. These wavelengths are proving useful since the peak in the continuum emission from protostellar sources occurs in this region, characteristic of their warm temperatures. As well, the lower opacity in this band makes it possible to penetrate deeper into the circumstellar cloud. If only in this way, new submillimetre telescopes such as the JCMT have proven their worths. Furthermore, the Infrared Astronomy Satellite (IRAS) mission has opened up a wealth of new opportunities. The fact that its database is in the form of an all-sky survey has made IRAS that much more invaluable. This access to the far infrared sky afforded by IRAS will continue to be exploited by astronomers for years to come, even though the telescope itself has terminated operations years ago. On the theoretical side, the strictly “stellar” component, has been well understood for some time. This includes not only the main sequence and subsequent evolution but also the pre-main sequence activity as characterised by Hayashi (1966) and Larson (1972). Current efforts seem to focus on the circumstellar component and its interaction with the protostar. This includes the gas and dust in the circumstellar nebula, a disk, if any, and associated questions of angular momentum. Behind all this is the origin and nature of the molecular bipolar outflow (BPO) so ubiquitously observed. As the review by Bachiller and Cómez-González (1992) indicates, there are now more than 200 such BPOs known in the galaxy, always found in association with active sites of star formation.  Chapter 1. Introduction  6  There also appears to be an emerging new class of Extreme High Velocity (EHV) outflows with velocities exceeding 100 km  s’  which are thought to be responsible for driving the  “standard” high velocity (SHV) outflows. [See Bachiller and Gdmez-González, 1992, also Lizano et ci 1988, Koo 1989, Margulis and Snell 1989, RodrIguez et ci 1990 and Bachiller and Cernicharo, 1990.] The problem is in putting the observed properties together with the theory, since that component which is relatively well understood is difficult to observe, while there is no one clear theory of the outflows so commonly observed. Although this section has reviewed the topic of star formation only in a cursory manner, many of these issues have been addressed in review articles by Znckermann and Palmer (1974), Shu et ci. (1987), Lada (1988) and Mitchell (1993), to name only a few. Interested readers are referred to these excellent works. 1.3  Objects Studied in This Work; Background and Review  The objects studied here are separated into two categories: the IRAS selected protostellar candidates and the northern edge of the prominent molecular cloud complex, NGC 6334. They represent two separate research projects involving different groups of collaborators. However, since they represent much of my own research efforts in addition to employing much of the same facilities and techniques, they are described together in this thesis. Of course, their common objective is to learn more about the physics of star forming molecular clouds. After the sources are introduced in this chapter, observations for both projects are described together in Chapter 3. The results are then described separately for the IRAS sources and NGC 6334 in Chapters 4 and 5, respectively.  Chapter 1. Introduction  1.3.1  7  IRAS Selected Protostellar Candidates  A sample of 39 protostellar candidates was initially selected based on their characteristics as they appear in the IRAS Point Source Catalog. 3 This process has been described in detail elsewhere [McCutcheon, Dewdney, Purton and Sato (1991), hereafter MDPS]. Briefly, these sources represent cool galactic sources with star forming cores but without previous optical identification. The purpose then was to identify previously undiscovered objects undergoing early stages of star formation and to make survey-style observations, in an attempt to discover some patterns as well as individual objects meriting further study. Our previous observations as described in the first paper were made at various wave lengths with numerous telescope facilities. They have formed the basis of the first phase of the project and are described in detail in MDPS. The data there include, for each of the 39 sources, the original IRAS broad-band measurements, both Low Resolution Spectra also from IRAS, J at the NRAO  “  =  1  —*  0 rotational transition lines of CO, 3 ‘ C 0 and C’ 0 obtained 8  12 meter telescope, as well as C-configuration VLA  observations at  6cm. The optical image from the Palomar Observatory Sky Survey (POSS) E print is also shown. The majority of our sources was found to have very wide (V  10 km s  at  T  0.2 K) 7 CO lines, many consistent with strong outflow activity. Eleven were classified to ’ 6 lnfrared Astronomy Satellite (IRAS), among its many tasks, made an all-sky survey at 12, 25, 60 5 and 100 pm bands. The Point Source Catalog (PSC) is one of the chief data products available from this project. National Radio Astronomy Observatory is operated by Associated Universities, Inc., under contract with the National Science Foundation. The Very Large Array, operated by NRAO is a dedicated aperture synthesis telescope capable of subarcsecond resolution and working at wavelengths now down to 7 mm. zXV: In “radio” astronomical spectroscopy, frequency shifts of spectral lines are often expressed in 6 terms of the velocity that would cause that shift via the Doppler effect. In the same manner, line widths are expressed in velocity units. see definition, p.55.  Chapter 1. Introduction  8  be pre-main sequence objects; another four may also belong to this list. Among our higher luminosity sources, those with strong molecular outflows were generally associated with pre-main sequence objects whereas the sources in our narrow line category appeared to have embedded objects already on the main sequence. Our Hertzprung-Russell diagram [Fig. 3 of MDPS] shows no high luminosity main sequence objects with wide CO lines. This lead us to suggest that unlike our less luminous sources, the outflow activity somehow ceases or perhaps is disrupted on the high luminosity sources before they reach the main sequence. Similar surveys based on the IRAS database have been made by other groups. [e.g., Wilking et at. (1989), Moriarty-Schieven et al. (1992), Tamura et at. (1991), Beichman et at. (1986), Snell et at. (1988), Snell et at. (1990), and Carpenter et at. (1990).] Of these, the work of Wilking et at. (1989) is perhaps most similar to our own, albeit an independent effort (and unknown to us at the time). Indeed, the search criteria through the IRAS PSC bears close resemblance to our own. As one might expect, our two surveys contain 13 objects in common. The majority of their sources was found to be associated with recent star formation sites due to strong CO emission and high gas column densities. Molecular outflow activity and compact dust emission in the millimetre continuum were detected from a large fraction of their objects. Two classes of dust clouds emerge in this study; one small and dense, the other more diffuse. Moriarty-Schieven et at. (1992) have made a CO J = 3  —*  2 survey of a similar class  of objects within the Taurus cloud complex. They too found outflow in many of their sources. However, their source list does not overlap with ours, as we happen not to have any sources in the Taurus region. In the stage of this research programme described here, new observations have been  Chapter 1. Introduction  Source No. # 01 # 02 # 04 # 05 # 06 # 07 # 09 # 13 # 14 #15 # 18 # 21 # 22 # 23 # 25 # 26 # 31 # 36 # 38 # 39  9  IRAS-PSC Name 18134 1942 18151 1208 18162 2048 18258 0737 18265 1517 18316 0602 18517 -I- 0437 20178 + 4046 20188 + 3928 20216 +4107 20286 + 4105 21334 + 5039 22272 + 6358A 23545 + 6508 00338 + 6312 00420 + 5530 03235 + 5808 05553 + 1631 06103 + 1523 07427 2400 —  —  —  —  —  —  —  Coordinates (1950) Pre-Main R.A. Declination Sequence? 14 h 18 2 m 6 s 3 —19°42’25” maybe 19 h 18 0 m 0 s• 5 —12°08’34” yes h 18 1 m 8 s• 6 2 —20°48’51” yes 21 h 18 5 m 5 s 5 —07°37’30” no g2 1 3 m 26 9 s h —15°17’Sl” maybe h 18 3 m 0 s 1 9 —06°02’08” yes 55 h 18 4 m 3 s 1 +04°37’42” yes 13 h 20 5 m 0 s• 7 +40°47’OO” maybe 10 h 20 5 m 7 s 8 +39°28’18” maybe 27 h 20 3 m 6 s 1 +41°07’56” yes 28 h 20 6 s 40 rm +41°05’39” don’t know 34 h 21 2 m 0 s 3 +50°39’43” yes 29 h 22 1 m 9 s 7 +63°58’21” don’t know 54 h 23 3 m 1 s +65°08’29” no 0033m53s.3 +63°12’32” don’t know 45 h 00 0 m 4 s 2 +55°30’54” yes 23 h 03 3 m 1 s +58°08’56” no 50 h 05 2 m 3 s 5 +16°31’46” don’t know 13 h 06 2 m 0 s• 0 +15°23’28” yes h 07 4 m 0 s 2 5 —24°00’22” yes  Table 1.2: Protostellar candidates from IRAS PSC. The original list of MDPS contains 39 sources. Sources investigated in this study form a subset of the original 39. Observational coverage varies from source to source due to practical considerations.  Chapter 1. Introduction  10  made using the JCMT 5 in both the continuum and molecular line emission in the mil limetre to submillimetre wavelength region. The continuum observations were designed to probe the dust density distribution and to measure the far infrared luminosity of each source. The molecular lines were used to determine the density and the dynamics of the gas cloud. In later sections, these are compared with theoretical predictions as well as with  each other. Of the original 39, a number have been dropped from the list for further  study as constraints are placed by the available telescope time. In particular, our con tinuum mapping efforts are concentrated on the less evolved, pre-main sequence objects. However, we were able to include objects from every region of our Hertzpruug-Russell diagram, on and off (pre-) the main sequence, for the line observations. Table 1.2 shows the sources targeted in this phase of the study. 1.3.2  NGC 6334  This giant molecular cloud complex is an optically prominent object in the southern galactic plane.  The complex, with coordinates R.A.  =  l7hhl8m, Dec.  =  —35°42’, is  located at a distance of 1.74 + 0.31 kpc (Neckel 1978) in the Sagittarius arm. In this study, we wish to investigate the nature of the molecular material in the northern end of this complex encompassing the two peaks, NOC 6334 I and NGC 6334 I(North). Previous investigations as outlined below suggest the two sources represent objects at different stages of very early evolution. Given that they are side by side and equidistant, they form a convenient and reliable pair for comparative study. In addition to the CO and CS data that are presented here, there has been a number of previous investigations, as described below, focusing on far and near infrared, radio continuum or molecular line (including maser) emissions. For this reason, NGC 6334 The James Clerk Maxwell Telescope is operated by the Observatories on behalf of the Particle 5 Physics and Astrophysics Research Council of the United Kingdom, the Netherlands Organisation for Scientific Research and the National Research Council of Canada.  Chapter 1. Introduction  11  is also a region exceptionally rich in nomenclature. In this work, attention is focused on NGC 6334 I [nominally, a [a  = m s, 1 h 17 3 7 5  6  =  =  s 1 h 17 3 m 7 2  6  =  —35°44’07”] and NGC 6334 I(North)  —35°42’17”j.  The entire NOC 6334 complex was mapped in the 1.0 mm continuum by Cheung et ci. (1978). A succession of bright peaks (I through IV, in their numbering scheme) with regular angular separation is revealed in this map and a suggestion of an age sequence is made with our source I(North) being the youngest member. I(North) is also the brightest feature in the map. The complex was also mapped at 69 pm by McBreen et ai. (1979); peak I is found to he the brightest feature at this wavelength while I(North) is undetected. [It may be noted here for clarity that peak I of McBreen et ci. coincides with peak II of Cheung ci ci. which is source F in the 6cm VLA maps of Rodriguez ci ci. (1982). Peak I of Cheung et aL is renamed I(North) (and II as I) by Gezari (1982) who was one of the authors of the former paper, in order to avoid future confusion with the McBreen ci ci. numbering scheme.] In Gezari (1982), a 400 pm map of the NGC 6334 complex is presented. Their dust models show T  =  33 + 5 K for peak I and T  =  19 + 5 K for  peak J(North). For I(North), an inferred gas density of 3 x 3 cm is given. Source 5 10 J(North) remains faint at the shorter JR wavelengths in that it is undetected in the first two (probably three  9)  of 21, 42, 71 and 134 pm band maps of Loughran ci ci. (1986)  while source I is seen in all four bands. Harvey and Gatley (1983) find similar results in their near and far infrared mapping work of the NGC 6334 complex employing three different telescopes. The map of Emerson ci ci. (1973) over a 40—350 pm band shows the brightest peak at the position of I but shows no counterpart at J(North). Although the maps shown by Becklin and Neugebauer (1974) do not extend to the position of I(North), they did search for and did not find any compact 20 pm objects at this position. On the other hand, the maps clearly show emission peaks at 2.2, 10 and 20 pm at the position 9 T here may be some extended emission indicated in their maps at 71 pm over this position.  Chapter 1. Introduction  12  of NOC 6334 I. This source is found to be quite confined in the 10 pm and 20 pm maps with diameters less than 1 arcsecond in each case. The IRAS Point Source 17175  —  3544  corresponds to NGC 6334 I. No counterpart to I(North) is listed in the Point Source Catalog or the Small Extended Source Catalog. As Moran and RodrIguez (1980) point out, the non-detection of a far—infrared compact object suggests that NOC 6334 I(North) is still in the earliest stage of star formation in that there are no compact luminous objects yet established. In this pure accretion phase, they continue, diffuse heating is provided by escaping photons from the central regions or by a large number of low mass stars. Emission from the molecular component of NOC 6334 has also been well studied. Jackson et at. (1988) mapped peak I with the VLA in the 3 NH ( 1, 1) main hyperfine line. Two lobes of emission are seen and their dynamics have been modelled as a rotating molecular disk of 30 M®, diameter 0.3 pc, thickness 0.1 pc with gas density of around a 31 M® central star. An integrated line emission map of J  =  2  r-J  3 c 5 l0 m 1 C 0 1 5  —*  together with the 1300 pm continuum map was made by Schwartz et at. (1989) using the NRAO 12 meter. Both peaks are clearly seen in both maps with their 30 arcsecond beam. More along the lines of our own work (but unknown to us at the time), Bachiller and Cernicharo (1990) have mapped the high velocity wings of CO J J  =  3  —k  2 and J  =  2  —*  1, and HC N J 3  =  17  —÷  =  2  —+  16 lines around peak I using the IRAM  30m telescope. As described in Chapter 5, the wings of the CO J  =  2  —*  1 line observed  by Bachiller and Cernicharo, including the bipolar nature, are similar to our J and J  =  3  —*  1, SiO  =  2  —÷  1  2 data. The velocity structure seen previously by Jackson et at. (1988)  is reproduced in their HC N data and they offer an alternate explanation in which the 3 low velocity gas motion is a companion feature to the high velocity gas. A host of other lines is detected here and they derive some physical parameters for the outfiowing gas. These enormous wings are not seen in the CO J  =  1  —*  0 data of Dickel et at. (1977)  who mapped the entire NGC 6334 complex. (See discussion in section 5.7.2.)  Chapter 1. Introduction  Straw  13  and Hyland (1989B) present a map of shocked molecular hydrogen emission in  the 2.12 pm v  =  1  —,  0 5(1) line. Here, I(North) is again undetected while I is a distinct  feature. Straw, Hyland and McGregor (1989) and Straw and Hyland (1989A) present results from extensive near infrared mapping in J, H and K bands. ° Extended emission, 1 as well as many compact objects are seen associated with source I but not with I(North). This is perhaps due to a much higher internal extinction within source I(North) although the compact near infrared objects around peak I do indeed appear to form a cluster. NGC 6334 peaks I and I(North) are also seen to be exceptionally bright in maser emission. For example, methanol masers are found by studies of McCutcheon et at. (1988), Menten and Batrla (1989) and Haschick et at. (1989) at the position of I. The OH maser observations of Clegg and Cordes (1991) on source I show variability in their dynamic spectra over the time scale of minutes. Forster et at. (1987) observed I(North) [7 distinction between I and I( N.orth) is vague as their map is made with a 84 arcsecond beam at 2 arcminute grid spacing] to be the brightest NH 3 maser in their southern sky survey and derive some physical parameters: the resulting gas kinetic temperature is c-i  30 K and the H 2 density is  mass is inferred to be  e-i  c-s  7x  io  , and for a source diameter of 3 cm  1 pc, the  10 M 3 ®. The survey of Moran and RodrIguez (1980) for H 0 2  masers in the NGC 6334 complex detected maser emission at both I and I(North) along with three other sites. In continuum radio emission, the 6cm VLA survey of Rodriguez et at. (1982) found “source F”, a “nozzle” shaped H II region at the position of peak I. No compact source is observed near I(North). However, a featureless “source E” is found between I and I(North). The 1.95cm map of Schraml and Mezger (1969) shows no peaks discernible with the 2 arcminute beam of the 140 ft telescope at either position, although the limit 10  j, H and K are three of the standard wavelength bands, or filters, in the near infrared used for astronomical photometry. The wavelengths of their bandpasses are approximately 1.1 -s 1.4pm, 1.5 1.8prn and 2.0 —s 2.4pm, respectively for J, H and K.  Chapter 1. Introduction  14  of the extended emission appears to lie between I and I(North). In the present work, observations of CO and CS in their rotational transition lines are described. These submillimetre wavelength lines were observed nsing the JCMT. One immediate result from these new observations is the vast improvement in angular resolution. The JCMT beam can be as fine as 7 arcseconds wide, compared to the 48 and 65 arcsecond beams nsed for the 400 pm and 1.0 mm maps. Thus we can attempt to reveal finer features such as the structure of the cores. Since the observations are of spectral lines, we have also been able to extract valuable dynamical information. As well, the structures of the lines and their wings can be examined for evidence of outflow activity. Further use of the data is made in conjunction with radiative transfer models employing simultaneously the many lines observed in order to deduce the physical parameters of these regions. Of particular interest is the molecular gas density. 1.4  Radiative Transfer Model/Code and Applications of its Results  While observations using molecular rotational transition lines constitute the primary probe into molecular clouds, their interpretation is too seldom straight forward. This is because the observed line is sensitive to changes in the density, temperature and dynamics within the clouds, often in a very non-linear fashion. Thus, numerical modelling plays a key role in the interpretation of observed data. Given the density, temperature, and velocity structures and thus a source function, one can solve the equations describing the physical processes relevant to spectral line radiation (such as the equations of statistical equilibrium and radiative transfer) to com pute the profiles of the CO emission lines and those of other molecules. By following the approach of Goldreich and Kwan (1974) and de Jong et al. (1975) for example, one can  Chapter 1. Introduction  15  attempt to reproduce our observed line profiles and line intensity ratios among the var ious isotopic species as well as among different transitions. Here, the velocity structure is of particular importance, especially for ‘ 0, 1 C 2 6 since the high optical depths would quickly saturate these lines if all parts of the cloud were at the same velocity. (Even then, the 0 6 C 2 ‘ ’ line can still he optically thick.) Thus, we appeal to the Large Velocity Gradient (LVG) model (first investigated by Sobolev, 1957) in which the difference in velocities between spatially separated parts of the same cloud is significantly greater than the combined local thermal and turbulent line widths (which represent the only impor tant mechanisms for line broadening on the local scale) so that CO is coupled radiatively only locally. Alternatively, we can introduce large and ubiquitous turbulent velocities, spreading the opacity over a very wide line so as not to saturate it. In extremely dense regions of molecular clouds, such as those under study here, line saturation is still not eliminated by widening the lines. However, the effects of optical thickness (saturation) can he accounted for using these model calculations. One might say there are  two  distinct approaches toward modelling: one in which  physical assumptions are made for the purpose of simplifying the numerical problem, and one in which the numerical problem is solved by brute force so as to avoid a priori assumptions or “conclusions.” In this thesis, the former approach is taken using an exist ing code (Avery, private communications) while a new code was prepared to undertake the latter. The physics incorporated into the new code is described in Chapter 2, together with the details of the associated computing. The usefulness of this code is hoped to be long-lived, extending well beyond this thesis. These models must, of course, be consistent with other observed data. While I have not, at present, made any specific provisions in the computational code to ensure unique ness in our models, constraining data from other wavelengths are expected to go a long way toward this purpose, in addition to using sensible initial guesses (solutions are found  Chapter 1. Introduction  16  iteratively). For instance, the kinetic temperature and dust density must be consistent with the JR emission. Where ambiguities persist, model predictions have enabled us to suggest what additional observations are warranted or are expected to be most profitable. One example of supplemental data of this nature is the CS J  =  5  —*  4 line observations  pointed out in Sections 3.2 and A.2.3.  1.5  The Objectives  To summarise, the primary scientific objectives of this thesis will be in two parts. First, new observational data are collected using the JCMT on our selection of star forming regions in CO, CS and their isotopes and in the (sub)millimetre continuum. Next, these observations are interpreted in the context of radiative transfer models, in the hopes of enhancing our understanding of the gas component in star forming regions. With our MDPS IRAS sources, we are able to compare data on a set of objects for which we have already considerable amounts of observed and derived information available. In our first paper, this resulted in placing our objects on a Hertzprung-Russell diagram and identifying main sequence and pre-main sequence objects.  In a similar  vein, we wish to undertake further examination of our sample, with regard to some new parameters. The NOC 6334 portion of this work provides an opportunity to study the cloud structure by high resolution line mapping across the complex in combination with model analysis.  The detailed information assembled allows us to study features of the two  peaks of emission, I and I(North), including the remarkable bipolar outflow around I. The two peaks, which are suggested to be at different stages of formation, because they are observed in the same manner, and because they are at the same distance, render themselves well to systematic comparison.  Chapter 2  The Radiative Line Transfer Model: The Physics and The Computing  This chapter describes the multi-level line trausfer model code prepared as a tool to be used in the work to follow, within this thesis and beyond. As such, the nature of the discussiou in many sections leans toward that of computer documentation, rather than original scientific research. It is included here for completeness but readers may wish to skim or skip this chapter on first reading. 2.1  Introduction  The primary tool available to us in probing molecular clouds is their molecular line emission. However, interpretation of the observed line is complicated as it depends on the density, temperature, dynamics and the radiation field inside the cloud, often in sensitive and non-linear manners. Fortunately, the physics describing the formation and transfer of the line formation is relatively well understood in terms of the individual steps (although the choice between line broadening mechanisms remains a question.) To understand the collective effect of these mechanisms operating simultaneously, one resorts to numerical modelling. Following the approach of de Jong, et al. (1975), Leung (1978), Bernes (1979) and Cabrit and Bertout (1986), to name only a few, we start by examining the equations describing the radiative transfer of line radiation within a molecular clond. Our goal here will he to predict the observed line shape and intensity when physical and dynamical conditions in the cloud are specified. In this way, we can postulate models of the cloud 17  Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing  18  and then compare the predicted emission with the observed one. Unlike my predecessors’ approach, mine is to refrain, as mnch as practical, from making assnmptions about the system, which would then be incorporated analytically into the model. While being more costly in a computational sense, we preserve a great deal of generality by nsing this approach. By keeping the physical problem in its general form, input models can be substituted with dramatically different ones with ease. [N.B. The term “generality” refers only to the ability to specify a variety of input models. The ability of this code to produce realistic results for each input case is a separate matter. Tests for some specific cases are discussed later in this chapter.] The computational powers required in this approach are quite modest by current standards. It was decided to pursue this approach to supplement (or complement) the model code already made available to us by Dr. L. Avery (private communications). This latter code uses simplifying analytical approximations, rather than numerical brute force, to help arrive at the solution. 2.2  The Model Basics  We start the construction of our model with its one major assumption, that regarding its geometry. We assume that the observed molecular cloud can reasonably be represented by a series of slabs (or a “stack”), infinite in the tangential direction and individually homogeneous (c.f. Figure 2.1). As we shall see below, the advantages of this method are many-fold. First, since the molecular clouds of interest to us are generally large and smooth compared to the beam sizes of modern submillimetre wavelength telescopes, we can see intuitively that the infinite extents of our slabs do not present a large problem. This point is again examined in Section 2.7.2. Second, since we are now able to specify, with this model construction, the physical and dynamical parameters of the layers at will, to  molecular cloud modelled as layers of slabs  _./  —  \ (cosmic) background I 1 radiation  ni,  3 nvT  VN,TN VN-i,TN-1  flN-1,  flN,  Vi,Ti  2  obseer  observed emission  Figure 2.1: Model geometry. This schematic diagram illustrates how the model cloud is constructed and used to predict the observed emission. See text for more details.  /  (ID  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  20  any functional or tabulated form, the model allows us to examine “new” effects such as self-absorption or outfiowing wind. However, the greatest advantage of this method by far is the fact that it has essentially the same geometry and mathematical structure as the “plane parallel atmosphere.” The plane parallel atmosphere has been studied extensively in the first half of this century by scientists who made the pioneering investigations into the theory of radiative transfer in stellar atmospheres. [See, for example, Chandrasekhar (1950) and references therein.] Thus, we can rely on many of the proven methods from that era to yield useful results in this current and future efforts. With this in mind, we consider the following equations. From standard texts (e.g. Bowers and Deeming, 1984), a position or depth r within the cloud can be referred to by its optical depth r, and the equation of radiative transfer can be written as 1 IV(rV)  =  IV(0)e  +  T J  (T’T)d  (2.1)  where IV(TV) is the specific intensity of the radiation, IV(0) represents the radiation en tering the cloud [for an isolated cloud, IV(0)  =  B(v, Tbg), the specific intensity of a  blackbody at the temperature of the cosmic background], and  j(= SV) is the ratio of  emission to absorption inside the molecular cloud and is known as the source function. For the J  =  i  —>  j transition line, it can be written as =  2hi  [:  -1  -1]  for complete redistribution. Here, gi is the statistical weight, given by gi  (2.2) =  2i + 1, and  n is the molecular gas density for the ith rotational state. To find n, the equations of llere. we adopt the notation in standard texts (e.g., Chandrasekhar, 1950, Bowers and Deeming, 1 1984) in which a v-subscript denotes a function of frequency and its absence specifies the integral over frequency, except that the integration extends only over the line and not from zero to infinity. For example, = June Idv.  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  21  statistical equilibrium, n(r)EPj(r) = En(r)Pi(r)  (2.3)  ueed to he solved. Using J, the mean (over direction) intensity averaged over the line [i.e., ‘ =  .14r  ‘line I(Q)dvdct], the transition probabilities are given by Fj ( 1 r) =  where  and  A +  BJ ( 3 r) + C(r), i >  j  (2.4)  -  I.  B J 1 ij(r) + C (r), i 1  <j  are the Einstein coefficients 2 for spontaneous and induced transitions,  and C 1 are collision induced transition probabilities from the ith to the jth rotational state. (Note that  are also functions of position due to the positional dependencies of  n and T.) Though we have not yet specified the value, form or 3 physics of  or ‘r(r), we can  see that we have come full circle back to Equation 2.1 via the mean intensity. Thus, we see that it may be possible to solve this system of equations numerically by a series of iterations for a steady state. That is to say, if we start with some initial conditions, for instance LTE  populations,  we can compute the corresponding mean intensity by use of Equations 2.2 and 2.1. This can then be used in Equation 2.4 to determine the transition probabilities between the rotational levels. These can in turn be applied to find new densities (Equation 2.3, but also see Section 2.5.3) which will be the starting point of the next iteration. In the following section, I shall discuss the physics and the subtleties of evaluating the optical depth function. Here, as in de Jong, et al. (1975), I have defined the Einstein coefficients in terms of the mean 2 intensity instead of the customary energy density. This introduces a factor of 4w/c in some equations. (See Section 2.3.2, Transition Probabilities.) 1n fact, in order to preserve generality in these models, I have purposely not specified any form for, 3 or structure in, n(r), v(r) or Tkfl(r) all of which influence r(r). “ Local Thermodyna mic Equilibrium. In this context, the term LTE is used to describe a condition where locally, the relative populations among the rotational states of the molecule of interest can be described by Boltzmann factors of a single, common temperature. = ThIn)  Chapter 2.  2.3  The Radiative Line Transfer Model: The Physics and The Computing  22  The Detailed Picture  2.3.1  Optical Depth  In any radiative transfer investigation, a fundamental quantity of interest is the optical depth. Consider first, ‘j(r, v  —  v ( 0 r)), the normalised, local line shape. This is the  shape with which the lines are emitted or absorbed at some particular region in the cloud. Note that  ii,  the frequency of the line centre, is a function of position, as we  expect to use significant velocity gradients throughout the cloud. This will shift the line centre via the Doppler effect. In the models thus far computed, I have used Gaussian functions to describe  .  The line widths are due to thermal Doppler broadening, Avh  (v/c)/iiT/mmo:, and turbulence  /.IVturb.  =  (N.B. the question of turbulence will be raised  in Section A.2.2.) The two widths are combined in quadrature. Next we consider the absorption coefficient, jk 0 j(r)  [nj(r)Bj  —  j. 13 n(r)B  =  (2.5)  The optical depth can now be expressed simply as r(v, r) =  for the i  —>  j  j  1.66k q 0 (r’)(r’, v  —  (v 0 r’))dr’  (2.6)  transition. This integrand represents the probability of the photon being  absorbed at each point r’ along its path from depth r to 0. The factor of 1.66 is the “diffusivity factor” which approximates to a good degree the effect of averaging over directions. It results from the exponential integral that arises under the plane parallel geometry (see, for example, Chandrasekhar 1950). 2.3.2  Transition Probabilities  In order to proceed with computations, one needs to evaluate the transition coefficients , 1 A  and  The Einstein coefficients,  and  are normally available from  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  23  any standard text in astrophysics. However, in writing Equation 2.4 in the way we did (following the approach of de Jong, et a!., 1975), we have defined (Aq and) B 1 in terms of the mean intensity. The customary definition involves u,, the specific energy density of the radiation. This departure from custom results in the relationship between  and  given by, B  =  A 23  (2.7)  which differs from the customary one by a factor of 4’ir/c. (Equation 2.5 is also affected.) The other standard relations of interest remain unaffected, so that we have (2.8)  =  and 1 A  =  64rv2  where the rotational dipole moment for the i p_  2 =  —*  2(  i  —  (2.9)  1 transition is given by (2.10)  Values for the dipole constant p for simple molecules can be found in the standard literature (e.g. Lang, 1980). For example, p  =  0.112 Debye for CO, and 1.98 Debye for  Cs. All that remain now are the collision probabilities. (Actually, “collision probability” is a loosely used term in this context since what we really mean is “the probability of a transition being induced by a collision.”) In my models, I simply use the probabilities computed by Green and Thaddeus (1976) and Green and Chapman (1978). These val ues are based on “extensive theoretical calculations using methods of known reliability”. Although experimental confirmation of these values by direct measurement is not gen erally possible, these rate coefficients are well accepted and used in the literature [e.g.  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  24  Cabrit and Bertont (1986), Bernes (1979), Lenng (1978).]. As the authors point out, the same extreme physical conditions found in interstellar space that make experimental measurements difficult facilitate theoretical determinations of collisional rates. 2.4  The Algorithm: An Outline  In developing this theory into computer code, the basic principle of keeping the algorithm and the code as general as practical has been followed. As such, the only constraints in volved are those required by the geometry. The equations of radiative transfer can be easily applied to plane parallel slabs. It is also a simple task to propose analytical ex pressions describing the cloud’s density, temperature and dynamics as functions of depth, in such a way as to simplify the numerical problem and lower the computational cost. This second step has been popular in the past with many investigators (e.g. Goldre ich and Kwan, 1974, de Jong, et al., 1975, Cabrit and Bertout 1986). However, I have deliberately stayed away from this approach in this investigation. My approach may cost extra computing time, but saves us from oversimplifying the problem or having to make a priori judgements on the models. Also, it renders itself to flexibility and future modifications or extensions. For each run, I propose a model, described by arrays containing  , 2 n-j  TM and  Vjsr  for  each layer. [At the risk of overemphasising the point with a comment, we note that we do not specifically refer to any velocity gradient. Thus, this is not specifically an LVG (large velocity gradient) model. LVG models have velocity gradients built into the theory and much of the work can be done analytically. This means that the equations to be solved can be tailored so as to make the numerical problem much simpler and less costly to solve. In recent times, however, computational cost of this magnitude is no longer the limiting factor. With this new model, I can (and do) recreate velocities whose gradients  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  25  happen to be large hut the approach is a different one. For example, I am not forced, a priori, to rule out a rnicroturbulence model. One can, if so desired, compute static models which would represent the opposite extreme from the models in the large velocity gradient limit.] A solution is obtained iteratively for populations at each rotational level in each layer. The chief output is taken in the form of the emerging intensity profiles (spectra) for each transition since these are the observable quantities.  2.5  Structure of the Code  In this section, discussion is made of some specific details describing how the physics already outlined has been encoded into a numerical form. In addition, methods used to find solutions to the physical equations are outlined. 2.5.1  Array Structure  As described earlier, and as depicted in Figure 2.1, our model is constructed with a series of plane parallel layers or “slabs.” Admittedly, specifying this, or any other geometry, restricts the generality of the model to some extent. However, the celebrated generality of this model arises from the following. The input physical parameters (density ri, temperature T & velocity v) are specified using arrays, where each element represents the value for a particular slab. (i.e., there is a one-to-one correspondence between the array index and the slab number.) Thus, the  layer of the cloud is characterised by by n, T and v,.  The array elements  are assigned values using a subroutine for this specific purpose, as part of the program initialisation. The powerful point of this design is that by making simple changes to that subroutine, the investigator has complete freedom to assign any value to any array element. In many existing applications, specific functional forms are assumed for the  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  26  physical parameters, often accompanied by specific relationships between the different parameters. In many cases, this can greatly simplify the numerical problem and shorten execution times. While there may also be good physical reasons to assume such relations, we do not restrict ourselves to such a priori assumptions, although we retain capabilities for doing so. In this application, the investigator can choose any functional or tabulated form for the input physical parameters. For the purposes of the above discussion, the density array was shown with a single index. In fact, the density array is further subdivided into another dimension, J, the rotational quantum levels. [Thns, we write nj, where i is the space index or layer number,  j  is for J.] This is only natural, since the transition spectra between the J levels will  be the chief output product to be compared to observations. The total density (as a function of space), n  nj, is assigned values as described above and is fixed for the  =  duration of the model run. Physically, this means zero net matter flow, consistent with the quasi-steady state assumption. Of course, the distribution among the J levels will be solved for a steady state solution. Introducing a third dimension, that representing frequency, allows us to define an intensity array, ,  ‘k  ‘ijk  Here, the k index refers to frequency across the line. For fixed i and  is a spectrnm for the J  two arrays,  k 1  and  1 k ’  =  j+1  —*  j  transition line at the t ti ’ layer. In fact, there are  representing the two directions (‘streams’) required to describe  intensity function under the plane parallel assumption. In gridding the variables (which are inherently continuous) into discrete array ele ments, care has been taken to ensure that both resolution and width of coverage are sufficient with regard to both space and frequency. In the spatial dimension, it is done by using a very large number of very thin layers. (N.B. all layers have the same thickness, typically  <  O.OOlpc per layer.) Thus, the  most rapidly varying parameter at its most rapidly varying location is still well behaved  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  27  numerically (i.e., layer to layer changes are small and smooth). Tests to ensure sufficient spatial resolution were performed as discussed in Section 2.8. The approach described here might be argued to be wasteful of computing resources, since spatial resolution is much finer than is required to model most of the regious well. Certainly, a more natural, computationally efficient, and commonly used approach is to parameterise the cloud in terms of the optical depth. However, this is not always straight forward when the input physical parameters (which are described in spatial terms) do not have a fixed or even an analytical form. Rather than programming a spatial to optical depth transformation facility, we simply ask the computer to work a little harder or a little longer. In the frequency dimension, the model array elements, (or spectrometer “channels,” since the output is to be compared to observed spectra) must resolve the intensity profiles at the local level. This is to ensure that the radiative flux is numerically well characterised in each layer and to ensure that adjacent layers do not becomed numerically decoupled, except by virtue of a real velocity gradient (see below). The frequency grid must be such that the local line profiles (which are dominated by turbulent velocity effects) are sampled by many grid points. Typically, “channel spacings” equivalent to  0.05km s  are used. Tests for these effects also are discussed further in Section 2.8. At the same time, we require a wide coverage in frequency since the lines to be modelled are often very wide. Thus, a large number of frequency elements are required in the arrays. Again, this calls for much more computational resources than is customary for this type of work. However, we specifically ignore this concern. At this level of demand, computational power is now plentiful enough that the astrophysicist should concern himself with the effective use of his time rather than that of the computer. We note also, that questions regarding spatial and frequency resolutions are coupled by way of the velocity gradient. That is, the line centre can shift from one layer to the next. Therefore, care is taken that (1) layer thickness is not so large that this shift is a  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  28  significant fraction of the local line width and (2) the frequency resolution is sufficient to recognise this shift. Unlike the variables for space and freqnency, the rotation levels are quantised and there is no concern over choosing sufficient resolution. It is sufficient to ensure that the highest rotation level included in the computation  (Jmax)  is taken high enough that  populations iu states above Jmax are too small to influence the (lower) transitions under study.  Tests for this effect are straight forward but, in practice, our choice of Jmax  is strongly influenced by the values of Cq available to us as tabulated by Green and Chapman (1978). 2.5.2  Initial Conditions  The only parameters in this code requiring initial values are contained in the density array nq described in Section 2.5.1. The values for n  (= >  n) are prescribed as part of the iuput and only the distri  bution among the J levels is left to be decided. Obviously, some choices of initial conditions will allow for faster convergence to a stable solution. However, there is no one, all-encompassing rule for choosing this dis tribution. In a manner of speaking, knowledge of such a rule would itself represent the solution to this entire numerical exercise. One example of a start-up distribution is to assume LTE. At the low densities of the interstellar medium, it is reasonable to expect the populations in the higher J levels would be subthermal. A start-up model mimicking this effect is another example. In any case, the exact choice of the initial model should not influence the final solution, only the rate of convergence, if the code is functioning as intended. This point will be tested in Section 2.8.  Chapter 2.  2.5.3  The Radiative Line Transfer Model: The Physics and The Computing  29  Iteration and Convergence  The iterative method used to find a steady state solution to the numerical problem may resemble how real systems move to steady states by time evolution or relaxation. Each step in the iteration involves the following. First, the current density populations are used to compute the source function everywhere in the cloud, via Equation 2.2. Next, the Equation 2.1 is integrated to determine the intensity everywhere in the cloud. The mean integrated intensity is then computed and used in Equation 2.4 to find the transition proabilities between the J levels for each layer. The probabilities are used with the current n array and a (initially small) time step to find new values for the density-population array. Thus we have allowed the system to evolve over that time step. Under numerically well behaved situations, the physics of the transitions ensures that the populations move toward the steady state. For example, if the ith rotational level is somehow overpopulated, the products riPj are elevated until the excess population is transferred out of that level. This method has certain advantages over solving the equations of statistical equilibrium (Equation 2.3) using standard algorithms such as the Newton-Raphson method. The Newton-Raphson method requires knowledge of the par tial derivatives of Pq in order to steer the parameters toward convergence. Unfortunately, the complexity of the stimulated emission term in  (involving space and frequency in  tegrals) makes differentiation non-trivial. The observant reader may have noticed that Equation 2.3 has the form of an eigenvalue problem. Again, the complexity and the non-linearity of P hinders an approach of this type. In any iterative application for solving a system of equations, the criteria for stopping the iteration can he somewhat arbitrary. In some cases, it is clear when one has reached some precision limit and the solution starts oscillating about some mean. In other in stances, we simply satisfy ourselves when solutions from one iteration to the next vary  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  30  by less than some small amount, determined perhaps arbitrarily. In this application, the latter is used to decide when to stop the iteration, although the former condition is often satisfied as well. Specifically, the stopping criteria are chosen based on the following observational principle. In the observational work described in this thesis, there have been a number of cases in which a particular source has been observed in one session, to be repeated in another, perhaps a year or more later. In such cases, we invariably see no significant changes in the observed spectra. Thus, we can say for the computed models that they must be stable under time evolution over periods of order one year within limits of detection. In the code, convergence is declared when the population densities change by less than a specified small (for practical reasons, adjustable) percentage over a simulated time period of one year. The number of iterations required, or the execution time in the computer, clearly depends strongly on the array sizes and complexity of the input physical parameters and often their specific values. It also depends on the machine used for computations, its speed and memory capacity. While there is no one, allencompassing answer, often when execution times exceed a few hours, array sizes are decreased or convergence criteria are relaxed, to the level indicated to be appropriate by the test cases (Section 2.8). Figure 2.2 shows a sample (CO) case of population densities for the four lowest rota tion levels approaching the steady-state values by iteration. The J how the high energy states (J  =  3 level illustrates  3, in this case) are quickly depopulated (from the initial,  L.T.E. values) as molecules make transitions to lower energies. The initial rise in the J  =  3 curve is due to the J  4 populations stepping through this rotational state on  their way to lower levels. The example shown is at a low density (n  400 cm ) and 3  is slow to converge, providing a good demonstration of the convergence mechanism. At very high densities where we expect frequent collisions to thermalise the populations,  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  31  0.008  0.006 I.,  S  0  >.  0.004  0.002  0.000 0  200  400  600  800  1000  Iteration Number  Figure 2.2: Iterating towards convergence. This figure illustrates the CO population densities for J levels 0, 1, 2 and 3 approaching the steady-state values at the centre of a low density model cloud. In this slowly converging example, the different rotational levels can he seen to reach steady-state at different rates. the L.T.E. populations used to start the iteration are already good solutions and the iteration process is trivial.  2.6  Sample Output  In order to demonstrate the effects of the model computations under discussion, two ex amples have been computed. They represent simplified cases to which analytical methods, intuition and/or experience provide us with expectations on the solutions. Figure 2.3(a) shows the computed CO line profiles for a molecular cloud with micro scale turbulence hut no structured velocities. The line profile is the main form of output and is computed as =  [I  -  Bv(Tbg)j  Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing  32  50  40 II  II 1 II  / I I I  \ \ \ \  /: / i; ,20  Cso  Is  C  II  \  I I  I  >%  \\  10  ‘.‘  ‘  ‘  I  I’  Is Is  —  ‘\ ‘\ ‘\  5  ,5  5  Is I, I, 0  —10  —5  0  5  10  Velocity (km/c)  50  /  40  —S  IS  I, II  I I  ‘:1  Is, Ij  I-  SI  III  >‘  20  IL  C  I  S  10  ‘5/  Isj 0  —10  I’  ii —5  0  5  10  Velocity (km/c)  Figure 2.3: Sample output spectra. (a) Top panel. A sample microturbulent model cloud CO spectrum is shown for each of J = 1 —* 0 (solid line), 2 —* 1 (dotted line) and 3 —* 2 (dashed line) transitions. (b) Bottom panel. Emission from a simulated LVC cloud is shown in the same lines. See text for details.  Chapter 2.  where I  The Radiative Line Transfer Model: The Physics and The Computing  is  the emergent intensity at the cloud surface.  33  (See also definition of T,  p.55.) The kinetic temperature and H 2 density are both constant throughout the cloud at Tlth  =  50K and nn 2  =  3 c 4 10 . m There is no velocity gradient or structure (v  everywhere), but there is a turbulent component of  VtUrb =  =  0  6.3 km s, as well as a small  thermal contribution to the line width. The cloud is 2 pc in thickness and the H 2 column density is 6 x 10 . 2 cm 22 For each transition, we see the line reaches a maximum intensity approaching the kinetic temperature (T  Ticjn), as one would expect at this high density and thickness.  For the high r transitions, the lines are saturated and become fiat-topped Also as ex pected, the line widths are consistent with the turbulence velocity. Although a series of runs is not shown here, this pattern is followed for other choices of Tk1 and  VtUVo.  Figure 2.3(b) shows the computed CO line profiles for an LVG cloud (recall Sec tion 1.4). That is, a cloud with an assumed structure that obeys the restrictions of our LVO code (except that it is not spherical). It is homogeneous in density (nil 2 isothermal (TkI  =  =  3 c 5 10 ) m ,  50K), and has a velocity gradient of 20 km r’pc’ over a total cloud  thickness of 0.75 pc. Although we do not expect to find interstellar clouds fitting this highly idealised description, it is useful to compute models in this limit because the results can be compared directly to the output of the LVG-specific code (see Section 2.9). In this limit, we would expect the computed lines to he fiat-topped, and the total width to be given approximately by (cloud thickness) x (velocity gradient). The width of this ‘rectangular’ line reflects the range in radial velocity across the cloud, as each localised region emits the line in its own rest frame. The intensity of the line is governed by the physical parameters (listed above) which are all constant throughout the cloud, giving rise to constant intensity for all velocity points. The ripples seen on the J  =  1  —*  0 line demonstrate a numerical artifact that can  arise when the spatial gridding is insufficient (see Sections 2.5.1 and 2.8.1). Each ripple  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  34  represents a model layer. We can see that the velocity difference between adjacent layers (or grid resolution) have become comparable to the local line width. The ripples are retained here for demonstration purposes but normally care is taken to avoid this and other numerical artifacts. Validity of the Models  2.7  There are two questions one needs to ask when considering the validity of numerical models and the results obtained through them. Of operational interest is the question: does the code solve the mathematical problem correctly? On the astrophysical side, we need to ask how well the mathematical model represents the astrophysical system. 2.7.1  Is the Code OK?  While it is difficult to know with certainty whether a computer program  of even this  complexity is functioning as intended, there are a number of tests that can be performed to help answer this question. One way to test this model code is to compute solutions in certain limiting cases of the input model where an analytical or other solutions are available for comparison. For instance, a static, dense (i.e. optically thick) cloud should result in a line intensity easily predicted from the gas kinetic temperature which would also be the excitation temperature. Since we have an established LVO model code, model solutions can be computed in the LVG limit (together with homogeneous and isothermal assumptions) such that a direct comparison of the results is possible. Tests have been performed in these limits and their results were found to be in good agreement, except for the effects of artificially sharp boundaries. (See Section 2.9.) In addition to the quantitative tests, qualitative behaviour of changes to the computed  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  35  50.0  40.0  30.0 I’ *  I  20.0 0 C  4)  C  10.0  0.0  —10.0 —20.0  0.0  20.0  40.0  Velocity (km/c)  Figure 2.4: Self absorbed profile. A numerically generated CO J = 2 1 line profile with a self reversal feature (thick dashed line) is compared to an observed spectrum (thin solid line) of IRAS 18162—2048 (see Chapter 4). In the model cloud, the line core features have been generated assuming a warm dense cloud with a cold foreground component. (For this run, no specific attempt has been made to reproduce the high velocity wings.) —,  line can be observed and analysed with variations in input parameters. For example, one can introduce a dense, cold foreground layer of gas and see if a self absorbed line profile re sults. One can also look for variations in the predicted line profile as the gas temperature or density structure is varied. Tests of this nature have been quite successful in attaining the expected results in a qualitative sense, giving some confidence in using the quantita tive results. Some examples of this model applied to observed data demonstrating these effects are shown in Figures 2.4 and 2.5.  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  36  50.0  40.0  30,0 *  20.0  10.0  0.0  —10.0 —10.0  —5.0  0.0  5.0  10.0  Velocfty (km/s)  Figure 2.5: Exploring the effects of a temperature gradient. Molecular lines observed in the ISM are often sharply peaked, as opposed to the rounded peaks of Gaussian profiles, for example. One way to produce a sharp peak in the computed line is to introduce a temperature gradient in the input model. The observed J = 3 —* 2 CO line of IRAS 20178+4046 (solid line) is shown against two model-generated line profiles. The isothermal model (thin dotted line) produces a rounded peak resembling a Gaussian profile. When a temperature structure is introduced, a sharp-peaked emission line can be obtained due to a number of mechanisms. In the example shown (thick dashed line), the gas kinetic temperature decreases roughly as r , effectively creating foreground layers 7 ’ 0 of colder, absorbing gas which affects one side of the line.  Chapter 2.  2.7.2  The Radiative Line Transfer Model: The Physics and The Cornputing  37  Is the Model Representative?  In order to answer this question, I shall will start by examining the underlying theory employed in the modelling. Fortunately, these are generally well understood. The equa tions of radiative transfer, statistical equilibrium and others, as laid out earlier in this chapter, individually are well established and involve no exotic physics. Of more concern are the rates for collisionally induced transitions. As mentioned earlier, these have been taken from the works of Green and his collaborators. Since the details of their calcula tions are beyond the scope of this work, we take it on faith that their results are correct, for our immediate purposes. That is, their rate coefficients represent the state of the art in collisional (de-)excitation theory. They have been successfully applied in predict ing molecular emission in the interstellar medium (c.f. Section 2.3.2). In addition, other methods of computing  compare favonrably with the Green and Chapman results (e.g.  see comparison by Goldsmith et al. 1983). The next point to consider is our ‘geometry’. My new code is based on a series of slabs reminiscent of the ‘plane parallel atmosphere’. While our LVG models assume a spherical cloud, when a molecular cloud is well resolved (i.e., many beam-widths across), a particular beam position represents or “samples” a column through a cloud which is well modelled by either a planar or a spherical geometry. This is a departure from the common practice in the earlier, pioneering works in molecular cloud model studies which tended to assume that their spherical clouds fit within the telescope beam. This is no longer an appropriate assumption as telescope beams have become smaller with increases in both frequency and antenna size. I have also improved on our LVG model by allowing for variations in density and temperature through the cloud. This is a much needed feature since effects such as self absorption cannot be reproduced under the restrictive assumptions of the LVG version (which, incidentally, does not generate a line profile).  Chapter 2. The Radiative Line Transfer Model: The Physics and The Cornputing  38  This feature also allows comparisous of lines of various species that may be generated over regions of varying extents (section A.2.1). As well, the implicit LVG assumption has been removed. While we can specify the infall/outfiow velocity structures such that the velocity gradients are indeed large, this is not a required part of my models. Although the exact mechanism for line broadening may not be critical [White (1977), see also Snell (1981) and Snell, et al. (1984)] we can experiment with various alternatives such as microturbulence. In summary, the model as described here is believed to be a fair representation of astrophysical clouds. These geometrical generalities do require greater computational resources than the simplified models, but this is no longer a prohibitive restriction. Thus, the code allows us the freedom to investigate (or not to investigate, by fixing some parameters) a number of effects.  2.8  Internal Checks  This section addresses concerns regarding numerical artifacts. One primary area of con cern is the grid resolution, both in space and in frequency. The number of rotation levels to be included in the computations should also be considered. Finally, we must ensure that the computed results are independent of the exact choice of initial conditions. These points are now addressed individually. 2.8.1  Grid Resolution  One way to describe the resolution of the space and frequency gridding is in terms of the optical depth function, r (v, r). The array representing this function must be smooth in 3 both dimensions. The reasons for, and the consequences of violating this condition have already been discussed in 2.5.1.  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  As a starting point, we take Av and r such that both  EAv  and  39  are small.  Numerically, when one such model run is completed, we compute a solution for the same model but using a finer grid, say by a factor of two. If the results do not differ significantly (i.e., the difference is less than the tolerance parameter used to declare convergence and stop the iteration), we conclude that our grid resolution is (more than) sufficient. In general, it has been easy to identify problems of this nature when they occurred during development. For example, there was one early case in which the spatial gridding was too coarse, and the emitted line was narrower than the velocity gap between adjacent layers. The effect was to decouple the layers radiatively, allowing each to emit its line unattenuated by the foregronnd layers. The “observed” spectrum resembled a picket fence. 2.8.2  Initial Values  Since the solutions here are derived iteratively, it is possible that the final result to which the model converges may depend on our choice of initial values. However, this only occurs for start-up values outside some bounds (Press et al., 1986), so that for all “reasonable” initial guesses; the system can be expected to converge to a common, appropriate solution. It only remains to define what is meant by “reasonable.” Intuitively, any set of population densities between zero and the LTE value would seem to be reasonable. Since our iterations are analogous to time evolution, any excess or deficiency in a population density element can be expected to be rectified by the appropriate transitions as dictated by the equations. Numerically, this has been confirmed by a number of trials. In all cases, the converged solutions agree within the specified tolerance (the value that defines “convergence”).  Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing  Texc (K)  Tki  2 H  (cm ) 3 iO iO iO 106  (K) 30.00000 30.00000 30.00000 30.00000  40  1—>0 30.00007 30.00002 30.00017 30.00168  2—*1 30.00003 30.00000 29.99998 29.99978  3—*2 30.00000 30.00001 30.00003 30.00027  Table 2.1: Models in the high density limit (> 3 cm 10 ) . The computed excitation tem peratures for CO J = 1 0, 2 1 and 3 —f 2 transitions are shown for homogeneous, isothermal model clouds and compared to the gas kinetic temperature. (In each case, the modelled cloud is 0.2 pc thick and has no velocity structure.) At high densities, col lisions dominate the transitions and cause Texc to approach Tk1, as verified here within the convergence tolerance. —  —  External Checks  2.9 2.9.1  Tests Against Expected Behaviour or Analytical Solutions in Limiting Cases  Under some conditions, quantitative results of computations can be predicted from an understanding of the dominant physical effect. Some of these cases will now he examined. In the limit of high densities, one expects the collisions to dominate the excitation and de-excitation processes. It follows that the excitation temperature approaches the kinetic temperature throughout such a region for all transitions. Table 2.1 shows a comparison of Tk and Texc for a small variety of high density runs. The agreement is quite good. In the extremely low density limit, collisions and emission originating within the cloud have little roles to play. The radiation field inside a low density (low r) molecular cloud is dominated by the comic background radiation (CBR) since it is able to penetrate throughout the cloud, and the molecules will he found in radiative equilibrium with the CBR. Thus, we expect Texc = Tbg or 2.8 K for all transitions. Although this is not precisely the case seen in the examples of Table 2.2, the values of the excitation  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  T (K) 10 20 30 50 100  1—*0 3.15 3.47 3.65 3.83 4.04  41  Texc (K) 2—÷1 3—2 2.89 2.87 3.12 3.20 3.26 3.39 3.43 3.59 3.63 3.82  Table 2.2: Models in the low density limit. The computed excitation temperatures at cloud centre for CO J = 1 —* 0, 2 —* 1 and 3 —* 2 transitions are shown for homogeneous, isothermal model clouds and compared to the gas kinetic temperature. In each case, the cloud has a gas density of H 3 and is 0.2 pc thick. At this low density, 2 = 10 cm the excitation mechanisms are dominated by the cosmic background radiation so that Texc — 2.8 K everywhere. temperature can still be seen to approach the cosmic background value. In the limiting case, no “line” will he observed above the continuum of the CBR. With respect to the model computations (because the output intensity scale is defined to be T] = 0 when it reaches the CBR level) whenever a T value of zero is generated, the zero point of the intensity scale is verified. This test also applies to intensity array elements near the edge of the spectrum where r  0 [so that T = 0, meaning I, = Bv(Tbg), or that the  intensity of the blackbody radiation at the CBR temperature is recovered]. 2.9.2  Tests Against LVG Solutions  Molecular clouds in the large velocity gradient limit form another class of special cases that avails itself to easy testing. Since we already have access to an established LVO code of Avery, we simply use the new code with input models that satisfy the same conditions such that results from each code can he compared directly. [See the example in Figure 2.3(h).] Table 2.3 shows some sample cases for comparison. The cloud parameters are typical  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  ) 3 (cm 1.0 x 106  T 1 1 (K) 20 K  Vel. Grad. pc’ 1 km r 5.0  5 1.0 x i0  30 K  10.0  3.0 x io  40 K  1.0  l0  50 K  20.0  2 H  3.0  ><  Transition J= 1 —* 0 2 —* 1 3 —* 2 1 —* 0 2— 1 3 —+ 2 1 —> 0 2 —> 1 3 —* 2 1 —, 0 2 —* 1 3 —* 2  42  T (K) LVG code this work 16.541 16.469 14.782 14.754 12.792 12.783 26.481 26.427 24.595 24.586 22.391 22.411 36.427 36.318 36.475 34.501 32.163 32.222 46.443 46.392 44.455 44.450 42.089 42.108  Table 2.3: Models in the LVG limit. Output from compnted models satisfying the large velocity gradient condition are compared directly with the output from an established, LVG-specific code. The established reliability of the latter can be used to check this, the more flexible code, at least in this limit. The computed radiation temperatures for CO J = 1 —* 0, 2 —* 1 and 3 —* 2 transitions are shown for some sample cases as computed with both codes. The only conceptual difference is the geometry; the LVG-specific code models a spherical cloud compared to our slab structure. Other transitions provide similar confirmation but are not shown here for space considerations.  Chapter 2.  The Radiative Line Transfer Model: The Physics and The Computing  43  for star forming clouds of interest in this thesis. While we do expect some differences in output due to the different geometries used (sphere vs. infinite slabs), the table shows this effect to be minor for the examples calculated.  Chapter 3  Observations  The new observational data for these projects have been acquired using the facilities of the James Clerk Maxwell Telescope (JCMT). The following section describes the JCMT for those readers who may be unfamiliar with the telescope or the basic techniques of (suh)millimetre astronomy. It is largely extracted from Matthews (1990, 1993) and is very introductory in nature. The initiated reader may wish to skip to Section 3.2 where observing sessions relating to the IRAS selected protostellar sources project are described. Observations of NGC 6334 are then detailed in Section 3.3. Section 3.4 describes the efforts and techniques used to calibrate the observed data. The transport and exchange of data between the many sites and software facilities are briefly outlined in the last section. The data are presented in Chapter 4 for the IRAS selected protostellar candidates and Chapter 5 for the NGC 6334 sources. Continuum maps and spectral line profiles for the IRAS sources and line emission maps for NGC 6334 are presented in Appendices C and D, respectively.  3.1 3.1.1  The James Clerk Maxwell Telescope Physical Description of the JCMT  Located on “The Big Island” of Hawaii near the Mauna Kea summit (at elevation 4092 m), the JCMT is a (sub)millimetre wavelength “radio” telescope.  Its 15 m  paraboloid antenna is mounted on an alt-azimuth system inside a rotating carousel.  44  Chapter 3. Observations  45  With surface deviations as small as 25 jtm, the JCMT operates with spectral line, het erodyne receivers working between 200 and 700 0Hz (A  =  0.43  ‘-  1.5 mm) and continuum  bolometers covering wavelengths between 0.35 and 2.0 mm. In the context of the present study, making observations with the JCMT has some immediate advantages. In contrast to earlier observations (in MDPS) using the NRAO 12 meter, the higher frequencies made accessible with the advent of this telescope enable us to study the higher rotational transitions of interstellar molecules. At the same time, observing at shorter wavelengths while maintaining a relatively large aperture gives us higher angular resolution (21 arcseconds or better). 3.1.2  Signal Paths and Receivers for the JCMT  The signal path for the JCMT is more or less a standard one for millimetre and submil limetre wavelength telescopes. Generally speaking, the astronomical signal arrives at the paraholoidal antenna and is reflected to a focus. In the case of the JCMT, the Cassegrain focus (f/12) is normally used for the heterodyne receivers and the continuum bolometers are mounted at the Nasmyth focus (f/35). For UKT14, the continuum bolometer on the JCMT at the time (of the observations described here), the incoming signal is sent to the detector system (at the Nasmyth focus) using a hyperbolic tertiary mirror in the receiver cage (at the Cassegrain focus). Inside the TJKT14 package, the signal is fed through a variable aperture, a Fabry lens, a filter wheel and a parabolic horn, on its way to the Ge:In:Sb detector element. The entire package is cooled to progressively colder, cryogenic, temperatures in order to reduce electrical noise and thermal emission from TJKT14 itself. At the sophistication level of this discussion, the inner workings of all heterodyne receivers used here are essentially identical. Briefly, the astronomical signal and a local oscillator (LO) signal are fed into a mixer at the front end of the receiver system. The  Chapter 3. Observations  46  resulting interference signal is the IF (intermediate frequency) signal, which is then am plified and fed to the spectrometer (see Figure 3.1.) Without an additional device such as a filter, this signal will contain astronomical signals from two frequency hands, those centred on LO -f- IF and on LO  —  IF. These are called the upper and lower sidebands  (USB and LSB, respectively) and can be a nuisance (e.g., added sky noise, unequal gain) or an advantage (e.g., observe lines in both sidehands simultaneously). The sideband to which a particular signal belongs can be identified easily by shifting the local oscillator frequency by small amounts. This causes corresponding shifts in the line position at the spectrometer output where the direction of the shift is opposite for the two sidebands. The operating frequency and the choice of mixer technology used are the key factors that set the tone for receiver characteristics and these are now discussed briefly for the instruments used in the course of this study. Receiver A, now superseded by Receiver A2, was part of the first generation of in struments available on the JCMT. It covered the frequency range 220 so-called “A-Band” at the JCMT. This band includes the 230 0Hz, J  —  =  280 0Hz, the 2  —+  1 line of  CO, an important molecule in observational interstellar astronomy. It used a Schottky mixer for electrical rectification (actually, one of two, depending on frequency). Schottky diodes operate as a result of a moderate potential barrier that exists between a conductor and a semiconductor (e.g., Au—GaAs). The “Sutton Receiver” was the 345 0Hz SIS receiver constructed by Sutton et al. (1990) and made available to the JCMT community on a collaborative basis. The CO  J  =  3  —*  2 line is among those accessed in this frequency range, the “B-Band.” An SIS  mixer is built around a Superconductor-Insulator- Superconductor junction and operates on the principle of the Josephson tunnelling effect. Receiver B2 is a Schottky system used briefly at the JCMT as a common-user in strument. It covered the range of 330  —  360 0Hz but has since then been superseded by  Chapter 3.  Observations  47  Antenn  Mixer  Main Computer Local Oscillator “Receiver”  Figure 3.1: Signal Path to the JCMT Spectrometer. The block diagram shows the signal from the antenna to the spectrometer through a “typical” heterodyne receiver. See text for a further description.  flow  Chapter 3.  Observations  Species 6 C 2 ‘ 0 ’ C’ 2 ‘ 0 6 C’ 3 ‘ 0 6 l316 l2l8  48  Transition J = 2 —÷ 1 3 — 2 2 —* 1 3 —÷ 2 2 1 2 —* 1 3 —* 2 5 —* 4 7 —* 6 7 —* 6 —  l C 2 lrO 121’7O 12325 l232 l2345  Frequency (GHz) 230.5380 345.7960 220.3987 330.5881 219.5603 224.7144 337.0611 244.9357 342.8833 337.3966  Receiver  Beam Size (arcsec) 21 14, 16 21 14 21 21 14, 16 21 14, 16 14  A Sutton, B2 A Sutton A A Sutton, B2 A Sutton, B2 Sutton  Table 3.1: Spectral Lines Observed. Their rest frequencies and the receivers used are also given. Where more than one receivers were used, beam sizes (half power widths) are listed in respective order. Receiver B3i, an SIS device.  3.2  Observations of IRAS Selected Protostellar Sources with the JCMT  There has been a total of five observing runs at the JCMT for this project. These are summarised in Tables 3.1 and 3.2. In June 1989, while still in the early commissioning stages of the telescope, six shifts, each eight hours long, were scheduled to observe a subset from our list of 39 sources in the CO J  =  2  —*  1 line (Receiver A), J  =  3  —÷  2 line (Receiver B) and in the  submillimetre continuum emission (UKT14). The unfortunate failure of Receiver B prior to our run precluded the J  =  3  —*  2 observations. The continuum observations turned  out to be of limited use due to problems in calibration. Although Receiver A suffered from a calibration problem as well, we were able to overcome this problem and construct five-point grid maps for sources #09, #14 and #25 in the J  =  2  —*  1 line of CO. Some  C0 and C 13 O 1 8 lines have been observed as well. However, because its frequency fell  Chapter 3.  Observations  Date June 1989 April 1990  April 1991 May 1991 May 1992  Target Line CO, ‘ C0, 0 3 18 2 — 1 C CO, ‘ C0, 0 3 17 3 — 2 C 34 7 —* 6 C CS, S CO, 13 0 2 —+ 1 7 C0, C’ 0 2 —* 1 7 C’ CS 5 —* 4 800, ll00tm 450, 800, 1100gm  49  Receiver A Sutton Sutton A A A UKT14 UKT14  1500  1800K 1200K  1100  1500K 1100K 1400K, 2700K  Table 3.2: Log of Observations for the MDPS IRAS Sources. [The system temperature is a measure of the total noise including contributions from the receiver and the atmosphere.] slightly below the good, low noise tuning range of Receiver A, C 0 1 8 observations were not pursued further. The next run was scheduled for five shifts for a period in April, 1990. At this time, a “B-window” receiver was made available to JCMT users on a collaborative basis by the group led by Sutton. [See Sutton et al. (1990) for a comprehensive description of the receiver.] Using this superb receiver, we were able to observe the J  =  3  —  2 lines  of CO, C 0 1 7 and 3 ‘ C 0. We were also fortunate to be able to observe, simultaneously, J  =  7  —*  6 lines of CS and C S 3 4 in the image sideband. Also during this run, J  =  2  -  1  lines of CO, C’ 0 and 3 7 ‘ C 0 were observed using Receiver A. These data were further supplemented in a run in April 1991. In addition to expanding our coverage using the same lines observed previously, we targeted new observations using the J  =  5  —f  4 line of CS. These were chosen for observations since preliminary  modelling work suggested that data on another transition of CS molecules could clarify some ambiguities in the models. (See Section A.2.3.) All of our spectral line observations were made in the position switching 1 mode in When a signal is detected at a high frequency telescope, it is normally dominated by systematic 1  Chapter 3.  Observations  50  order to eliminate much of the background emission. Initially, the “off” positions used were those used in our initial survey, as these were confirmed to be lacking in CO emission  in the J  =  1  —‘  0 line with the 1 arcminute beam of the NRAO 12 meter. However, as  these often translated into large slews of the telescope (many arcminutes), we adopted closer sky positions for some of our later observations. It is indeed reasonable to expect to find a suitable blank sky region closer to our sources given the smaller beam sizes (from 60 arcseconds down to  21 arcseconds) and that we are observing in a higher transition  (or a less abundant molecule). In any case, the new “off” positions were checked against the original ones to ensure that they were free from line emission. For all spectral work, the “Canadian” Acousto Optic Spectrometer (AOSC) was used as the backend instrument. This instrument gives an effective resolution of 330kHz over a bandwidth of 500MHz (normally centred around the target line frequency) sampled by a 2k photodiode array at 250kHz separation. Integration times were typically 10 to 30 minutes for each beam position observed. Finally, a run in May 1992 was dedicated to mapping a selection of these sources in the submillimetre (and millimetre) continuum. These observations  were  made using  UKT14, the standard continuum bolometer on the JCMT. “On-the-fly” (OTF) mapping techniques were used to map nine sources from our list at 1100 iim and 800 çtm. The nine were selected from our original list of 39 to concentrate our efforts on the younger sources background emission. These signals may have instrumental, atmospheric, as well as other (astronomical) origins such as the galactic plane. Position switching is one technique designed to eliminate much of this background signal at the time of observation. As a spectrum is taken ‘on source’, another is taken at a nearby direction which is then subtracted from it. The ‘off source’ position, when properly selected, will contain all the same emission except that from the astronomical sonrce under study. Thus we are able to correct for various effects (whose contributions may be rapidly changing) without having to know their exact magnitudes. There are alternative methods such as beam switching and frequency switching; the former moves the secondary mirror to access the blank sky whereas the latter uses a line-free region in frequency space. While being potentially more efficient with observing time, beam switching is impractical for extended sources and frequency switching is ill-advised for wide line sources. Since our sources are both extended and wide lined, we have elected to observe in the position switching mode exclusively.  Chapter 3.  Observations  Filter A ( pm) 450 800 1100  Aperture (mm) 27 47 65  51  Beam Width (arcsec) 8 14 18  Cell Size (arcsec) 2.0x2.0 3.0 x 3.0 5.0 x 5.0  Map Size (cells) 53x37 39 x 25 33 x 21  Chopper Throw (arcsec) 30.0 42.0 60.0  Table 3.3: UKT14 On-The-Fly Mapping Parameters. The apertures chosen correspond to the diffraction limited beam in the focal plane. The cell sizes are the increments in azimuth and elevation as the telescope is scanned. which have yet to reach the main sequence. Practical considerations such as limits on available telescope time and Right Ascension range helped to shorten the list as well. Of these nine, five sources were also mapped at 450 pm. Observations at this wavelength are more time consuming in addition to being more difficult due to the reduced transparency of the atmosphere. “On-the-fly” is a mapping technique used to eliminate some of the overheads asso ciated with performing point-by-point photometry in order to construct a map. The primary mirror is scanned across the source while the secondary mirror is chopped in the same direction. The signal is integrated using a phase sensitive detector, with a positive or a negative sign depending on the position of the secondary. (i.e., pointed on the source,  “—“  “+“  if the beam is  if off source.) This chopping is designed to eliminate much of  the background, ‘sky’ emission, around our source. For example, after performing a full raster scan with the primary mirror over a point source, one obtains an unprocessed map which is a pair of beam maps, one with positive and the other with negative intensity. The mapping parameters are summarised in Table 3.3. The construction of a “normal” R. A. vs. dec. map 2 is later done in software. More detailed descriptions of this process can be found elsewhere. [e.g., Matthews (1992), Salter(1985)] A Right Ascension 2 on the celestial sphere.  —  Declination display shows the intensity of an object as a function of position  Chapter 3. Observations  Date April 1990  April 1991  52  Target Line CO, C’ 0 3 —* 2 7 CS, S 34 7 —* 6 C 17 2 —* 1 C 0 CO, C’ 0 3 —* 2 7 CS, S 34 5 —* 4 C CS 7 — 6 C0 2 — 1 3 ‘  Receiver Sutton Sutton A B2 A B2 A  T 5 5 1200K 1100 2100 1200 2100 3200  1500K 3000K 2200K 2200K 3600K  Table 3.4: Log of Observations NGC 6334 I & I(North). 3.3  Observations of NGC 6334 with the JCMT  Observations of NGC 6334 in the context of this work were started at the JCMT during a run in April of 1990. This run was concurrent with the IRAS/protostellar candidates program session mentioned above. Again, the principal receiver used was the Sutton Receiver in the ‘B window’, supplemented by observations with the common user Receiver A. The same selection of lines was observed. This set of data was supplemented by another run in April, 1991 using receivers A and B2, a newly commissioned common-user receiver at the JCMT. Again, the J  =  5  —p  4  lines of CS and C S 3 4 were added to the list. These observations are summarised in Table 3.4. One complication in observing this source arises from its low declination. At  =  —36°,  it spends relatively little time at favourable elevations, making itself available only for about four hours at a time for airmasses 3 less than 2.0 atmospheres. In particularly good weather, this can be extended to about six hours by observing the source at elevations down to  20° (3 atm.).  The airmass, A, is a measure of the amount of air (in the Earth’s atmosphere) through which an 3 observation is made and is defined as A = 1 atmosphere in the zenith direction. The airmass is of concern at these frequencies, since the atmosphere can attenuate the astronomical signal, as well as emit its own.  Chapter 3.  3.4  Observations  53  Calibration  Although the photons for line and continuum observations arrive at the telescope in the same manner, due to different observing techniques used, line data and continuum data are processed and calibrated in ways that are slightly different. I now proceed to describe each process separately. 3.4.1  Calibration of Continuum Data  In order to calibrate the so called ‘on-the-fly’ maps, I am first required to calibrate the point by point ‘photometry’ observations. To explain, I shall first describe how the flux density of an astronomical source is measured. The quantity of ultimate interest is S’, the source flux density outside the Earth’s atmosphere. Before it reaches the telescope, this signal is attenuated by the atmosphere by a factor  c_TA  where r is the zenith optical  depth at the observing frequency and A is the airmass at which the observation is made. This flux is measured at the back end of the telescope as a voltage V 0  =  SGe_TA,  where  o is the effective ‘gain’ of the telescope system including the antenna, filter, receiver, etc. Each observation consists of a measurement of V 0 at a known A. On a ‘photometric night’ when r can be expected to remain low and essentially unchanged for hours at a time, its value as well as the value of the gain can be derived by frequent observation of planets (Mars and Uranus were used) and other, secondary calibrators. The planets make ideal primary calibrators since the intrinsic fluxes from them can be predicted accurately and routinely, as their locations and physical properties are well established. Using sources of known 8’, the values for gain and optical depths have been derived by graphical means aided by least squares fitting. This is a fairly simple exercise at 1100 jim hut is more of an art at 450 pm where the optical depth can exceed r  =  2 even on a ‘good’  night. [While the large value of r is not in itself the problem, its uncertainties, due both  Chapter 3.  Observations  54  to measurement errors and time variability which are both facts of life when working at these freqnencies, limit the precision to which the gain can he measnred. Further, what may seem like small errors in r can lead to large uncertainties in the derived value of O which is affected exponentially by r, or linearly by e . The factor 6  is not a good  measure of the error.] The results are summarised in Table 3.5. The gain values for 1100 pm and 800 pm were in line with the nominal values available from the local staff  at the Joint Astronomy Centre 4 but the 450 pm value was found to exceed the nominal ones by as much as a factor of three. At face value, this is indicative of a degradation in the beam quality. Fortunately, (or perhaps unfortunately) the estimated uncertainties on this value were found to be large enough that any departure from the nominal value, as large as it was, cannot be considered terribly 5 significant. Thus the nominal value of 16.5Jy/mV for the gain at 450 pm was adopted. While this large uncertainty may seem to render our 450 pm data valueless, we shall see later (e.g. Figure C.1) that errors of this magnitude at this wavelength do not influence the results profoundly. Also, because the error is systematic, source to source comparison of the 450 pm maps is unaffected. Investigations of source morphology are also unaffected. Unfortunately, in the case of the OTF maps, yet another factor must be determined in order to convert the map units into amplifier voltage, a quantity we now know how to deal with, having determined G and r. This can be accomplished by making a map of a calibrator source. For this purpose, “beam-maps” were made at each wavelength band by mapping Mars using the telescope in the same configuration. The total flux is obtained by integrating the intensity over the entire map and is used to derive a conversion factor based on the predicted, full aperture flux of this calibration source. The Joint Astronomy Centre (JAC) is the Hawaii local operation centre for the JCMT. 5 H owever, there are some indications that the telescope gain may have been mysteriously poor during this period. See Annual Report of the JCMT Board, 1992, . 21 p  Chapter 3.  Observations  Wavelength (m) 1100 800 450  55  Nominal Gain (Jy/mV) 12.5 9.5 16.5  Derived Gain I (Jy/mV) 12.07 + 0.33 10.0 + 1.3 15 50  Table 3.5: JCIVIT Calibration for Continuum Mapping. These valus are derived by repeated observations of standard sources as described in the text. “Nomi nal” values are ones derived by observatory staff over time whereas “derived” val ues are those determined based on observations made during our observing run only. [1 Jy = 10 erg s’cm 23 Hz’ = 10_26 W 1 2 Hz 2 m ] 3.4.2  Calibration of Line Data  The calibration of spectral line data at millimetre and submillimetre wavelengths is much easier in comparison to that of continuum photometry. All receivers involved in this study employ the chopper wheel technique [Penzias and Burrus (1973), see also Ulich and Haas (1976)] to eliminate much of the effects of atmospheric attenuation. The assumptions required for this technique to be effective do break down at large optical depths (Sato 1986); however, under those conditions of bad weather, the sky noise would be quite high such that it is generally unprofitable to attempt observations. Having eliminated the rA dependence, one simply needs to check the overall intensity scale by observing a few standard sources 6 from time to time. Sources used here for this purpose include S140, 1RC10216, Orion A, G34.3 and DR21. Generally, the line shapes and intensities were found to repeat well at the 10% level or better. The calibrated data are presented in Chapters 4 and 5 with intensities expressed on the T scale (Kutner and Ulich, 1981). Briefly, T is defined as the temperature of a blackbody that would emit the same specific intensity as our observed source above the ’Standard sources’ or ‘standard objects’ in astronomy are those objects in the sky with constant and 6 known intensities. Frequent observations of standards are useful in calibrating the telescope gain as well as monitoring numerous factors that influence overall data quality.  Chapter 3.  Observations  56  background. It is related to the antenna temperature T) by a factor that corrects for the forward spillover and scattering (i.e., T  =  7 ) 3 T/?]f . In this way, the intensity scale is  corrected for everything except for the actual coupling of the antenna power pattern to the source. (This last step is not possible to perform without knowledge of the source morphology, even if we were familiar with the the details of the antenna pattern.) 3.5  Telescope Pointing  Another factor that requires constant monitoring is the quality of telescope pointing. The JCMT operates with a pointing model which automatically corrects for much of the pointing shifts caused by known or predictable effects such as antenna flexing and atmospheric refraction related to the aiming of the telescope in different directions. From time to time, however, small offsets need to be measured and used to correct for pointing errors due to other causes. (These could include, for example, thermal flexing or some yet unknown effects.) Whenever possible, this was done by observing one of the planets in the continuum. They are most suitable for this purpose because, in addition to being bright, their positions can be precisely predicted and their morphologies are simple. Secondary pointing sources were used when no planets were available in order to ensure that some check of pointing was made once every hour or so. There is also an opportunity to check pointing performance by repeated observations of our programme sources. Many of our sources have structures on small enough scales that observed spectra can be noticeably different from one occasion to another if the pointing corrections are less than optimum. (Such observations may be separated by matters of hours, days or years.) In general, the pointing was found to have remained unchanged to within a few arcseconds when This efficiency factor, ?Jfss, was defined by Kutner and Ulich (1981) to denote the fraction of the 7 radiation incident on the antenna from the forward hemisphere that is contained in the primary diffrac tion beam. It clarifies the relationship between 7 and T, a previously used but sometimes ill-defined term.  Chapter 3.  Observations  57  updating with the newly measured corrections.  3.6  Transport of Observed Data  Due to the large number of computers and the variety of operating systems and analysis software involved, much care had to be exercised to ensure that our data remained in usable form throughout this project. Our data collected at the JCMT have been examined on the Mauna Kea summit, at the Hale Pohaku mid-level facilities, and at JAC in Hilo in the standard form with software facilities of the observatory. In moving the data to our home institution, the University of British Columbia (UBC), and its facilities available to us, many steps had to he taken to ensure that the data remained useful to us. The actual transport was done either by tape or through Internet, but of more concern was the conversion of data file formats required by the variety of computers and software involved. This process is described in some detail in Appendix B for the benefit of future users of the system at UBC.  Chapter 4  The IRAS Selected Protostellar Candidates  In this chapter, we first discuss the continuum data and then the spectral line data separately. Figures showing these data are contained in Appendix C. Trends and group behaviour among the sources are then investigated in Section 4.3. Finally, some of the salient features of each source observed are noted in the source-by-source discussion. 4.1  Continuum Data  Data on the continuum emission obtained at the JCMT as described previously are presented in Figure C.l. For each source observed, maps made at 1100 pm, 800 pm and, if available, 450 pm are displayed. The mean noise levels at each wavelength are 0.09, 0.15 and 1.1 Jy/beam, respectively, resulting in S/N ratios of at least abont 10, and often much higher, for the maps. In addition, a spectral energy distribution (SED) diagram is shown. This includes integrated fluxes obtained from these JCMT maps as well as the four IRAS bands (recall footnote 3, p.7, on the IRAS survey). The IRAS Low Resolution Spectra are also shown in the same diagram. The contour maps at a given wavelength are shown using the same contour levels for all sources to facilitate source to source comparison, with the following exceptions. The 800 pm emission of source #04 is particularly bright; for this reason, this map is shown with contours with values five times greater than for the other sources. Also, sources #15 and #21 were found to be particularly faint. Here, I have kept the usual contour levels to avoid confusion. However, they have been supplemented with “dash-dot” contours at 58  Chapter 4.  The IRAS Selected Protostellar Candidates  59  intermediate values which allows for finer contouring. 4.1.1  Results from Continuum Data  The integrated flux contained in each of the maps has been measured using facilities contained in AlPS.’ In integrating emission over the sources with consistency, I have chosen to include emission encompassed by the contour line at 10% of the peak intensity. This is particularly significant for the 450 pm maps in that the source boundaries are not as well delineated as in the 1100 pm and 800 pm maps. This may be due to the spatial smoothing associated with the larger beam size but is more likely attributable to the much higher S/N ratio achievable at these lower frequencies. The resulting flux values in Janskys are tabulated in Table  4.1.  They are also plotted as AFA in the  SED’s of Figure C.1, in keeping with the practice in MDPS and other works in the literature. The uncertainties in these values due to uncertainties in atmospheric opacity and telescope gain are estimated to be about 3% and 15% for 1100 pm and 800 pm fluxes, respectively. The corresponding errors for the 450 pm observations, unfortunately, are much larger, not simply because r and C are iU-determined but also because r is large. For values of r exceeding 2, a seemingly small error in r can affect the correction factor greatly, since it appears as  eTA.  e±. or S The uncertainty is estimated 2 to be a factor of 7  (+110%, —50%) for the 450 pm observations. While these “factor-of-two” errors might appear outrageously large, under the logarithmic scales of our spectral energy diagrams, they seem of little consequence. (See also the footnote below on dust models.) In each case, the source appears to be (barely) resolved by the JCMT beam and some features of source morphology are hinted at. Consequently, two dimensional Gaussians 1  Astronomical Image Processing System (AlPS) is a software package developed by and available from the (U.S.) National Radio Astronomy Observatory. This is a fairly liberal estimate. For example, the results of dust emission model fitting to be reported 2 in Section 4.1.2 suggest that these errors might be reduced by perhaps a factor of two.  Chapter 4.  The IRAS Selected Protostellar Candidates  Source No. # 02 # 04 # 06 N # 06 S # 07 # 09 # 14 # 15 # 21 # 25  1100 jim (Jy) 2.26 7.90 7.63 6.68 6.67 4.57 8.99 1.17 1.09 4.73  800 jim (Jy) 13.9 56.2 23.8 16.4 20.0 11.2 19.2 2.9 2.6 9.9  60  450 jim (Jy) 47 78 —  —  125 321 51 —  —  —  Table 4.1: Integrated continuum fluxes. Source fluxes are integrated over the continuum maps down to the 10 % contour. (See text for details of the procedure and uncertainties.) Source #06 appears to have two components which have been labelled North and South, or #06N and #06S as shown here. were fitted to each map. The information obtained can be used to compare the angular sizes of each source at different wavelengths after accounting for the different beam sizes. The results (“deconvolved” for beam sizes) are summarised in Table 4.2. There appears to be no significant variation in source size between the 1100 jim and the 800 jim maps, indicating that we are likely probing the same component of the cloud at each frequency. In moving to the 450 jim maps, the source sizes decrease for sources #04 and #14 while the others remain more or less constant. Also in Table 4.2, the position angles of the fitted Gaussians are listed. As one would expect, the position angles are similar at the three (or two) wavelengths, except for sources with low ellipticity. Sources #04 and #06 have also been independently observed in the survey work of Wilking et al. (1989). They have been able to estimate source sizes at .\  =  2.7 mm  from interferometric measurements. They obtain values of 13 + 6 arcseconds and 13 + 4 arcseconds for sources #04 and #06, respectively. Although, at first glance, these values  Chapter 4.  The IRAS Selected Protostellar Candidates  Source No. #02 #04 #06N #06S #07 #09 #14 #15 #21 #25  Source Size 1100 pm 800 pm (arcsec) (arcsec) 22x7 22x12 28x21 23x17 39x21 51x14 22x18 26x16 21x14 22x17 23x20 20x18 53x26 50x29 35x23 40x26 24x6 22x14 34x24 31x22  450 pm (arcsec) 20x9 17x11 —  —  17x11 21x17 28x23 —  61  Position Angle 1100 pm 800 pm 450 pm (degree) (degree) (degree) 78 69 73 91 86 53 61 38 -43 -77 -47 -21 6 66 10 50 -2 -8 7 -65 -56 -77 -84 -60 -65  —  —  —  —  —  —  Table 4.2: Source angular size and position angle. Measured by performing twodimensional Gaussian fits to the reduced maps and removing (“deconvolving”) contribu tions due to finite beam sizes. Typical errors are 0.4 2 arcseconds and 2 10 degrees, as given by the IMFIT routine in AlPS. are considerably smaller than the values presented here in Table 4.2 which are based on JCMT maps, the differences may not be significant as the results of Wilking et al. are not obtained from full mapping of the sources. One would expect some agreement with source sizes at 2.7 mm as the emission detected by them is also argued (by the authors) to be attributable to the dust component. 4.1.2  Dust Models  These data shown here are also being studied with dust emission models. The details of this effort will be described elsewhere in a separate paper (McCutcheon et aL, 1995). However, some of the conclusions are now discussed here. The continuum dust emission model is designed to reproduce the observed infrared intensities [in our case, at 12, 25, 60 & 100 pm (IRAS) and (450,) 800 & 1100 pm (this work)] by fitting the four parameters: opacity, (power-law index of the) emissivity  Chapter 4.  The IRAS Selected Protostellar Candidates  62  (function), source size, and dust temperature. For all sources modelled, best results were obtained by fitting a two-component model consisting of a small, hot larger, cool  4.2  (rs?  (-  130K) and a  35K) component. (The median size ratio is 50 for the two components.)  Line Data  The J  =  1  —÷  0 lines of CO, 3 ‘ C 18 have already been published separately in C 0, and 0  another paper (MDPS) along with the VLA and IRAS data. Subsequent observations made at higher frequencies using the JCMT are shown here in Figure C.2. Each source is presented on its own page. The five point maps of CO J  =  3  —÷  2 and CS J  =  7  —*  6  are made with 7 arcsecond beam separation so as to cover a similar area as the Receiver A beam which is used for the lower transitions. This provides for useful comparisons later in our modelling work. Spectra taken of various isotopic lines are also shown in separate panels. 4.2.1  Results from Line Data  A cursory look at the new line data tells us that the 12 O 1 C 6 lines of many of our sources are quite prominent. This immediately gives us a lower limit on the gas densities since a minimum density of approximately  io cm 3 is necessary to excite the CO  line, We see also that none of our sources shows a C S 3 4 J  =  7  —,  J  =  3  —‘  2  6 line detected clearly  above the level of the noise. This gives us an upper limit in density  3 c 6 l0 m at our  typical noise levels). In addition, the fact that we do detect lines of S 32 whose abundance C is only a factor of 20 above C S 3 4 (see Table 4.3) immediately places constraints on the density estimates. In order to extract more quantitative information from our observations, an analysis using a simple LVG model has been performed. The code used in this study assumes a  Chapter 4.  The IRAS Selected Protostellar Candidates  63  homogeneous, isothermal cloud under uniform collapse (Avery, private communications). It is used to predict TR* given the density, n, and kinetic temperature, Tk1, of the gas along with the velocity gradient,  ,  in the cloud.  The procedure used can be described in the following way. First, the gas kinetic temperature is fixed by using a line that is expected to he optically thick. Normally, our choice is 0 6 C 2 ‘ ’ J  =  2  1 or J  —,  3  =  —  2 line. Since r is very large at the high  densities expected for these protostellar clouds, TR* is insensitive to anything but Tk1 under the assumptions of this model. That is, the line acts as a good thermometer 3. The optically thick assumption can be checked at the end but is seldom necessary due to the high densities concerned and the high abundance of CO. Complications to this use of CO lines arise when the peak of the line is affected by self-absorption. However, peak values can he estimated using techniques such as the fitting of Gaussian profiles. Next, for each observed line, a series of (n,  pairs of solutions which represent the observed TR* is  )  computed. In order to perform the computations, some knowledge of the abundances of each molecular and isotopic species is required. Obviously, the choice of values for abundances affects our results at a fundamental level, especially in comparing data on different species. For this study, abundance ratios have been compiled from the literature and the adopted values are listed in Table 4.3. The LVG solutions are next plotted as This thermometer effect can be understood in the following way. In a simplified picture of a homo 3 geneous cloud, the excess radiation temperature one observes above the background can be expressed as =  0 T  [  eTa/Tx  —  I  —  eTa/Tog  —  i]  (i  —  er)  where T = hv/k-, Tb 9 corresponds to the cosmic background radiation, r is the optical thickness of the cloud and Tex is the excitation temperature of the transition, which is equal to the kinetic temperature, Tkin, at high densities where collisions are frequent and the levels are said to be thermalised. Also at high densities, r co thus we have —  T  which is a function only of  —o  eTa/Tkjn  —  1  + const.  Chapter 4.  The IRAS Selected Protostellar Candidates  Molecule 16 C 2 ‘ 0 C’ 3 ‘ 0 6 1218 l2l7 12325 1234  Abundance 3.0 x 10 3.4 x iO 9.0 x 10—8 1.5 x 108 3.0 x i0 1.5 >< 10_b  64  Reference adopted by de Jong et al. (1975) adopted by de Jong et al. (1975) from 160/180 ratio of Wannier (1980) from 180/170 ratio of ‘A annier (1980) T Walrnsley (1988) Walrnsley (1988)  Table 4.3: Molecular abundances. Adopted values from the literature for abundances of molecules observed in this study are given relative to the abundance of H . The references 2 cited are only examples of where these “typical” values are found. curves on a graph. (See Figure 4.1 for an example.) Where two or more such curves cross, each representing a specific observed line, we say that we have found a solution. While it is true that we rarely see three or more curves crossing at one point, when our “error-bands” are considered, our solutions give us cause for much confidence and optimism. Table 4.4 gives a summary of results obtained using this procedure. Column 2 of Table 4.4 lists the gas kinetic temperature, for each source. The dust temperatures, Td,t, obtained for the large/cool component (McCutcheon et al 1995 and Section 4.1.2, this work), have been compared with these values which describe the molecular gas component. They are generally found to agree within reasonable error estimates. This agreement suggests that the molecular gas and the dust are co-extensive in our sources. That is, frequent and wide-spread collisions between the gas and dust particles keep these two elements that make up the cloud at the same temperature. Using this fact, the source size measured from the continuum map can be used in later calculations relating to the molecular matter. There appears to be a clustering of derived densities around n  3 c 5 10 . m This effect  appears not to be an artifact of the LVG analysis, as discussed in Appendix A.1.1. The disagreement with the higher densities one might expect in a protostellar cloud may be  Chapter 4. The IRAS Selected Protostellar Candidates  65  iog  0 1 C 7 3—2 C0 3—2 13  0 1 C 7 2—1  108  /  S 3 C 4 7—6  CS 5—4 7—6 / CS / /  7 io E  /  0  /  > (0 C 1) U,  o  solution in this region  1  I  1  10  ...,....  I  102  Velocity Gradient (km spc’) Figure 4.1: Example of LVG solutions. The curves shown here are for Source #14. The dashed lines are upper limits in density derived from lines not clearly detected above the noise. See text for a full description.  5 io  Chapter 4.  The IRAS Selected Protostellar Candidates  Source No.  #  01 #02 # 04 # 06 # 07 # 09 #13 # 14 #15 # 18 #21 # 22 # 25 #39  (K) 44 50 37 36 34 42 44 31 26 29 19 20 39 41  Density (10 cm ) 3 Nominal Range 15 4 50 4 2 8 15 100 3 13 20 6 11 20 3 13 40 5 6 4-’ 7 14 18 9 6 4’-.’ 10 15 50 3 11 25 15 60 66 15 120 42 —  —  66  Veloc. Gradient (km s 1 pc’) Nominal Range 17 0.04 100 3’15 6 9 3 300 9 3 30 15 2 75 7 3 37 3’10 5 8 12 5 3’--’lO 5 7 1 30 9 26 10 75 70 10 100 53 ‘  —  —  Table 4.4: LVG model results. The total gas density and velocity gradient for each source is presented with the adopted, ‘nominal’ value, as well as a range of values reflecting the agreement between various combinations of lines modelled. T 1 is the gas kinetic temperature determined as described in the text.  Chapter 4.  The IRAS Selected Protostellar Candidates  Source No. #02 #04 #06 #07 #09 #14 #25  67  Molecular Mass 22M® 23M® 26M® 82M® 64M® 307M® 42M®  Table 4.5: Masses of the molecular componeut. These values are derived usiug the “nomiual” gas densities from Table 4.4. Estimates of the uncertaiuties cau be derived using the ranges of density given there. For Source #06, the mass represents both North and South components. indicating the presence of other effects such as the beam filling factor. 4 This would be important if there were a number of small condensations within the telescope beam. The density information can be used to derive a mass for the molecular component of each source. For sources with well measured sizes from the continuum maps, this has been possible, assuming spherical geometry to obtain the third dimension. Since we already have the distances from MDPS, it is a simple matter to estimate the volume. These results are summarised in Table 4.5. These might be regarded as the mass of the parent molecular cloud for each of the protostars in our list. 4.2.2  Column Densities  Since the density ranges derived in the above were disappointingly wide, another measure of the cloud gas density was computed in order to guide us in the process of physical interpretation. 4 T he filling factor represents the ratio of source size to the telescope beam size and quantifies the  dilution of the source signal when its value is less than unity (e.g., when the beam is larger than the source or when the source is clumpy).  Chapter 4. The IRAS Selected Protostellar Candidates  Source No. # 01 # 02 # 04 # 05 # 06 # 07 # 09 # 13 # 14 # 15 # 18 # 21 # 22 # 23 # 25 # 26  0 Nc17 ) 2 (cm 3.7 x 1015 4.8 x i0 1.4 x 10’s 7.9 x 10’s 1.1 x 1016 6.8 x 1015 6.1 x 1015 7.7 x 1015 6.9 x 1015 4.1 x i0’ 6.5 x iO’ 3.9 x 1015 4.2 x 1015 2.6 x 1015 7.4 x 1015 8.1 x i0’  TaMe 4.6: 0 17 Column Densities. C  68  Chapter 4.  The IRAS Selected Protostellar Candidates  69  Values for column densities 5 for the C’ O molecule, Ncl7o, were computed using its T J = 3  —,  2 line and are listed in Table 4.6. This can be accomplished with standard  techniques using the C’ O intensity integrated over the line T  (f TAdv)  and assuming that  the line is optically thin. This assumption can be verified by examining the values of r computed during the LVG analysis already performed, to see if the line is indeed optically thin. The excitation temperature is assumed equal to the 2 ‘ C 0 excitation temperature and is listed in Table 4.4 as In giving up any information about the third dimension, we have been able to reduce the random component of the uncertainty significantly. +10% in each of Tk1 and  f Tdv  Estimated random errors of  result in 6Ncl7o of only +12% when combined in  quadrature. These values can be converted to Nn 2 by scaling by the molecular abundance listed in Table 4.3 or by using the relation given by Frerking et al. (1982). 4.3  Possible Trends and Patterns  One of the original aims of this project was to search for any patterns that might exist in a large sample of protostellar objects. In our first paper (MDPS), for example, we were able to place our sources on a H-R diagram and identify objects forming the main sequence. Although our list is now somewhat restricted, a number of additional parameters have been observed or derived and can now be examined, particularly for correlations with characteristic parameters of the emerging main sequence object. Figure 4.2 shows the gas density plotted against Tea, the effective temperature of the stars, derived in MDPS, for all sources modelled. Teff is a measure of the zero Column density is a two-dimensional density obtained from the three-dimensional space density of 5 particles projected to the celestial sphere and has units of number per unit area. It measures the number of particles (in this case 0 17 molecules) in the region sampled by the telescope beam, which resembles C a “column” through the molecular cloud. No information in the radial direction (along the line of sight) is given, implied, or sought.  Chapter 4.  The IRAS Selected Protostellar Candidates  10 6  I  70  I  I  4.3 log T ff 0  4.2  . ‘I,  E 0  C  5 io Cl)  C ID  0 0  4 io  I  4.5  Figure  4.4  4.1  4.2:  Patterns in our sample. Densities derived from modelling the observed line data are plotted against the stellar effective temperature in search of correlations. The filled squares indicate sources confirmed to be pre-main sequence (PMS) in MDPS. The open squares are the unconfirmed PMS objects. Error bars in log Tea, though not shown, are not negligible. See text for a brief discussion on this uncertainty.  age main sequence  (ZAMS)  mass or spectral type of the central star.  [Uncertainties in  the effective temperature are difficult to estimate and are perhaps large. described in  MDPS,  However, as  many of the steps that contribute errors to the final value of  are systematic in nature.  Tea  Therefore, for the purposes of the present discussion, while  the overall scale might be affected, we do not believe the  scatter  to be affected to such a  degree as to mask an inherent correlation in the data.] Unfortunately, inspection of this diagram reveals no striking correlation. In any event, the sizes of the error bars compared to any variations seen suggest no trend can be found in this set of data. Other pairs from our list of parameters (including  Nciro, molecular mass and spectral type) have  Chapter 4.  The IRAS Selected Protostellar Candidates  71  also been plotted in search for a correlation. No obvious trend has been found. A similar conclusion was reached in our investigation of the continuum map data and derived dust model parameters (McCutcheon et al., 1995). If there is no pattern emerging from the data, we may ask why this is the case. The lack of precision as seen by the sizes of the error bars in Figure 4.2 have already been discussed and is almost certainly a factor. Unfortunately, improving the precision significantly is not straight forward without some fundamental change in our methods. Nonetheless, this was the reason for which C’ 0 column densities were calculated. In 7 forgoing any information on the third dimension, the random part of the errors has been reduced to +12%. While the sizes of individual error bars have been reduced, the degree of scatter seems unaffected. If there is truly no underlying pattern here, we will be faced with some different possibilities. Quite possibly, we have already a sample that is very uniform. Certainly, there have been great many selection steps, starting with the original compilation of the MDPS catalogue from the IRAS PSC. Figure 4.2 shows that our sources span a zX log Teff of only 0.35, or ZAMS spectral types between 08 and B3.5 only. Thus, differences in the observed and derived quantities due to differences in the main sequence stellar mass may not be large enough to be revealed by our methods. If, on the other hand, the patterns we are searching for are due to age differences, then we reach another conclusion; the range of evolutionary stages represented by sources that meet our selection criteria is so short-lived or so unchanging (in terms of the observables) that there are no appreciable differences among the individual sources. Recent theoretical work of Palla and Stahler (1993) indicate that “stars with masses greater than 8 M® have no pre-main-sequence phase, since they are already burning hydrogen by the time protostellar accretion has ended.” Our sources fall into this category according to the mass range of 10  r’.’  25 M® inferred from the spectraltypes (Mihalas and Binney, 1981).  Chapter 4.  The IRAS Selected Protostellar Candidates  72  This is short-lived indeed and the stellar component may not have sufficient time to influence the observed properties of the parent cloud. One last limitation of note concerns our principle of quantifying the properties of the parent molecular cloud iu order to learn abont the emerging protostar. If the character istics of the protostar are subject to many other (often external) factors that influence the star forming environment, then there will not be a simple, well defined correlation between the molecular properties and the properties of the embedded protostar. In any event, our sample of star forming clouds appears homogeneous in the param eters investigated to the best of our abilities. 4.4  Future Work  Certainly, there is much sense in following up the work already described by modelling the molecular lines in increased detail. For the most part, such a project would require no additional observations. The line data already available, particularly in CO, show much structure and contain much mysteries to be examined. The results and insights gained through the LVG analysis are expected to form an invaluable starting point for this phase of the ongoing investigation. From the outset of this survey, we have concentrated on star forming objects of high luminosity. It may be of interest to make a companion survey of low luminosity star forming regions for a number of reasons. For example, compilation of the same type of data for two classes of objects may reveal some distinguishing characteristics (other than the luminosity). However, to a large extent, this has already been accomplished by other investigators such as in the works referred to in Section 5.6. Although the observations there cannot be compared directly to those presented in this work, in that the focus and instrumentation are not identical (as would be the case for a companion work specifically  Chapter 4.  The IRAS Selected Protostellar Candidates  73  designed for comparison purposes), they do constitute a useful database for comparison. As already mentioned, for example, the low and high-luminosity star forming sources do display differences in the dynamical parameters.  [l4nax,  K.E., and Lmech are all smaller  for low-luminosity protostars, r is larger.]  4.5  Individual Sources  During the course of this study, some features of the individual sources have been noted and are discussed here briefly. Also, some results from MDPS are given inside square brackets. (Where ambiguities exist for kinematic distances, D 6 ± 1 , the preferred values as described in MDPS are shown here as Dne or Dias.) In addition to the data already discussed, a fraction of our 39 sources has been mapped in the J  =  1  —*  0 lines of CO  and 3 ‘ C O with the NRAO 12m, beyond the standard five point grid. Where applicable, the existence of this database is noted. (Source #08 has also been mapped in this way though it has not been observed with the JCMT.) Source #01; IRAS 18134 sequence  B2. Dnear  =  —  1942 : [Compact H II region. Close to, or on main  1.5 kpc.] The CO peak at v  separate cloud and is also seen in CO J  =  1  —*  e’-’  22 km  s appears to  be a  0 data. The absorption feature in CO  coincides in velocity with the main peaks of 3 ‘ C O spectra. (i.e., self absorption.) It is not seen as distinctly in CO J  =  1  —  0 spectra, most likely due to beam dilution. That  is, the self absorption appears to be confined to a small region. A CO J  =  1  —>  0 map is  available. 6  Kinematic distance, or is perhaps the primary method for estimating distances to spectral line sources within the galaxy. It is derived from the observed radial velocity of the source and an established kinematic model of galactic rotation. The latter describes the velocity of objects in orbit about the galactic centre as a function of galactocentric distance. X’Vith some simple geometry, a radial velocity distance relationship can be derived for any specific line of sight from the solar neighbourhood. For objects inside the solar circle (our orbital path through the galaxy), this method yields two solutions, Dnear and Dtar, and the choice between them must be made through independent means. —  Chapter 4.  The IRAS Selected Protostellar Candidates  Source #02; IRAS 18151  74  1208 : [Pre-main sequence  —  BO. Dnear = 2.8 kpc.]  Enhanced wing on the positive velocity side of line peak. Molecular mass Source #04; IRAS 18162 sequence  —  2048 : [Compact H  II  22 M®.  region. Probably on main  B0. 10 pm absorption feature. Dnear = 1.7 kpc.] Emission at 800 pm is  exceptionally bright. This is the only source for which the far—infrared source angular size varies with wavelength in a significant way. (Size decreases with decreasing A.) This is not an artifact of the differing beam sizes, as this effect has been specifically accounted for (and is not manifested in other sources). Self absorption in CO lines. Molecular mass 23 Al®. Wilking et al. (1989) report a continuum source size of 13 + 6 arcseconds based on 2.7 mm interferometric measurements, in comparison to our values (from maps) of 11  —.‘  28 arcseconds. The peaks of emission in the 6 cm, 1100 pm and 800 pm maps are  all coincident, within the IRAS position centroid. However, the 450 pm peak is displaced by  12 arcseconds, although it is well within the IRAS beam. Source #05; IRAS 18258  —  0737 : [Extended H  II  region. Main sequence  BO.  10 pm absorption feature prominent in LRS 1. Dgear = 2.8 kpc.] (Line shapes are simple and conducive to good modelling.) Source #06; IRAS 18265 sequence  —  1517 : [Compact H H region. Close to or on main  B2. Dnear = 1.6 kpc.] The continuum maps show two components. They  have been labelled #06N and #06S or North and South. This causes problems in dust modelling since the IRAS data have insufficient angular resolution to enable us to study the two components separately. Wilking et at’. (1989) report a continuum source size of 13 + 4 arcseconds based on 2.7 mm interferometric measurements, somewhat smaller than our maps indicate. Source #07; IRAS 18316 sequence  ‘-  —  0602 : [Compact H  II  region. Probably pre-main  BO. 12 pm absorption feature. Dnear = 3.0 kpc.] Pronounced self absorption.  Molecular mass  ‘-.‘  82 M®. LRS 1 is noisy but is shown for completeness.  Chapter 4.  The IRAS Selected Protostellar Candidates  75  Source #09; IRAS 18517 + 0437 : [Pre-main sequence  feature. Dnear = 2.6 kpc.] There is a CO J = 1 perhaps also in CO J = 2  —,  Source #13; IRAS 20178 + 4046 c-  0 feature at v  ‘-S’  32 km  seen  e-’  64 M®.  [Compact H  II  region. Close to or on main  09. 10 pm absorption feature. Df = 3.1 kpc.] Line shapes are simple and  conducive to good modelling. CO J = 1  —*  0 map is available.  Source #14; IRAS 20188 + 3928 : [Compact H sequence  B1. 12 pm absorption  1 but not in other lines. (Line shapes are simple and  conducive to good modelling.) Molecular mass  sequence  —*  r’  H  region. Probably on main  BO. D 1 = 3.2 kpc.] The appearance of 0 6 C 2 ‘ ’ J = 1  are quite different, with J = 2  —,  —*  0 and J = 3  —*  2  1 line taking what is perhaps an intermediate line  shape (as would be expected with its intermediate excitation and beam size). Molecular mass s 307 M®. This is our highest value, due to its large angular size and distance. Gas density itself is not exceptionally high. LRS 1 is noisy hut is shown for completeness. Source #15; IRAS 20216 + 4107 : [Probably main sequence  B1. Di =  3.3 kpc.] This source is relatively faint in its far—infrared emission. The contours in the continuum maps have been supplemented with intermediate ones (dash—dot contours). The CO feature at v  ‘  11 km s seen in J = 1  likely a separate cloud. A CO J = I  —*  —i  0 line can also be seen here but it is  0 map is available.  Source #18; IRAS 20286 + 4105  [Main sequence  ‘—‘  B0 and extended H  H  region if associated with the radio continuum object. If not associated, object moves off the main sequence to the right. 12 pm absorption feature. Dkj = 3.5 kpc.j The five spectra of CO J = 3  —>  2 are supplemental, “service” style, observations made in 1992  using Receiver B3i and replace the one spectrum at (0,0) taken originally with the Sutton Receiver. However, they have been scaled (and the scaling was necessary) such that the (0,0) line matches in intensity with the same observation made earlier with the Sutton receiver.  Chapter 4.  The IRAS Selected Protostellar Candidates  Source #21; IRAS 21334 + 5039 : [Compact H quence  BO. 1 D r .j  =  76  II  region. Probably main se  5.0 kpc.] This source is relatively faint in its submillimetre emis  sion. The contours in the continuum maps have been supplemented with intermediate ones (dash—dot contours). A CO J  =  1  0 map is available.  —*  Source #22; IRAS 22272 + 6358A : [On main sequence sequence. Probably won’t produce H  II  region. Dk1  =  B3.5, or pre-main  0.8 kpc.]  Source #23; IRAS 23545 + 6508 : [Compact H  II  region. On main sequence  B2. Possible 10 um absorption feature. Small Extended Source IRAS X2354 + 651 is associated.  =  1.2 kpc.] The CO J  =  3  —*  2 line appears to suffer from a lot of  self absorption, as opposed to showing two separate components. A CO J  =  1  —*  0 map  is available. This object has been studied separately in more detail by Dewdney et al. (1991) and was found to be a prototype “dissociating star.” Source #25; IRAS 00338 + 6312 : [Close to main sequence  B3 or pre-main  sequence hut may have a weak radio continuum source in which case it is a compact H  H  region and on the main sequence. D  2  =  1.1 kpc.] Self absorption in 3 ‘ C 0 J  =  3  —*  indicates a high gas density, which is confirmed by the modelling, as it yields our highest density of 6.6 x . 3 c 5 10 rn Molecular mass shown for completeness. A CO J mapped in the CO J  =  1  —*  =  1  —*  42 M®. LRS 1 and 2 are noisy hut are  0 map is available. This source has also been  0 line at the FCRAO 14m telescope by Snell et al. (1990)  and Carpenter et al. (1990). Snell et al. assign a distance of 1.6 kpc and show a bipolar outflow. Carpenter et cii. report that no 6cm continuum source is detected in association with this IRAS source in agreement with our own observations reported in MDPS. Source #26; IRAS 00420 + 5530 : [Probably pre-main sequence  BO. Dkj  =  5.3 kpc.J Source #31; IRAS 03235 + 5308 : [Compact H sequence  BO. 10 im absorption feature. Dkj  =  II  6.0 kpc.j  region. Probably on main  Chapter 4.  The IRAS Selected Protostellar Candidates  Source #36; IRAS 05553 + 1631 : [Compact H sequence  ‘  B3. 8.5 zm emission feature.  =  77  II  region. Probably on main  0.8 kpc.] The CO J  =  1  0 emission  —.  has been studied extensively in earlier efforts (MDPS and McCutcheon, Sato, Purton and Dewdney, unpublished) and found to be a bipolar outflow. The CO J  =  1  —>  0  line has also been mapped with the FCRAO 14 rn telescope as reported by SneU et at. (1990) and Carpenter et at. (1990). In Snell et at., a distance of 2.5 kpc is adopted (by associating the source with the 5254—5258 complex of H  II  regions) in contrast to our  kinematic distance. However, the same bipolar outflow structure is observed. Source #38; IRAS 06103 + 1523 : [Probably pre-main sequence  r’  B1. Dkj  =  4.0 kpc.] Strong and self-reversed 3 ‘ C 0 line suggests a high gas density for this source. Unfortunately, the high noise in the CS data prevents us from improving on the upper limit in gas density of . 3 c 6 10 m Source #39; IRAS 07427 sequence  08. Dk  =  —  2400  [Compact H  II  region. Probably pre-main  7.7 kpc.] Strong 3 ‘ C 0 lines including self-absorption in J  =  2  —  1 indicate a high density, as is shown by the model work, yielding the second highest density in our list.  Chapter 5  NGC 6334 I & I(North)  Observed Data; Overview  5.1  Molecular line spectra have been observed at a large number of beam positions around the northern end of NOC 6334 encompassing peaks I and I(North). The observed posi tions are summarised in Figure D.1. The coverage varies for each line due to practical considerations during the observing runs. In addition, the lines observed using Receiver A are subject to coarser sampling reflecting the larger beam size. That is, the grid po sitions for Receiver A lines are separated by 20 arcseconds while the B-band lines have grid intervals of 10 arcseconds. In both cases, the beam spacing is less than twice the interval suggested by the Nyquist Theorem for complete sampling. 5.2  CO Spectra at I and I(North)  In lieu of displaying all of the spectra (there are 453 of them), a small selection of CO  J  =  3  —*  2 lines which are of particular interest is shown in Figure 5.1. Upon inspection,  one immediately notices the extremely wide lines at the centre of NGC 6334 I extending almost 100 km  s  wide. While the raw spectra are not shown here, it should be noted  that the quality (in particular, the flatness) of the baselines is excellent throughout the spectrometer bandpass, giving added evidence that the very wide wings are indeed real. It is easy to recognise the disparity in line shapes of CO at I and I(North) peaks of emission. Figure 5.1 clearly shows the enormously wide wings at NGC 6334 I while the  78  Chapter 5. NGC 6334 I St I(North)  79  40.  *ct  -  L,SJ  F-  )AA  M  (40ri10)  20  (—30,—i 10) 10  -  -  -  (—20,—iou) 0  —100  —50  0  50  100  Velocity (km/s) Figure 5.1: Sample CO J = 3 —> 2 spectra. CO line profiles from beam positions corresponding to peak I(North) [(—20, 0)] and peak I [(—40, —110), (—30, —110) and (—40, —100)]. The coordinates are R.A. and declination offsets in arcseconds from the 34 m h1 17 98 map reference position (a = 8, S = —35°42’17”). For I, spectra from three positions are shown to illustrate the bipolar wing structure.  Chapter 5. NGC 6334 I & 1(North)  80  line at the I(North) peak is “quiescent” by comparison, although by normal interstellar standards, this line would itself be regarded as a wide one Al4wzI  80 km  -1).12  (L\Vj’wHM  ‘-  20 km  s  and  The line at this position also shows symmetric outflow activity,  in contrast to the positional dependence seen around peak I. Indeed, the spectrum centred on the CO J  Figure 5.2 which also shows the C 0 1 7  —  =  3  —*  2 line on peak I is remarkable. (See  5 3 C 4 spectrum.) In addition to the enormous  width of the CO line, there are a number of other lines (identified and unidentified) seen in both sidehands, suggesting either a very high gas density or a high temperature, or both, in this region. These lines are not seen at the position of peak I(North). It is plausible that these unidentified lines represent not some other molecules but clumps of CO at different velocities. The existence of such fast moving CO “bullets” has been established in other outflows (Bachiller and Gómez-González, 1992). Before this hypothesis can be confirmed, however, the suspected lines must be found to be (1) in the same sideband as the main CO feature and (2) at the same velocity in another transition of CO or in some other species. In our case, the J although we would prefer to examine the J  =  2  =  —,  if one were available (since the abundance of C 0 1 7  3  —*  2 transition of C 0 1 7 is available  1 spectrum of 12 C0 at this position is  a factor of 2000 lower). There are  no spectral features that clearly satisfy both these criteria, thus favouring the original theory of high density/temperature and rich chemistry. The sharp “absorption” feature at as  vi =  +6.5 km s appears to be very much real,  it remained with the main features when we retuned the receiver to slightly different  frequencies to determine which of the features were in the image sideband. As we used the same “off” position in position switching throughout the entire map, which itself has been checked against another blank sky position, it can also be argued that the ‘FWHM: Full Width at Half Maximum. FWZI: Full Width at Zero Intensity. In practice, “zero intensity” means one follows the signal until it is indistinguishable from the noise. 2  Chapter 5. NGC 6334 I & I(North)  81 (LsB)  30  20  *  345.5  345.6  345.7  345.8  345.9  346.0  (usB) (LsB)  30  20  *  0  337.0  337.1  337.2  337.3  337.4  337.5  (usB)  Frequency (GHz) Figure 5.2: Spectra centred on NGC 6334 I. Each panel shows two frequency scales corresponding to the upper and lower sidebands, labelled USB and LSB. The top panel includes the CO J = 3 2 line (345.80 GHz, USB) and the CS J = 7 6 line (342.88 GHz, LSB). This is the same spectrum shown as (—30, —110) in Figure 5.1. The bottom panel includes the C’ 0 J = 3 7 2 (337.06 0Hz, USB) and S 34 J = 7 —* 6 C (337.40 GHz, USB) lines. A host of other lines can be seen in the bandpass in addition to the target lines. —  —  —  Chapter 5. NGC 6334 I & I(North)  82  absorption featnre is not due to the presence of a CO line in that reference position. The same feature was also present in spectra taken The CO J  =  2  —*  a year later using a different receiver.  1 spectrum of Bachiller and Cernicharo (1990) (see their Figure 2)  shows a hint of a similar feature along with the same wide wings we see in J  =  3  —*  2.  Unfortunately, its usefulness as confirmation is diminished by the fact that the absorption feature in their spectrum appears to be only one channel wide, although that is the width we would expect. [We measure SV c 1.5 km  s  (7 channels) from our spectrum, whereas  the Bachiller and Cernicharo spectrum has a resolution of 1.3 km s per channel.] On closer examination, this “absorption” feature is visible at the same velocity in spectra at other beam positions. (It is not as prominent perhaps because there is less background radiation to be absorbed at this frequency.) A plausible explanation is that we are observing the entire cloud through another, foreground CO cloud. 5.3  Molecular Line Maps  Using the two spatially well sampled lines, CO J  =  3  —÷  2 and CS J  =  7  —i  6, a number  of contour maps have been constructed. Figures 5.3 and 5.4 show the integrated line emission. The CS map clearly shows the two peaks, I and I(North), with the southern component being the brighter at its peak by a factor of two. In the CO map, I appears with a more complex morphology and is much brighter than I(North), although I(North) is still clearly recognizable. The CO map brings out another feature approximately 30 arcseconds to the northwest of I. It is also recognizable as a lobe or an extension from the main source in the map of integrated CS emission, although not as prominently. [For future reference, this feature is designated NGC 6334 I(NWX) or simply NWX.  This  feature is not to be confused with the features to the northwest of I mentioned in Harvey  Chapter 5. NGC 6334 I & I(North)  30  35° 42 00  30  83  I  I  38s  36  I  I  I  I  -  -  -  0 LO  0)  z  0 —35° 43 00” -  z -J  C-) 0 30  oc”  350  44  350  44 3Q  O m 4 17” l7  34S  32  30  28  RIGHT ASCENSION (B1950)  Figure 5.3: Map of velocity integrated CO emission. The CO J = 3 —* 2 line emission integrated over the velocity range —50 . The first contour and the contour 1 +50 km s interval are both 50 K• km s . 1 —  26  Chapter 5. NGC 6334 I & I(North)  84  I  I  36  34S  I  •  I  30  35° 42 00”  30 0 10  a)  z  2  _°  43• 00”  2 -J  0 uJ 0 30  _350  350  44 00”  -  44 30  h 17  m 17  4O  38  328  RIGHT ASCENSION (B1950)  Figure 5.4: Map of velocity integrated CS emission. Similar to the CO map but the velocity interval is —35 —+ +25 km s 1 as the line emission does not significantly extend beyond this range. Contour levels are multiples of 10 K km s . 1 .  Chapter 5. NGC 6334 1 & I(North)  85  and Gatley (1983). The authors refer to two such extensions or lobes but these corre spond in position to their IRS—1—2 (6 arcseconds away from IRS—I—i) and the H  H  region  NGC 6334 E (1 arcminute from IRS—I—i).] Figure 5.5 shows the positions of the compact near infrared objects from the JHK photometry (A  1  —  2.Sjtm) work of Straw et a!. (1989) [recall description in Chapter 1,  p.1:3, including a footnote on JHK photometry] overlaid on the integrated CO map. The positions of the H  II  regions E and F from Rodriguez et al. (1989) [marked in the figure  as “11CM F” and “RCM F”] and IRS—I—i through IRS—I—4 of Harvey and Gatley (1983) [“HG1,” etc.] are also shown as is the IRAS point source 17175  —  3544 [“IRAS”]. (N.B.  The size of the markers shown on Figure 5.5 are not meant to be indicative of source size, telescope beam size or positional uncertainties, any of which can often be much larger. For example, the positional uncertainty for IRS—I—4 is listed as 10 arcseconds by Harvey and Gatley; the radio source E is 20 arcseconds in diameter.) We see that indeed the near infrared objects appear to form a cluster around peak I while their distribution is rather sparse toward I(North). In particular, there are no near infrared objects detected in the immediate vicinity of the peak of I(North). On the other hand, IRS 10 (of Straw et a!., 1989, marked “SHM 10” on the figure) appears coincident with the peak of CO emission from source I. This object is also coincident with NGC 6334 I  /  IRS 1 of Becklin and  Neugebauer (1974) which was then compared to the BN source in Orion. The “nozzle” shaped H  II  region F of Rodriguez et a!. (1989) [size  ‘—  3 arcseconds] is also more or less  coincident with this CO peak. Also in this area is IRS-I-i of Harvey and Gatley. The observed and derived parameters from these studies are discussed in Section 5.6 with our own results. We see no significant molecular feature centred on the position of F. However, NGC 6334 E [size  —  20 arcseconds] is situated on the edge of the northwest molecular exten  sion of I. In Straw et a!. (1989), the authors attempt to associate their IRS 20 with  Chapter 5. NGC 6334 I & I(North)  86  I  +SHM3O  30  —35° 42 00”  30  I  I  •  I  I  •  ÷SHM29  -  -  0 U) O)  z  0  _350  43 QQ  -  z -J  C-) LU 0  30  -  —35° 44 00”  —35° 44 30  + SHM 2 + SHM 1 I h 17  m 17  •  4O  I  I  38  36  •  I  30  RIGHT ASCENSION (81950)  Figure 5.5: Overlay of near JR and other compact objects. Locations of compact objects in our map area from the literature are shown overlaid on the CO integrated emission. The objects marked SHM are the near JR sources of Straw et al. (1989). RCM E and RCM F are VLA H II regions from Rodrfguez et al. (1989). The object marked IRAS is the Point Source IRAS 17175 3544. IRS—I—i through JRS—I—4 of Harvey and Gatley (1983) are shown here as HG1, etc. (See caution in text regarding marker size.) —  I  Chapter 5. NGC 6334 I St I(North)  87  NGC 6334 E, with some problems in positional coincidence. IRS—I—4 of Harvey and Gatley (1983) is found to be closer in position. However, it is interesting that we find no signs of significant molecular activity at the positions of these objects. In the context of this work, the Straw et al. IRS 17 can he seen associated with our NWX, the northwest molecular extension (Fig 5.5). Figure 4 of Straw et al. (1989), a (K, J shows IRS 17 to be an A6 (or later) star, with A  =  —  K) diagram,  10 mag or more. In this light, NWX  appears to he a separate centre of star formation activity. It pales in comparison to (the main peak of) NGC 6334 I and perhaps this is why it has escaped attention until now. Of course, many of the previous studies cited in Chapter 1 have not had the required angular resolution to distinguish it from I. To bring out the velocity dependent features, maps averaged over 5 km  s  intervals  (“slices”) have been made from the same data. These are shown as Figures D.2 for CO and D.3 for CS. We see immediately the high velocity wing emission of CO from source I throughout all slices. The emission from source I(North) is more or less confined to between —25 and +15 km s. The northwest extension to peak I, seen in the integrated CO map but not obvious in the CS version, can be seen prominently in CO slices with velocities between —25 and +15 km s , same as those occupied by I(North). We see 1 that the I(North) peak appears in the velocity integrated maps due to the lines being broader near this position, while the intensity remains more or less uniform at  r’.,  30K.  NWX is both bright and broad. The mechanism for increasing turbulence (to account for the increased line width) is unclear if there is indeed a lack of a luminous object at the core of I(North). However, in the context of collapse velocities toward the core, it is reasonable to expect this trend in line widths as it simply reflects the range in projected infall velocities at different projected distances from the core. That is, at lines of sight away from the projected core, much of the infall (or outflow) motion would be tangential to the line of sight, while our observations are sensitive only to radial velocities.  Chapter 5. NOV 6334 I & I(North)  88  It is perhaps more instructive to examine the CS slices; the northwest extension feature is even brighter than peak I(North) in the sixth slice [vlsr but is conspicuously absent in the adjacent slices.  =  —10  —*  —5 km  s9  The individual spectra show the  presence of enhanced emission on the blue side of the line centre. The wing emission is perhaps best summarised in Figure 5.6. This diagram shows maps of blue and red shifted CO emission superposed on each other. While peak I(North) is featureless at these velocities, we clearly see the bipolar nature of the outflows around peak I with the peaks of blue and red shifted emission separated by The H  H  ‘-  22 arcminutes.  region F, IRS 10 and IRS—I—i (of Rodriguez et at., 1982, Straw et at., 1989,  and Harvey and Gatley, 1983, respectively) all appear to be located at the centre of this outflow motion and likely refer to the same object. This wind, as well as the material in the northwest extension must represent a great deal of mass and momentum. This point will be examined further with model studies. An unfortunate consequence of these lines being so wide is that we cannot see, as clearly, in our own data, the rotating molecular disk found by Jackson et al. (1988) pointed out earlier in Chapter 1. The amplitude of their rotation curve is ouly about 1 making it too small to extract from our wide and complex lines of CO. Nonethe 3 km s less, with the CS data, a R.A. J  =  7  —*  —  velocity diagram has been made (Figure 5.7). The CS  6 data were chosen because the lines are relatively narrow in addition to being  well sampled. Unlike the ammonia data of Jackson et at. which contains no emission from the centre of the source, the CS emission is peaked in the centre. Thus we do not see two islands of emission, in this type of diagram, as seen by Jackson et at. in their Figure 2a. Instead, the blue and red shifted emissions are connected through the centre. However, a similar bipolar nature of the emission (upper left and lower right) can be seen superposed on the contribution at the systemic velocity (centre). Here, we note that the ammonia lobes of Jackson et at. and the peaks of our CO wings  Chapter 5. NGC 6334 I  I(North)  89  I  I  I  I  30” -  / /_/ 35° 42 00”  \  /  N  /  N /  30  N  -  /  0 0)  a z o  N  / / _350  43 00  -  ,-  N  \ N  z  —  o  \/  I  —--  -  —  LU  0  /  \  If” N _350  44 00  -  \  I  N  /  _350  44 30” -  I m l7’ 1 7  I s 40  I 348  32  O 3  28  RIGHT ASCENSION (B1950)  Figure 5.6: CO 3 —* 2 wing emission. The CO line emission is averaged over velocity intervals (—40 km s 1 —* —15 km s ) (dashed contours) and (+5 km s 1 1 —* -1-30 km s’) (solid contours) to bring out the blue and red shifted wings, respectively. The contour levels are 0.0, 1.040, 2.013, 3.001, 4.041, 5.154, 6.357, 7.665, 9.093, 10.66, 12.37, 14.25, 16.31, 18.57, 21.06, 23.79, 26.79, 30.09, 33.71 and 37.68 K.  Chapter 5. NGC 6334 I & I(North) I  90  I  I  36  328  I  5.000  >  0.000  -  (1) -j  C’,  E  —5.000  -  C-) 0 -j  uJ  >  —10000  —15.000  h 17  m 408 17  RIGHT ASCENSION (B1950)  Figure 5.7: R.A. velocity diagram for peak I. The CS J = 7 —* 6 data for declinations below —35°43’45” are used to construct this diagram. The contour levels are 0.7000, 1.458, 2.231, 3.123, 4.186, 5.469, 7.024, 8.914, 11.21 and 14.00 K. —  Chapter 5. NGC 6334 I & I(North)  91  seen in Figure 5.6 are indeed coincident in angular position. One is left to explain the difference in the velocities of these systems which spans more than an order of magnitude, (AV  100 km s 1 for CO, LIV  2.5 km r’ for NH ) although the signs of the velocities 3  are in agreement. As Bachiller and Cernicharo (1990) point ont, the system is surely not a molecular disk in Keplerian orbit around the centre of peak I as originally proposed by Jackson et al. In light of our data as well as those of Bachiller and Cernicharo showing the molecular outflows, we would not expect the disk material to be aligned with the outflow axis and be of comparable size as the outflow. In the standard theories, (see, for example, Shu at al., 1987) one predicts the axis of the disk to be aligned to the outflow which will also be much more extended than the disk. In any event, a disk would very likely be disrupted by this high velocity flow. These authors suggest further that the slower outflow delineated by their own HC N data as well as the NH 3 3 data of Jackson at al. are generated by the presence of the fast CO outflow. The exact mechanism for this coupling between the high and low velocity flows remains unspecified, although there is ample mechanical energy available (see Section 5.6). However, if the low velocity  flow  is being ‘dragged out’ by the high velocity material, one might expect more turbulence than is evident from the HC N and NH 3 3 lines. An alternative explanation is offered in Section 5.6.  5.4  The Mystery of NGC 6334 I(North)  We have thus far tended to concentrate our discussion on NGC 6334 I, perhaps due to its many remarkable features. However, as highlighted below, we can see that source I(North) is very remarkable in itself. In the first place, we have already taken note of the widened lines, indicating the presence of outflow activity. However, it does not display a beautiful bipolarity as in  Chapter 5. NOC 6334 I & I(North)  92  the case of I. Rather, the outflow appears “isotropic.” We do not see separate, spatially distinct, blue and red shifted lobes in our maps. Of course, this could simply be due to a chance alignment of the outflow axis with the line of sight. Nonetheless, the outflow region covers an angular extent of  ‘-.‘  35 arcseconds (corresponding to  -‘  0.3 pc), compared  to our 14 arcsecond beam, and represents many map grid positions. If there is truly such an extended outflow around a core so little evolved (as also seen by the lower density/temperature and simpler chemistry) that there is not yet a thermonuclear energy source, then we must also ask ourselves what is driving this flow. The obvious source of energy is the collapse itself but then there must be some mechanism which imparts a greater share of the infall energy to a small fraction of the mass in order to arrange this outflow. Perhaps the CO wings we observe are not due to outfiowing of the gas but to the infall itself. The question of infall vs. outflow can, to some extent, be settled using the conclusions of Leung and Brown (1977) based on line profiles computed specifically to address this point. In particular, the similarity between the line shapes of 12 CO and C0 favour arguments for outflow. Also, the required mass of the central, gravitating 13 object(s) to cause this infall would be extraordinarily high (e.g. Zuckermann et aL, 1976). 5.5  LVG Models  By running a simple LVG program, the core component of the observed lines (i.e. not including the wings) at each beam position has been modelled as a separate, spherical and homogeneous cloud. This choice of geometry, which came with the LVG code, may be justified to first order if we consider it in the following way. While the region sampled by the telescope beam resembles one of many contiguous columns through a large cloud, the observed emission from within a specific column is likely dominated by that from some  Chapter 5. NOC 6334 I & I(North)  93  central (in the radial direction) region which in itself might resemble a homogeneous sphere. The procedure used is essentially the same as that used for the IRAS sources which has been described in Section 4.2.1. The results from this modelling are listed in Table 5.1. 5.5.1  A contour map of the derived densities is shown in Fignre 5.8.  Model Results  As entries in the table indicate, and as expected from the initial examination in Sec tion 5.2, there is indeed a disparity in densities between I and I(North) [1.3 x 10 3 c 7 m and 3 x 3 cm respectively.] In the context of the evolutionary sequence suggested 5 10 across the NGC 6334 complex, in which peak I corresponds to a very young object and I(North) an even younger one (e.g. Moran and Rodrfguez, 1980), the lower density de rived for I(North) is perfectly expected. That is, one would expect I(North) not to have yet developed a high density molecular core of the kind developed inside NGC 6334 I. [This is intuitively the expectation when comparing I and I(North) in isolation. However, in the context of the MDPS IRAS sources for which we found no correlation in density with other parameters (Chapter 4), this may appear to be an outdated expectation. This point is discussed further in Section 5.7.2 and shown not to be a concern here.] The high density at peak I, together with its higher gas temperature [T 11  =  44 K, compared to  33 K for I(North)] would tend to explain the host of lines observed at this position. We note that this density above 10 3 c 7 m appears only at one grid position. Rather than attributing this to an error, we believe it is a reflection of the small size of the high density core. (See also the discussion in Section 4.2.2.) Errors are, nonetheless, a consideration here, as is the case everywhere. In Chapter 4, density uncertainties, estimated during the model fitting, have already been discussed for the IRAS sources. They are based on the range of solutions as given by different combinations of observed lines and similar error bounds apply here. In addition, Table 5.1  Chapter 5. NGC 6334 1 & I(’North)  Position Offset (“) (—80, —80) (—60, —60) (—60, —50) (—60, —20) (—60, 0) (—60, +20) (—60, -1-40) (—50, —120) (—50, —110) (—50, —100) (—50, —60) (—40, —40) (—40, —20) (—40,0) (—40, -1-20) (—40, +60) (—30, —120) (—30,—hO) (—30, —100) (—30, —10) (—30, 0) (—30, +10) (—20, —100) (—20, —40) (—20, —20) (—20, —10) (—20, 0) (—20, +10) (—20, +20) (—20, +40)  94  2 flH  (K) 34 29 30 24 23 26 29 39 40 39 35 26 26 25 24 31 39 44 35 33 33 28 33 28 31 37 33 31 33 25  (cm) 1.6 x io 5 3.4 x i0 4.4 >< i0 2.0 x i0 5 4.0 >< iO 6.0 x iU 8.0 x iO 3.0 x i0 5 5.0 x iO 5.0 x iO 3.0 x iO 1.6 x iO 5.0 x iO 1.4 x i0 1.7 x iO 2.5 x iO 4.0 x iO 7 L3x10 1.3 x 106 1.8 x i0 5 2.3 x 1O 3.0 x iO 4.0 x i0 1.0 x iO 1.3 x ho 5 2.2 x iO 4.5 x iO 4.1 x iO 8.5 x iO 4.5 x i0  Comments 4 lines only 4 lines oniy 4 lines oniy 4 lines oniy 3 lines only, Tk guessed  4 lines only  4 lines only 3 lines only Ipeak I peak 3 lines only 3 lines only 3 lines only  3 lines only 3 lines only  Table 5.1: L\7G model results over NGC 6334. See text for derivation of these values. Positions for which only three or four lines are available for modelling have been noted as the derived densities are expected to suffer from greater uncertainty. Other positions have five or more lines observed.  Chapter 5. NGC 6334 I  I(North)  Position Offset (“) (—10,—b) (—10,0) (—10, +10) (0, —80) (0, —60) (0, —20) (0,0) (0, +20) (0, +40) (+20, —60) (+20, —20) (-1-20,0) (+20, +20) (+20, +60) (+40, —60) (+40, 0) (+40,+20)  95  Tk1  2 nH  (K) 34 34 33 32 27 33 33 27 24 28 28 28 28 24 28 26 23  ) 3 (cm 1.3x10 5 3.0 x iO 3.4 x iO 1.3 x iO 2.0 x iO 1.2 x iO 3.0 x io 1.6 x i0 4.0 x iO 1.0 x i0 1.3 x 1.2 x iO 9.0 x iO 3.2 x i0 2.0 x iO 6.0 x iO 1.0 x  Comments 3linesonly 3 lines only 3 lines only 4 lines only 4 lines only I(North) peak 4 lines only 4 lines only 4 lines only 4 lines only 3 lines only 4 lines only 4 lines only  Table 5.1: LVG model results over NGC 6334, continued.  Chapter 5. NGC 6334 I & I(North)  I  96  I  I  38  I 36  I  I  345  32  •  I  •  I  30”  _350  2  42’ 00”  35° 43’ 00”  Z  5°M’30”.  I h m 17 17  I  4Q5  28  RIGHT ASCENSION (81950)  Figure 5.8: Derived gas densities over NOC 6334. The contour values are (4, 12, 20, 28, 36, 60, 100, 1000) x 3 cm See caution in the text regarding numerical artifacts. 4 10 .  26  Chapter 5. NGC 6334 I & I(North)  97  notes map grid positions where the number of observed lines is four or less, indicating the degree of overdeterminancy. Three lines is the minimum required to obtain a solution, i.e., a value for each of Tkj, n and  .  Figure 5.8 shows the same results in the form of a contour map. Since much of the errors are expected to be systematic in nature, spurious noise features are not generally expected in this map. Unfortunately however, it is not free from numerical artifacts, par ticularly those inherent to the process (and algorithms) of drawing contour lines through irregularly sampled data. Features at the periphery of the mapped area such as the sharp ridge in the southeast corner and the manner in which the lowest contours seem to fill the page elsewhere are probably not real. Despite this problem, we can clearly see the two principal peaks, I and I(North). We also see another peak, apparently at the position of the H II region E. The “peak” immediately to the north of that, and to the west of T(North) is a suspected numerical artifact as described above. We note that since these densities are derived by modelling the cores of the lines, there is no corresponding distinct peak for NWX which is a feature conspicuous by its wing emission (and is distinguished from Tin that way). 5.5.2  S 3 C 4 J  =  7  —*  6 Anomaly at Peak I  In running these LVG models it became apparent that interpretation of the high intensity of the C 5 3 4 J  =  7  —*  6 line at peak I is less than straight forward. While the line is not  detected in T(North), it appears as a  =  8 K line at the southern peak. Applying the  standard analysis yields a wide gap between solutions obtained using CS (but without 5) 3 C 4 and that obtained with C 5 3 4 (ignoring CS). That is, while the CS J line observed as  =  =  7  —*  6  18 K indicates (in conjunction with the CO lines) a gas density of  6 x , 3 c 5 10 m the C S 3 4 line favours  ii  ‘-  3 c 7 l0 . m  One possible explanation is that, for some reason, the  345  isotope is overabundant in  Chapter 5. NOC 6334 I & I(North)  this object. Under this hypothesis, one finds a  98  325/345  ratio of about 5 from our observed  intensity ratios, rather than the ‘usual’ 20 used elsewhere in the modelling. Alternatively, it may be that the gas density is indeed as high as the C S 3 4 J  =  7  —÷  6 line indicates and  that the CS lines have become optically thick, or that the transition has thermalised, and in either case are insensitive to the exact value of the density. This is expected to occur at densities above  cm (Mnndy 1984 and Snell et al. 1984), a value consistent 6 10 7 x 3  with our C 5 3 4 derived densities. It would also tend to explain another anomaly, that the ratio IA[C S 7 34  —  5 5 34 6]/lj[C  —  4] has a value of 1.5 where one would normally expect  a value not exceeding unity [since lines of molecules as rare as this are normally found optically thin.] That is, perhaps observations of the J  5  =  —÷  4 transition of C 5 3 4 also  suffers from the non-linear effects of optical thickness. In order to resolve this question, a proposal was submitted for “Canadian” service observing at the JCMT 5  —*  4 and J  =  7  —*  .  We requested observations of the 3 ‘ C 5 molecule in the J  =  6 transitions. Since this molecule is expected to be 3 to 18 times  less abundant than the C 5 3 4 molecule (depending on the latter’s ‘yet to be determined’ abundance), we expect neither transition of that molecule to he influenced by the effects of high or intermediate optical depths. Further, the interpretation requires no knowledge of the 32 S ratio. In fact, our data would have enabled us to assign a value for this 34 5/ ratio. The proposal had been approved and scheduled for observations. Unfortunately, they were not carried through due to unsuitable weather conditions. We currently plan to re-submit the proposal at a later opportunity. The related question of the line ratio between the J  =  5  —+  4 and 7  —÷  6 transitions of  5 3 C 4 might he a simple matter of beam size mismatch. That is, the telescope beam for the lower transition observations samples a larger area of the sky. A proper comparison Service observing is one in which a set of observations with a telescope is made by someone other 3 than the proposers of the observations, usually a member of the observatory staff. It is most useful for short programmes with straight forward observational requirements.  Chapter 5. NOC 6334 I St I(North)  99  might most easily be made if we can simulate the larger beam for the 7  —>  6 data. Our  S 3 C 4 data base, unfortunately, is insufficient to resolve this question withont additional observations. (We do not have observations at all grid points.) The sampling of the C S 3 4 7  —*  6 line around peak I that we do have suggests that it is quite possible that emission  averaged over the area of the J  =  5  —*  4 beam would bring the line ratio closer to  unity. An alternative explanation, that the line intensities for these different transitions measured using different receivers have been miscalibrated in such a way as to give rise to this (erroneous) line ratio seems implausible since we have exercised some care during the calibration process (and with particular regard to this possibility). Additionally, similar line ratios would also be expected to be found with other molecules. One should not forget, however, that whatever the resolution to this problem, the question of sulphur isotopic ratios remains unanswered. For the present, the density of 1.3 x 10 3 c 7 m as indicated by C S 3 4 J  =  7  —,  6 line  (the most optically thin line available) is adopted.  5.6  Derived Parameters: The Bipolar Outflow at NGC 6334 I  As described in Section 1.4 and Chapter 2, a new computer code was developed to model the radiative transfer of molecular line emission with fewer restrictions than are required for the LVG code already in use. One of the prime applications of this new code has been to model the wide wings of the CO J  =  3  —*  2 line around peak I. The new model code  developed is particularly useful here, since the old model of a homogeneous cloud under uniform collapse seems not to represent precisely the case at hand. In addition to the geometry, some of the LVG model assumptions, as Leung and Brown (1977) point out, are specifically violated in cases such as this. The nature of the “violations” is not that the velocity gradient is not large, but, for example, it must be everywhere large compared  Chapter 5. NGC 6334 I & I(North)  100  Size, d Gas Density, n Mass, M Max. Velocity, 1/max Kin. Energy, E Momentum, F Mass Flow Rate, M Outflow Lifetime, rfi 0 Kinematic Timescale, rij Mechanical Luminosity, Lmech  0.2 pc 3 5 x l0cm 2.5M® 65 km s’ 1.8>< lO erg 46 82 M®km 51 8 x 10 M® yr 4 1 3.2 x io yr 3.0 x io yr 89 L®  Table 5.2: Physical Parameters for the Outflow in NGC 6334 I. to the turbulent velocities. [See Leung and Brown (1977) for a full discussion.] At the cost of increased computing resources, my method specifically refrains from making these assumptions. In any event, our LVG code is not capable of predicting line shapes which are of primary interest here. The best models of the line core and outflow wings yield densities of  n.’  cm 10 5>< 3  over a (0.2pc) 3 region for each wing. The mean velocity in the flow is < V >= 25km s. This corresponds to an outflowing mass of M = 2(5 x ) cm x (0.2pc) 3 10 3xm i = 2.5M® 0 with a kinetic energy of M mass  (=  2.0 InH),  <  <  2 >= 1.8 x l0 V erg, where 46  2 >= (37 km V  2 s’)  mmol  is the mean particle  is the second moment of the velocity, and  the factor of two accounts for the number of lobes. In units that are perhaps more familiar, the momentum represented in this wind is F = M  <  V >= 82 M®km s’.  The corresponding “mass flow rate” obtained by estimating the mass flow through a cross-sectional surface A is M = AnVmax = 8 x 10 M® yrt The outflow lifetime 4 can then be estimated as  Tfiow =  M/M = 3.2 x  io  yr. A second timescale can he  derived in the following way. The minimum “crossing time” (or kinematic timescale) for the outflowing gas to reach the far side of the CO lobe at its maximum speed can  Chapter 5. NGC 6334 I St I(North)  be calculated as  =  0.2pc/65 km  101  s =  3.0  ><  l0 yr, in agreement with Tifow. The  mechanical luminosity 4 ascribed to this flow is Lmech  =  V >= 89 L®. < 2  [These  values are summarised in Table 5.2.] The reader is cautioned that these values are derived ignoring the effects of velocity projection to the line of sight. However, since the positive and negative velocity lobes partially overlap in the maps, the flow direction is likely not far from the line of sight and the projection effect can be expected to be very small. Further, if the line of sight lies within the opening angle of the outflow [see, for example, Figure 3 of Lizano et  iii.  (1988)] then the observed radial velocity will he the true outflow velocity without need for corrections. If corrections are needed, however, they come into play as cor 1 e for F and M, cor 2 e for E, and sin 9 cor 3 9 for Lmech, where 9 is the angle between the flow axis and the line of sight [for a detailed discussion, see Cabrit and Bertout (1990)]. For 9 as large as 45°, the correction factors are only 1.4, 2.0, and 2.0, respectively. Thus, we do not expect projection ambiguities to be the dominant source of error. However, after some analysis, Cabrit and Bertout (1990) argue that the best estimates for momentum and mechanical luminosity, for example, still suffer uncertainties by factors of 10 and 60, respectively, due to uncertainties in the input parameters. These values compare well with those derived for NGC 6334 I by Bachiller and Cer nicharo (1990). They found M E  n  =  =  erg, and Lmech 46 4.3 x lO  2.3 M®, F =  170L®.  =  92 M®km s , M 1  =  10 x 4 10 M ® yr’,  Although Jackson et al.  (1988) found  3 in the NH i0 crn 3 lobes, these were estimates based on the kinematics of a  molecular disk in a Keplerian orbit. Since this interpretation is no longer supported, we need not concern ourselves with the density discrepancy. Harvey and Gatley (1983) estimate the far infrared luminosity of this source, their IRS—I—i, to be  L®. This is based on the observed combined flux of IRS—I—i, 4 8 x 10  Mechanical Luminosity  output per unit time of kinetic energy through the outfiowing gas.  Chapter 5. NC C 6334 I & I(North) T  102  2 & 3 and an estimate of their relative contributions to the total flux. We see that the far infrared, radiative luminosity is much greater than the mechanical luminosity in the outflow  (kin  > Lmech), or that the outflow represents only a small fraction of the total  energy budget. We can estimate some dynamical parameters of the system following the approach of Lizano et al. (1988). In their investigation of HR 7—11, they propose a model in which an Extreme High Velocity (EHV) neutral H  I  wind is ejected in two opposing  streams from a stellar source. When the atomic wind comes in contact with the ambient molecular cloud and becomes entrained in it, momentum is transferred to that part of the cloud, thus driving the molecular bipolar outflow. The bipolar structure of the H  I  flow in RH 7—11 has since been confirmed by VLA mapping (Rodriguez et al., 1990). Applying this type of model to NGC 6334 I, we can also derive a value for the stellar mass loss rate. On initial contact, the H  I  CO observed, approximately 65 km  As the two components interact, momentum is  r’.  is moving at the speed of the fastest moving  transferred. To account for the molecular momentum derived above, the required mass of the accumulated mass from the H I  flow is  =  (82 M® km s’)/(65 km s_ ) = 1.3 M®. 1  This is then the total mass ejected from the protostar (or its disk). The rate of mass loss is then, roughly, 1l/I values for i1I and  = 1.3 M®  /  3200 yr = 3.9 x 4 10 M ® 1 yr The true .  are possibly higher since the present calculation assumes 100%  efficiency in momentum transfer. An implied efficiency in the transfer of kinetic energy is 33%. This is obtained by comparing the kinetic energies of the molecular outflow and the assumed EHV H  I  wind. Key to this discussion is this assumption that such a  neutral wind actually exists in the NUC 6334 I system. This has yet to be confirmed observationally. Direct observation of the EHV H  I  emission is certainly desired before  proceeding much further with this analysis. However, this model does offer an explanation for the low velocity NH 3 (Jackson et al.,  Chapter 5. NGC 6334 I & I(North)  103  N (Bachiller and Cernicharo 1990) and CS (this work) lobes seen at the same 3 1988). HC position as the CO outflow. It is reasonable to expect to find these molecules in greatest concentration at the frontiers of the swept-np material (or the “working surfaces”). These are the locations where the outflow enconnters the ambient molecular cloud (shock), the swept-up material accumulates (high n) and the oldest of the outflowing material is found (time to form molecules). The angular coincidence with the CO outflow is to be expected if, as we argue, the outflow direction is almost coincident with the line of sight. The lower velocity of the flow  (r  2.5 km s’) represents an effective terminal velocity in this sense.  Edwards and Snell (1984) provide a convenient list of the properties of 17 molecular outflows (associated with Herbig-Haro objects). Our values for the outflow timescale r for NGC 6334 I ranks among the smallest of the entries in their Table 2. The kinetic energy for NGC 6334 I is a full order of magnitude greater than the largest values found in their list. (Median values from the list of Edwards and Snell are lO y r, E 3x 4  =  =  25 km s ,r 1  =  2.5 x lO erg.) More recently, Morgan et al. (1991) mapped and analysed 44  nine outflows from their survey of low luminosity (> 220L®) young stellar objects in the  of  L1641  region.  magnitude  lower  Typical  than  values  our  value  of  for  Lmech NGC  from  6334  this  I.  sample  are  Dynamical  two  or  three  parameters  orders  derived  by  Bachiller et al. (1991) for another low mass star formation outflow, IR.AS 03282 + 3035, appear to fall in the same category. On the other hand, Bally and Lada (1983) have mapped and compiled similar parameters for outflows near more massive young stellar objects and found M  0.3  —  100 M®, V  10  —  50 km r’, and ‘r  lO y 4 r, typically.  Our values for the outflow in NGC 6334 I are in line with those of this group of high mass star forming regions.  It should be noted that the attributes of this outflow that make it so unusual or perhaps even unique can all be traced to the unusually high velocities of the outflow ing matter. As will be discussed in Section 5.7.2, if wide wings such as these seen at  Chapter 5. NGC 6334 I & I(North)  104  NGC 6334 I turn out to be common, then some aspects of the implied relative youth of this system may need to he questioned.  Discussion  5.7 5.7.1  Relative Ages  In one of the earliest investigations on NGC 6334, Cheung et al. (1978) suggested that the complex displays evidence of sequential star formation across the region, since the emission peaks were located in succession with regular spacing. While we cannot com ment on star formation sites elsewhere in the NGC 6334 complex, the relative ages of peaks I and I(North) are apparent here. NOC 6334 I is clearly more evolved than I(North) for the following reasons. For one, the modelled density of I(North) is lower than that of I, indicating the latter to be the more collapsed object. The same can be argued from the difference in gas temperature. The richer chemistry found in the spectrum of I also supports this point of higher density, in addition to implying a greater age directly, for the molecules may require time to form. Since we find no compact IR objects and no evidence of a thermonuclear energy source in I(North), we may suppose it is still collapsing (but see discussion in Section 5.4). Finally, we have seen that the outflow at NGC 6334 I is highly developed. It has had time to expand and accumulate material since its initiation. From the age of this outflow alone, we expect AAge 5.7.2  yr between I and I(North). 3 3 x lO  Are EHV Outflows a Common Phenomenon?  In light of the above discussion on NOC 6334 I and the detection of EHV molecular outflows in other recent works (e.g., Bachiller et al., 1991, Bachiller and Cernicharo, 1990, Margulis and Snell, 1989, Koo, 1989, Lizano et al., 1988), we may ask ourselves the  Chapter 5. NGC 6334 I & I(North)  105  following questions. Are these EHV outflows more common than previously believed? Have we systematically missed detecting them in the past by observing with insufficient baseline and resolution? Do we need only to look with the appropriate, newly avail able instruments and methods to find that EHV outflows are more the “rule” than the “exception?” There is one, seemingly straight forward way to answer these questions. This very outflow in NOC 6334 1 is a prime example of this observational selection. At first glance, one may he curious why the CO high velocity wings around NOC 6334 I so prominent in J  =  2  —+  1 (Bachiller and Cernicharo, 1990) and in J  work) were not reported in the J  1  —,  =  3  —>  2 (this  0 line by Dickel et aL (1977) who mapped  the entire NOt 6334 complex in CO. One may point to theoretical arguments favouring wing formation in the higher J transitions (e.g., Mitchell, 1993). However, more careful inspection of the Dickel et al. observing parameters yields an explanation which as much as ensures that, present or not, the J  =  1  —*  0 counterparts of these wings would not  have been detected. Not only do they suffer from beam dilution due to the 70 arcsecond beam of the NRAO 11 m but their observations were made in the frequency switching mode. The 20 MHz shift used corresponds to L\V  =  52 km  s, restricting  the likehood  of noticing the very wide, but relatively flat, wings. Even in this present work, if the receiver system had not given such a confidence in spiring, flat baseline or if the spectrometer (AOSC) did not provide such a wide handpass (> 500 km r’) without sacrificing resolution, it is quite conceivable that, during pre processing, we would have fit and removed a “baseline” right through the wing emission. Had we been observing at a lower transition and with a larger beam and not specifically looking for the wide features, this would almost certainly have been the case. Another example to illustrate this same problem is the survey work of Edwards and Snell (1984). The FCRAO 14 m telescope in the CO J  =  1  —÷  0 line gave a heamwidth  of 45 arcseconds and allowed a maximum bandpass corresponding to 333 km s. HH  Chapter 5. NGC 6334 1 & I(North)  106  7—11 was included in this work but the EHV flow had to wait for discovery by Bachiller and Cernicharo (1990). The Bell Laboratories 7 m used by Bally and Lada (1983) for their CO J  =  1  —,  0 survey used a filterhank capable of AV  =  1300 km  but its large  beam biased against the detection of such confined features. A campaign to this end has already been undertaken by Koo (1989) and Margulis and Snell (1989) using a technique slightly different from the one suggested here. They observed known outflow sources in principally the CO J  =  1  —*  0 line with moderate  resolution. [NRAO 12 m (Koo 1989) and FCRAO 14 m (Margulis and Snell 1989)]. They detected EHV features in a handful of sources in their lists by making very low noise observations (Ia noise as low as 3 and 8 mK, respectively). Of course, we have already a wealth of useful observational data on known outflows in our MDPS sample. Except for the declination limit, the IRAS source at NGC 6334 I does have the required characteristics to he included in the MDPS list. Since we have seen no EHV features in our sample, observed using the same instrumentation as for NGC 6334, the apparent conclusion is that EHV winds are not very common. However, the issue is a complex one and we need to address at least the following points. First, with the angular resolution involved, detection of wide wings is dependent on the exact direction to which the telescope is pointed. If we had observed NGC 6334 I only at the position of the IRAS object, the EHV wings may not have been discovered. There is only the red shifted wing at relatively low levels. Without an expectation of finding the wing, the feature could easily have been ignored. Thus, it appears important to map each source. As it happens, sources #13 and #22 have recently been fully mapped in CO J  =  2  —*  1  (Purton and McCutcheon, unpublished). These maps show simple source morphology and do not indicate the presence of EHV bipolar outflows. Thus, in the cases of sources #13 and #22, we can conclude that no hidden EHV features were there to be discovered.  Chapter 5. NGC 6334 I & I(North)  5.7.3  107  Neutral Hydrogen Wind in NGC 6334 I?  In Section 5.6 we made some simple calculations based on the assumption that an EHV neutral H I wind exists at peak I as is found at HH 7—li by Lizano et aL  (1988).  Despite the rich observational history of NGC 6334, there are, as yet, no equivalent H I observations known to this author. While in principle this is easy to perform, in practice, the instrumentation for suitable H I observations of this source does not exist. Normally, the instrument most ideally suited for this type of observations is the Arecibo 300 m telescope. This is the very instrument used to measure the H 1 spectrum at HH 7—11. It offers the spatial resolution and sensitivity of a large, filled-aperture telescope, and  is equipped with a good wide-band, high-resolution spectrometer. Unfor  tunately, it cannot he steered to the declination of NGC 6334 (—36°). One may, however, use the Arecibo telescope to conduct a systematic search for H I winds in the other known bipolar outflows accessible from it. This will he a good counterpart the the CO programme eluded to in Section 5.7.2.  Chapter 6  Conclusions  6.1  The IRAS Selected Protostellar Candidates  From the original list of 39 sources, (sub)millimetre continuum maps have been made using the JCMT for nine of them. In all cases, the maps show the source to be resolved by the telescope beam. Continuum fluxes have been measured from each map. A separate study using the same data with dust emission models has shown that each of our sources consists of two components: hot & small and cool & large. The latter is identified with the molecular cloud observed here. Rotational transition lines of CO and CS have been detected and measured from all (up to 20) sources attempted. Isotopic species of CO are also observed. The C 5 3 4 line has not been clearly detected in any of our sources. This molecular emission has been studied using LVG models with resulting gas densities of the order of 10 3 c 5 m for all sources investigated. These gas densities, as well as other derived quantities (including column density, stellar effective temperature, spectral type and molecular cloud mass), have been examined for patterns and correlations, perhaps a manifestation of the main sequence but none has been found. Thus, the well observed portion of our sample appears to constitute a homogeneous collection of protostars, within the limitations of our precision.  108  Chapter 6. Conclusions  6.2  109  Northern End of the NOC 6334 Complex  The northern end of the NGC 6334 complex encompassing peaks I and I(North) has been mapped extensively with CO J  =  3  —*  2 and CS J  =  7  —*  6 lines and with other  lines to a lesser extent. The two peaks show mnch difference in observed characteristics, starting with CO line wing structures. Peak I shows bipolar outflows at extreme high velocities approaching 65 km/s accompanied by a low velocity flow. An extension to peak I, 30 arcseconds to the northwest, has been identified in the velocity integrated line maps due to increased line width at this location. LVG models indicate densities in excess of 3 cm for peak I while the results for I(North) show a much lower value of 7 10 4.5 x . 3 c 5 10 m AU observed and derived parameters are consistent with the suggestion of an evolutionary sequence across NGC 6334 in which peak I is very young but I(North) is an even younger object. The high velocity ontflowing matter around NGC 6334 I has been modelled us ing a general radiative transfer model.  The best models yield outflow densities of  cm for each wing, corresponding to an outfiowing mass of 2.5M®. Values for 10 5 x 3 physical/dynamical parameters have been derived (Table 5.2) and are seen to be in line with those of other high luminosity protostars. The one exception is the extremely high CO velocities in the wings. The BPO has been compared to that of the HR 7—il system whose EHV molecular outflow is thought to be driven by a H  I  wind. The proposed H  I  wind for the NGC 6334 I system is estimated to have accumulated 1.3M 0 of stellar ejecta over a lifetime of  —  3000 yr, at a mass loss rate of 4 x 4 1V M ®/yr. This is a parameter  of the forming star, rather than of the parent molecular cloud, thus providing a check for, or a connection to, stellar formation theory. The age of the outflow, since it is well developed in I but not in I(North), sets a lower limit on their age difference at years.  r’j  3000  Chapter 6.  Conclusions  110  Model studies also indicate that there may be an anomalously high abundance of the 345  isotope at the position of peak I, perhaps indicative of some stellar activity.  6.3  General Conclusions  With regard to our analytical tools, the Large Velocity Gradient model for a spherical, homogeneous, isothermal gas cloud used in this study has shown itself to give useful insights, even though many of the implicit assumptions were challenged (by myself) or pushed to the limit in this current application. When increased amount of information is available, or when the increased effort is warranted, the line transfer model code developed for this study has been used. In particular, the wide CO wings at NGC 6334 I was modelled using this tool. On the observational side, the importance of fully mapping star forming molecular clouds has been recognised, if one is to detect and recognise some subtle features of significance. A single pointed observation at the IRAS position appears not always to be sufficient. 6.4  Summary of Suggested New Observations  In various parts throughout this thesis, suggestions for desirable future observations have been made. In this section, a brief summary is made of these suggestions. Already proposed are the 13 CS J  =  5  —*  4 and J  =  7  —*  6 observations of NGC 6334 I  (Section 5.5.2). They are designed to resolve the choice between the two main, likely explanations for the anomalous C 5 3 4 line intensities at this location.  Also regarding NGC 6334 I, obtaining direct evidence for the presence of an atomic wind by measuring its H I spectrum has been discussed in Section 5.7.3. However, it was  concluded that appropriate instrumentation for this undertaking does not exist at this  Chapter 6. Conclusions  111  time. Perhaps the most significant among the suggestions listed here is the related project to search for H  I  and CO EHV features in known young BPO sources as suggested  in Sections 5.7.2 and 5.7.3. The hope is to clarify whether indeed NGC 6334 I is an exceptionally young and unusual system, or if similar features can be found in a large number of sources. Additionally, observations of the MDPS objects in the J  =  1  —*  0 or J  =  2  —*  1 lines  of CS are suggested in Section A.2.3 in order to constrain further the model solutions.  Bibliography  Bachiller, R., and Cernicharo, J., 1990, Astron. & Astrophys., 239, 276. Bachiller, R., and Gómez-González, J., 1992, The Astron. Astrophys. Rev., 3, 257. Bachiller, R., Martin-Pintado, J., and Planesas, P., 1991, Astron. & Astrophys., 251, 639. Bally, J., and Lada, C.J., 1983, Astrophys. J., 265, 824. Becklin, E.E., and Neugebauer, G., 1974, Proc. of the Eighth ESLAB Symposium, Hil Regions and the Galactic Center, A.F.M. 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Snell, R.L., 1981, Astrophys. J. Suppi., 45, 121. Snell, R.L., Dickman, R.L., and Huang, Y.-L., 1990, Astrophys. J., 352, 139. Snell, R.L, Huang, Y.-L., Dickman, R.L., and Claussen, M.J., 1988, Astrophys. J., 325, 853.  Bibliography  116  Snell, R.L., Mundy, L.G., Goldsmith, P.F., Evans, N.J.II, and Erickson, N.R., 1984, Astrophys. J., 276, 625. Sobolev, V.V., 1957, Soviet Astr. -A.J. 1, 678. Straw, S.M., and Hyland, A.R., 1989A, Astrophys. J., 340, 318. Straw, S.M., and Hyland, A.R., 1989B, Astrophys. J., 342, 876. Straw, S.M., Hyland, A.R., and McGregor, P.J., 1989, Astrophys. J. Suppi., 69, 99. Sutton, E.C., Danchi, W.C., Jaminet, P.A., and Ono, R.H. 1990, Internat. J. Infrared Millimeter Waves, 11, 113. Tamura, M., Gatley, I., Wailer, W., and Werner, M.W., 1991, Astrophys. J., 374, L25. Ulich, B.L., and Haas, R.W., 1976, Astrophys. J. Suppi., 30, 247. Walmsley, C.M., 1988, Galactic and Ext ragalactic Star Formation, R.E. Pudritz and M. Fich, eds., Kiuwer Academic Publishers, Dordrecht, p. 181. Wannier, P.G., 1980, Ann. Rev. Astron. & Astrophys., 18, 399. Wells, D.C., Greisen, E.W., and Harten, R.H., 1981, Astron. & Astrophys. Suppi., 44, 363. White, R.E., 1977, Astrophys. J., 211, 744. Wilking, B.A., Mundy, L.G., Blackwell, J.H., and Howe, J.E., 1989, Astrophys. J., 345, 257. \Villiams, D.A., 1985, Quarterly J. R.A.S., 26, 463. Zuckermann, B., Kuiper, T.B.H., and Rodriguez Kuiper, E.N., 1976, Astrophys. J., 209, L137. Zuckermann, B., and Palmer, P., 1974, Ann. Rev. Astron. & Astrophys., 12, 279.  Appendix A  Other Discussion  Much discussion on the data and results has been made in Chapters 4 and 5. Some points of discussion of a more general or parenthetical nature but nonetheless worthy of note are now addressed. More importantly, some discussion relating to the MDPS sources have been reserved for this chapter since it builds on experience from the NGC 6334 portion of this thesis.  A.1  TRAS Protostellar Candidates Revisited  The following points concerning the MDPS objects have been reserved until now as they make sense only after reading the chapter on NGC 6334. A.1.1  Artifacts in the LVG Model?  In Chapter 4, the derived gas densities have been noted to cluster around  t—’  10 cm . 3  Originally, this was cause for some concern in that our LVG code might have some built—in limitations that constrain the range of possible solutions. However, the results obtained using the same code for NGC 6334 indicate that the code (and my own application of it) is indeed capable of arriving at solutions at both higher and lower densities, given appropriate observed parameters. Also, the lack of a detected 5 34 J C  =  7  —,  6 line in  any of these sources supports the idea of an upper limit to density. Thus, we could now look for an astrophysical explanation for this common density with some confidence that we are not suffering from a model artifact. 117  Appendix A. Other Discussion  A.1.2  118  Future Work  In the NOC 6334 portions of this thesis, we learned of the advantages of mapping a molecular cloud. The discovery and subsequent investigation of the bipolar outflow is a prime example. Since we believe this BPO may have gone nnnoticed if we had observed it only at the coordinates in the IRAS catalogue, it is possible that there are more interesting and/or complex features in our IRAS sources yet to be discovered. Maps of our IRAS sources similar to the NGC 6334 maps (CO/CS combination) may prove very profitable. This discussion is also examined from another point of view in Section 5.7.2. A.2  In general  In addition to topics raised with respect to one or the other of the two projects, there are some points common to both efforts. These matters are now discussed. A.2.1  Potential for Problems with the LVG Analysis  The LVG code used in this study has been tested by its author and used to produce reasonable and insightful results (e.g. Richardson et al. 1985). In addition, our own tests and examinations indicate it is performing properly within the assumptions of the model. (See for example, Section A.1.1. Also, models have been computed in certain limiting cases where analytical solutions are possible.) We must now consider whether or not there are problems with the way in which the code has been applied. That is, “is the use of these LVG models appropriate here?” It seems generally safe to assume there are no significant problems with our method for determining the gas kinetic temperature from the 2 ‘ C 0 lines (recall section 4.2.1). That is, the temperature of the gas is well represented by 12 C0 emission. This optically thick line, as stated earlier, is a good thermometer since it is insensitive to all other  Appendix A. Other Discussion  119  parameters. While it is true that self absorption is sometimes an impediment, corrections to the required precision are easily made in practice. However, we might expect problems as we apply this T 1 to calculations of other transitions, isotopic species, or worse, other molecules. This is because while the temperature obtained will be some ‘effective’ temperature for, say the 12 C0 J  =  2  —*  1 line, the gas contributing to the CS J  =  7  —*  6  line emission, for example, may largely be restricted to a much smaller spatial region, perhaps some central core, where both temperature and density may be much higher. If indeed we are sampling different spatial regions (or extents) with different molecules or even isotopes, results obtained using homogeneous model clouds cannot be accepted at face value. One idea is to separate the CO problem from the CS one and solve for them in dependently. However, this method is not without its own problems. In addition to having  fewer  independent data, our curves in the (n,  )  plane tend to run parallel to  each other (separation is normally within the error bars) over the ‘reasonable’ portion of the parameter space for both the CO-only and CS-only plots. (See Figure 4.1 for an example.) Thus, it is normally the combination of CO and CS data that yields a solution in practice. (See also Section A.2.3.) It is also more difficult to obtain a value for Tk using CS only. The available lines are of intermediate optical thickness such that all three quantities (T , n and 1  )  have to be solved for simultaneously. In the CS (and C S) 3 4  works of Snell et al. (1984) and Mundy et al. (1986) for example, the authors simply make a priori assumptions for their values of T . An alternative approach is to drop 1 the homogeneity assumption. This is discussed again in Appendix 2.7.2. There are other obvious limitations to these models, having to do with the simplifying assumptions regarding geometry. One is that the cloud size is assumed to match the telescope beam size (with a fiat response) exactly. While it is difficult to correct for the contribution due to the gas infall motion having perhaps a significant transverse  Appendix A. Other Discussion  120  component, the required correction for the (over and under) filling factor can be made more easily to first order. An assnmption with perhaps a more profonnd consequence is that of homogeneities in density and temperature. One difficulty arising from this assumption has already been discussed above. While this assumption can simplify the numerical problem greatly, it also renders the model incapable of reproducing such effects as self absorption, a phenomenon often seen in dense molecular clouds, and, in particular, the data presented here. Whenever practical, one would prefer not to be restricted by these assumptions since we generally expect dense and hot cores to be located in star forming clouds. However, the results from dust modelling of the continuum maps does provide support for using a homogeneous model (Section 4.1.2 and McCutcheon et aL, 1995). The fits obtained with the two component models are of excellent quality. Since the two components individually are homogeneous ones (in density and in temperature) and one of them (large & cool component) represents the same material modelled here with the PVC gas model, then it can be argned that the gas can also be approximated as homogeneous. A.2.2  Line Transfer Model  In moving from a simplified LVG analysis to a full—fledged multi-level line transfer code, a number of advantages and disadvantages arise. Certainly, it has been a good learning exercise, in that an intimate understanding of all known processes is necessary in order to express each effect in a quantitative manner as is required to write the computer code. Having a flexible modelling tool allows investigation of a number of astrophysical effects. For example, our initial LVG analysis did not allow proper treatment of self absorbed lines which are quite common among the sources investigated here. As well, nonuniformities are allowed in the physical quantities, making the model process more realistic. In addition to simple tapering—off of molecular gas density, this feature has  Appendix A. Other Discussion  121  been used to model the matter in the high velocity winds seen in the lines. On the other hand, a comprehensive model such as this suffers from the very flexibility it is designed to allow. Preservation of generality can be its own enemy in some cases in that while the models allow us to investigate many effects, we are, in effect, required to investigate all of them. This is the common pitfall of many models that attempt to explain everything in one giant step. For example, we cannot truly separate the line broadening mechanisms of turbulence and a large velocity gradient. With this level of generality, one cannot ensure any sort of uniqueness in the solutions, especially in light of the observational uncertainties. In practice, however, it is not at all difficult to fix the value of a certain parameter while investigating others. For example, during this study, turbulent gas velocities were fixed to nominal values in order to obtain numerical results. This practice is certainly no worse than making implicit assumptions (as with our LVG analysis) and is also not uncommon. The choice of the turbulence parameter can be reviewed by comparing a selection of computed models. A.2.3  Additional Lines for Observation/Modelling  Originally, the J  =  5  —,  4 transition of CS was not considered for observations. However,  it was found during preliminary analysis of data from the April 1990 observing sessions that inclusion of an additional line may prove useful. Model calculations indicated that the available data at hand allowed for large ranges of values (for density, etc.) in the so lutions consistent with the observed line intensities. It was hoped that the CS J  =  5  —  4  line, having slightly different excitation characteristics, could serve as that additional line. We realised it may not be different enough, hut since the line was observable with the JCMT, it was included in our subsequent proposal. Also, using a different molecule in search of more contrasting excitation characteristics, would require knowledge of ad ditional parameters including its abundance and it was decided to use this conservative  Appendix A. Other Discussion  122  approach of using the same molecule and the same telescope. In modelling the J  =  5  —*  4 as well as J  =  7  —*  6 transitions of CS, we find now  that the two lines tend not to give independent information in the density range of the solutions as obtained. In retrospect, a separate initiative such as a programme to observe the J  =  1  —*  0 or 2  —*  1 line from a Nobeyama—class telescope, or perhaps the CBT,  might have been more profitable. This might be a topic for a future study.  Appendix B  Data Transport  It is too often the case in modern astronomy that the astronomer toils over computers for a significant fraction of the time simply converting data formats as he moves from one site, machine or program to another, as necessitated by the facilities available to him. This project is no exception and the steps undertaken to bring the JCMT data to our home institution in a useful form for analysis are outlined in the following. B.1  Spectra  The flow of observational data for spectral line work is summarised schematically in Figure B.l. Initially, line observations made at the JCMT are recorded into ‘GSD’ data files accessible by 1 SPECX, the reduction software in common use at the JCMT. SPECX has been used to examine the data at the Mauna Kea summit as they are collected and also for first stage reduction (such as baseline and bad channel removal). It runs on VMS platforms including the computers at JAC. In order to continue the work, it was necessary to transform and transport the data files to forms readable by the computers available to us at the University of British Columbia (UBC). These are the university main frame computer running under what is known as the Michigan Terminal System (MTS) and our SUN 4 running UNIX. Origi nally, the SUN was not available and all post-reduction was done on the MTS platform 1  SPECX is written by ft. Padman and  has been provided by her for use by the JCMT community. 123  Appendix B. Data Transport  /  Figure B.1: Data flow for line observations. See text for further description.  124  Appendix B. Data Transport  125  using local software systems (called ‘IRApS’ and ‘CLOUDS’) which use data in what I call the ‘clouds.hig’ format. To put data in this format, it was first necessary to transform the GSD files of SPECX into a more accessible form. The best way seemed to be to use a SPECX facility to make an ASCII dump of each spectrum. This makes an ASCII table of channel values preceded by a few lines of header information. Files containing these ASCII tables were transported to the UBC MTS system originally on tape and, later, as it became available, by ftp via Internet. A short program was written to convert the ASCII tables to the ‘clouds.big’ format. One of the first software packages we installed on the SUN as it became operational was  2 It has proven quite effective, not only in the presentation of data with its IRAF.  plotting facilities, but also in basic reduction of the kind once done using SPECX. To read the data into IRAF, one of two things was done. New data from JCMT/JAC were put into their ‘FITS’ format before leaving the site and transported to UBC either on tape or by Internet. This, so called ‘FITS’, is not quite the same as the ‘real’ FITS 3 but lists the data elements in ASCII form; the convention of the header is much the same. (NRAO 12m data used to come in this form for a time.) Fortunately, IRAF has a facility for reading data of this form called ‘rtextimage’. In order to combine this new data set with ones already stored on MTS, short programs to convert this ‘FITS’ to the ‘clouds.big’ format and vice versa were prepared. Figures C.2 which shows the line data were prepared using export software provided by the Dominion Radio Astrophysical Observatory (DRAO), namely ‘madr’ and ‘plot’. The DRAO software take data in yet another form. For the spectral line data, another short program was written to assist in the required conversion from the ‘clouds.big’ 2  IRAF is distributed by the National Optical Astronomy Observatories (of the U.S.), which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the (U.S.) National Science Foundation. FITS (Flexible Image Transport System, Wells, et al., 1981) is a data format standard designed to facilitate the exchange of astronomical data among different institutions and computational platforms.  Appendix B. Data Transport  126  format.  B.2  Continuum Maps  The on-the-fly mapping data are stored, as they are collected, into GSD files at the JCMT. The first step in reducing these data is to make R.A.— dec. maps ont of them nsing 4 This program contains facilities for correcting for atmospheric extinction (which NOD2. varies across a map) and deconvolving the dual beam response pattern. There exist standard procedures for this step at the JCMT which may be found at the observatory. [See Matthews (1992), Salter (1985) or Sandell (1988).] These can be written onto a tape in (real) FITS format for transport.  Locally at UBC, our map reduction, analysis, and plotting were done using AlPS, IRAF or DRAO’s ‘madr’ and ‘plot’. Fortunately, all three packages, while storing data in their own internal formats, have FITS readers for two-dimensional map data as parts of the packages, making this particular step relatively painless. The exchange of continuum data between these systems mentioned here is also shown schematically in Figure B.2.  “  NOD2 is a software package that is used at the .JCMT to extract maps out of raw ‘scan’ data by performing such tasks as deconvolution of the dual-beam response pattern. The program originates from Jodrell Bank and Bonn [see Haslam (1974) for a succinct description of the system and the universal need to free the astronomer from programming chores which he attempts to satisfy with NOD2] but the version used at JAC appears to be imported from NRAO.  Appendix B. Data Transport  127  ‘Observatory  --  VAXNMS  telescope & continuui bolometer  I; /  ,“UBC-- MTS “FITS” on disk  z:zzz:hzz*  UBC/Physics  --  SUN 4/ UNIX  Figure B.2: Data flow for continuum observations. See text for further description.  Appendix C  Figures in Series: IRAS Protostellar Candidates  Some figures in series occupying many pages displaying observed data on the IRAS selected protostellar candidates are placed in this appendix.  128  Appendix C. Figures in Series: BiAS Protostellar Candidates  129  Figure C.1: Continuum Data on the MDPS IRAS Objects. For each source, the three (except two where 450tm data are unavailable) shaded contour maps show the continuum emission observed with the JCMT at the wavelengths as shown. Circles showing the half-power beamwidths are shown in the upper left corner of each map. The shade and contour levels for the 1100tm maps are 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00, 2.25, 2.50, 2.75, 3.00, 3.25, 3.50, 3.75, 4.00, 4.25, 4.50, 4.75 and 5.00 Jy/beam. The shade and contour levels for the 800im maps are, similarly, multiples of 0.50 Jy/heam. The shade and contour levels for the 450jm maps are multiples of 2.5 Jy/beam. There are exceptions to this rule, as follows. The contour levels for the 800gm map for source #04 are greater by a factor of five from the other sources. The contours for faint sources, #15 and #21, have been supplemented by “dash-dot” contours at intermediate values. For source #15 these are 0.0625, 0.1250 and 0.1875 Jy/beam at 1100tm and 0.25 and 0.75 Jy/beam at 800gm. For source #21 these are 0.125 and 0.375 Jy/bearn at 1100tm and 0.25 and 0.75 Jy/beam at 800tm. The lower right panels are spectral energy distribution diagrams showing the emission integrated over each source, together with the IRAS broad band fluxes and Low Resolution Spectra.  I,  08s  Right Ascension  h 15 18 m 128  —12° 09’  08’  0  08°  Right Ascension  12°  800Am  h iSm 18  —12° 09’  I  C’,’, C  U S  0 C  0  0  h 18  -  S  08°  I  ..  0•  Wovelength (jim)  102  I  Right Ascension  1515 12°  0  102,, 10  ‘<10-1  E 10  c;i  102  10  —12° 09’  08’  450pm  Source #02 RAS 18151—1208  Figure C.l (i) Source #02. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and contour levels for the llO0im, 800gm and 450gm maps are multiples of 0.25, 0.50 and 2.5 Jy/beam, respectively. See also the group caption on p.1 29 and a complete description in the text.  0  C-, 5,  C  0  C 0  0  S  I-)  C  0  0  C  08’  1100Am  0  0 0  OD  Cl,  ct  (b  0.  s:.)  18 i6’ 16  —20° 49’  Right Ascension  I2  2 iO_  <10_1.  10 •.‘  Wavelength (Lm)  102  Right Ascension  7  6 16 bJ 18  20° 49’  10  Note unusual contour levels for 80Om map.  Source #04 IRAS 18162—2048  Figure C.1 (ii) Source #04. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the half-power beamwidths are shown in the upper left corner. The shade and contour levels for the 1100gm, 800gm and 450im maps are multiples of 0.25, 2.5 and 2.5 Jy/beam, respectively. (N.B. The levels for the 800gm map are higher than the standard values for the other sources.) See also the group caption on p.129 and a complete description in the text.  C  0  C  48’  800#m  Right Ascension  0  0 C  2O  C 0  C 0  48  450pm  ci,  Cb  e-  -  OD  ct  0,  C 0  l8I 26m 36  —15° 18’  .  “—I I  800pm  Right Ascension  32  I  Right Ascension  / 10  io • 2 ’  ‘<10  e  2 7,1o  io’’’’  102  i  C  10  C.  C.  •‘‘‘“I  Wavelength (pm)  C  .‘.‘,I  Figure C.1 (iii) Source #06. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and contour levels for the 1100pm and 800pm maps are multiples of 0.25 and 0.5 Jy/beam, respectively. See also the group caption on p.129 and a complete description in the text.  0  C 0  17’  —15° 11 a  0 C  Source #06 IRAS 18265—1517  Ct  07  I.  I  Er  0  o.  07  Ct  Ct  I-..  C 0  • 18” 31m S 40  —6° 03  02  0  Right Ascension  m 18° 31 40°  80Om  Right Ascension  3S  36°  102  10  03  10_2  _i 10 ‘<  E  60  02  10  0 0  Wavelength (JLm)  102  I  Right Ascension  18° 31m 40°  459gm  36°  10’s  Source #07 IRAS 18316—0602  Figure C.1 (iv) Source #07. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and contour levels for the 1100tm, 800gm and 450am maps are multiples of 0.25, 0.50 and 2.5 Jy/beam, respectively. See also the group caption on p.129 and a complete description in the text.  0 S  C  a  —6° 03  C.) S  C.)  .1) O  C C  0  C  a  02  a  0  C  I  C.’,’  1100gm  CT.) Cl,  0  C)  Cl,  0 0  CO  Cb  rJ) Cb  C 0  40  37  38  37 is” 5;m 48s 44$  44$  I  Right Ascension  18h1 51m 4.5$  0  800Lm  Right Ascension  10  10  10’  37  10—’  10—1  D1  OS  Is  40  38  10  44$  Wavelength  102  Right Ascension  18 51m 45$  j  (pm)  D  ci  10  D  #09 IRAS 18517+0437  Source  Figure C.1 (v) Source #09. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and contour levels for the 1100am, 800am and 45Oitm maps are multiples of 0.25, 0.50 and 2.5 Jy/beam, respectively. See also the group caption on p.129 and a complete description in the text.  a, a  C,  C  0  40  a  S  0  0  c c) a, a  0  c  0  C,’.  0  38  450m  11OOWn  Cl:,  ci  Cr,  0 0  Cr)  0  (b  Cr)  c tf  j 0,.  390  28  .0  Right Ascension  20” 18’” 52”  --—---‘T48s  4  10  10  28  1 0_2  <10_i  D1  E  390  29  Right Ascension  20” 18’” 52  ,  10  .1  48”  0  Wavelength (ILm)  Q2  44DD  0  450gm  Source #14 IRAS 20188+3928  Figure C.1 (vi) Source #14. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and contour levels for the llOOtim, 800irn and 450tm maps are multiples of 0.25, 0.50 and 2.5 Jy/beam, respectively. See also the group caption on p.129 and a complete description in the text.  C, a, o  V C  C 0  29  800pm  Right Ascension  • 20” 18m 52  O  C) ‘I,  28  S  O  390  0 C  0  0 C  0  C  CI.’.  c  29  110Om  ct  Cb  0 0  iD  Cb  41° 07  08  41° 07  08  h 20  0  I  s 36  S 36  LI  Right Ascension  21m 40s  i/  .  Right Ascension  h 21 20 m 40s  SOOjim  ,  \  •,  I  10_2,,..1 10  <101.  I  2 1  ‘1102  i0 • 3 •’•I  D  Wovelength (Lm)  102  I  D  0  I  Source #15 IRAS 2021 6+41 07  Figure C.1 (vii) Source #15. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and solid contour levels for the 1100gm and 800tm maps are multiples of 0.25 and 0.5 Jy/beam, respectively. Since this source is particularly faint, “dash-dot” contours at 0.0625, 0.1250 and 0.1875 Jy/beam are shown for the 1100gm map, and at 0.25 Jy/beam for the 800tm map, to supplement the usual solid contours. See also the group caption on p.1 29 and a complete description in the text.  0 C 0 S O  C 0  w c  0  0 C  C 0  1100pm  I.  ci,  C)  ci’  0 0  ci’  ci’  s:.)  40  39’  500 39  500  40  m 33  210  33m  0  800  h 21  240  240  Right Ascension  28s  ‘—  L.  Right Ascension  28  ,  Iv  200  200  I  1 0_2  _i 10 ‘<  E  10  1 0’  10  Wovelength (pm)  102  I  D I—.  l0  D  I  Source #21 IRAS 21334+5039  Figure C.1 (viii) Source #21. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and solid contour levels for the 1100gm and 800im maps are multiples of 0.25 and 0.5 Jy/beam, respectively. Since this source is particularly faint, “dash-dot” contours at 0.125 and 0.375 Jy/beam are shown for the 1100um map, and at 0.25 and 0.75 Jy/beam for the 800gm map, to supplement the usual solid contours. See also the group caption on p.129 and a complete description in the text.  0 1) 0  0 C  0  C  0 0 O  C  0  C 0  Cc  1100gm  -4  Cl)  0  0 0  -  o  63° 12’  13’  I  m 34  52’ 43’  I •  52’  I •  Right Ascension  00$ 56’  0  48  I  ‘III,  I  Right Ascension  00 56  00mm 8  h 34m 0  63° 12’  C  I  2  ‘  -  10  2  2 lo_  10 —1  1  10 3  10  ‘‘‘‘I  102  0  Wovelength (pm)  D  3 io  I  Source #25 IRAS 00338+6i12  Figure Cl (ix) Source #25. The continuum maps made with the JCMT are displayed here together with a spectral energy distribution diagram (SED, lower left panel) showing the emission integrated over the source. Also included in the SED are the IRAS broad band fluxes and Low Resolution Spectra. For each map, circles showing the halfpower beamwidths are shown in the upper left corner. The shade and contour levels for the 1100pm and 800pm maps are multiples of 0.25 and 0.5 Jy/beam, respectively. See also the group caption on p. 129 and a complete description in the text.  I  C  (2  0 S  0 C  0  C  13’  1100tm  I.  0)  Ct  0)  1  Appendix C. Figures in Series: IRAS Protostellar Candidates  139  Figure C.2: Molecular Line Data for the MDPS IRAS Objects. For each panel, the vertical axis is the intensity in T (K) and the horizontal axis is the LSR velocity (km s’). The five point map on the upper left shows CO J = 3 —* 2 line offset by 7 arcseconds in NSEW directions as indicated. This is used for comparison with the J = 2 —* 1 data (centre) and other lines whose beams are larger. Isotopic variations are shown in panels below. Upper right is the five point map for CS J = 7 —* 6. Below that is S 34 C I = 7 —* 6 followed by CS J = 5 —k 4. See also the “guide,” next page.  C0 2—1 13  17 2—1 C 0  C0 3—2 13  0 3—2 7 C’  CO 2—1  axis labelled here only  CS 7—6  (+T’,o)  (o,+7”)  CS 5—4  34 7—6 C S  CS 7—6 (0,—?”)  CS 7—6 (0,0)  CS 7—6  Source ID  CS 7—6 (—7”,O)  40  60  204’060  20  0  I  20  40  I  60  OV  ‘  5  10  15  20  0  c7 1 o 3—2  C0 13 3—2  CO 3—2  (K)  TR*  20  0  0  20  40  3  60  o  I  I  40  (km/s)  K Ao 5.  0  10  20  30  40  Visr  axis labelled here only  o 1 c 7 2—1  C0 13 2—1  CO 2—1  0  0  5  20  40  60  2’0460  cI  0  Cs 5—4  s 3 c 4 7—6  CS 7—6  #01: 18134—1942  20  60  0  0  5  10  —5 40  Cl 7 3—2  —5 I  204060  0  0  0  0  3—2  1300  FVI  0  5  10  25 20 15 10 5 0  CO 3—2  (K)  TR*  20  20  Visr  40  40  —  ‘I  I...  60  60  Cl 7 2—1  13 co 2—1  Co 2—1  20  40  60  .1. Ji.. M  0  0  20  40  60  :0:2040,60.  5111  0  CS 7—6  Cs 5—4  s 3 c 4 7—6  I iiLiiliiili”  I  LlMI’  #02: 18151—1208  ,,,I,,,I,,,I,.. IlIllIlillIll  t vf’f\  0  5  (km/s)  axis labelled here only  0  10  20  30  40  —  —20  0  5  0  20  40  I  C 3—2  0  20  40  0  20  40  Af —20  J  (km/s)  .JI,,  —20 7  —  Visr  ,,,I,,,I,,,I,  —20  20 15  0  3—2  0  10  0 40  40  20  5 20  20  .  30  40  10  0  0  I  A  —I  5  0  -;  3-2  15 10  20  I.  IlIlIllIjIlIl  .1...  (K)  axis labelled here only  2—1  Cl  2—1  CO 2—1  id.  0  .I.i. ii  20  40  .1.  —20  I-’  0  20  40  54  —20  0  5  LLn  CS 5—4  S 3 C 4 7—6  CS 7—6  #04: 18162—2048  -  10  20  0  5  0  10  20  20  20  40  40  40  60  60  60  C7 1 o 3—2  3—2  CO 3—2  R  (K)  5  0  10  0  10  20  20  Visr  40  60  0  5  (km/s)  axis labelled here only  o 1 c 7 2—1  2—1  Co 2—1  ‘III  -  —  —  20  —  -  rnriqyv  40  v!  I  -  60  TJ  I  40  60 —  20  40  60  LLI.A*AIi.I vIw’qvvv  ,,I,,,I,,,I,.  20  5111  n  CS 7—6  Cs 5—4  s 3 c 4 7—6  IIIIIIIIIIIII.i  I  #05: 18258—0737  -ç  E  -zn  0  5  0  5  10  15  III  :.‘I’.’  -  60  80  20406080  40  20406080  liii  h  I  C7 3—2  3—2  Tv  3-2  5  10  i’  20  V!v  A  40  60  WvV.I  60  0  5  (km/s)  40  i  20  ‘Isr  labelled here only  axis  r.  —,  80  80  C7 1 2—1  2—1  l3  Co 2—1  5.•  40  60  .ka L. i 1  80  I  60  I  40  I  20  80  I,.,I,,,I,,.  20  .IIIJ.LI  IllilIlIllIll.  CS 5—4  s 3 c 4 7—6  I,III,,I,  CS 7—6  #07: 183 16—0602  1  —  50 40 30 20 10 0  —‘  n  5  10  25 20 15 10 5 0  I•’’I’I,,.  I  60  40  I  A.  20  _  80  80  00680  iliiiliiiliii  C 1 3—2  7  C0 13 3—2  CO 3—2  0  5  10  25 20 15 10 5 0  50 40 30 20 10 0  —5  (K)  ‘R  T*  20  20  40  40  60  60  24•  Visr (km/s)  axis labelled here only  a  80  80  )  Cl 7 2—1  2—1  2—1  Co  I-’  5  5  20  I  ‘ri,.  20  40  I.  40  60  60  80  V.  80  CS 5—4  S 3 C 4 7—6  CS 7—6  #09: 18517+0437  10  20  30  40  —20  0  20  0  5-  —20  0  20  ‘J.  9n  Cl 7 3—2  3—2  C0 13  CO 3—2  (K)  TR*  0 c1  U  5  (km/s)  —20  0  20  0 v-  5  0  5  10  15  20  Visr  labelled here only  axis  Cl 2—1  C0 13 2—1  0  5  0  5  0  20  0  I  20  —20  0  20  L  —20  %%  —20  CS 5—4  S 3 C 4 7—6  CS 7—6  #13: 20178+4046  0  5  0  5  10  15  20  —20  0  20  ;4; —20  0  .1  20  2—1 0  0170 5  2—1  Co 2—1  5  0  ,,II,,II,,I,I  “9  I  ,  I  I  J’•  I  0  I  20  —20  0  20  -20020  —20  --iIiiiIiiiIii  i  CS 5—4  7—6  sc34  ..,I,’II••I’’  CS 7—6  #14: 20188+3928  —  —— wá_ —  0020  0  5  (km/s)  3—2  0  5  10  15  20  0  10  20  30  40  Visr  01 7  13 C0 3—2  CO 3—2  (K)  -I- *  axis labelled here only  10  20  30  —20 0  20  —20 0  20  o,k  0  5-  C O 1 3—2  32  -  10  20  l3  0  15  —20  Co 3—2  (K)  TR*  5  Visr (km/s)  axis labelled here only  0  5  0  5  .  0  20  LLfl. If 1  0  —20  y’  0  A4AAA 2 j. 7••9  —20  20  20  —  —20  ‘.v  LLkEJ  ,,I,,I,,,I,,.. IlIlIllIllIll  kiIYW  CS 5—4  34 C S 7—6  CS 7—6  #15: 202 16+4107  —  50 40 30 20 10 0  I  —40 10  —5 -3—40  0  5  —20  0  I  20  -  0  —20  20  .1  LaaAiI..L... t1 LaP  I  LI  I  N.. p  L  —40  25 20 15 10 5 0  I  3—2  Cl 7  3—2  I  CO 3—2  (K)  TR*  .  —40  40 30 20 10 0  S.,’.,  I  —20  Visr  0  (km/s)  axis labelled here only  20  CO 2—1  0  20  I.  hi  0  20  —40  0  —20  I  0  I  20  I  5’I’II  —40—20  0  5III  —20  I.  &i 11 IA  -  rwww iir  iflilijü  ,,,I,,,  —40  0  5  CS 5—4  7—6  34 c s  CS 7—6  #18: 20286+4105  0  .‘.  —60  I  —40  I  —20  —80  0  —80 5  A  —60  —60  —40  —40  —20  —20  5J , , 1 .  10  —80  0 ; øA  10  20  V  C7 1 o 3—2  3—2  CO 3—2  —80  0  10  20  —60  Visr  —40  (km/s)  axis labelled here only  —20  CO 2—1  —80  —80  0  5  —80  —60  —60  —60  —40  —40  —40  —20  —20  —20  CS 5—4  S 3 C 4 7—6  CS 7—6  #21: 21334+5039  U,’  0  10  —2  0  2  4  0  5  10  —40  —40  —20  —20  0  0  20  20  Cl 7 3—2  3—2  CO 3—2  (K)  TR*  0  10  20  —40 —20  Visr  0  0  5  (km/s)  axis labelled here only  20  Co 2—1  JuLL  —40  I  0  20  —20  0  I...I  20  I  ‘::  —20  I...  .:  —40  I.  04MMAV  5III  2  iA  Cs 5—4  s 3 c 4 7—6  %4w  CS 7—6  I-)  #22: 22272+6358A  0  10  20  n  5  0  5  10  —40  —40  I  —20  1ST,  —20  0  9 r 1 rr  0  20  ,‘  20  3—2  Cl 7  co 3 ‘  3—2  CO 3—2  (K)  TR*  Visr  0  5  (km/s)  ax is labelled here only  I,,,I,,,),’’  5  I.  I...  I.  —40  —40  —20  —20  0  0  ilIlilIlil  5,  ,I,,,I,,,I,,,  —,  20  20  CS 5—4  7—6  34 c s  CS 7—6  #23: 23545+6508  U’ uJ  0  10  20  —40  —40  —60  —60 —20  —20  0  0  . 1 A 01 7 3—2  13 C0 3—2  CO 3—2  (K)  T*  -  —60  0  10  —60  0  10  20  —40  —40  Visr  0  I-  —20  0  -< 1 L  A  —20  (km/s)  labelled here only  axis  ii  11 i k1I  2—1  1300  -  1 A  —60  0  5  —60  5  —40  —40  L... .L 1  —20  —20  0  0  CS 5—4  s 3 c 4 7—6  .HAIL A1  CS 7—6  #25: 00338+63 12  —80 —60  —40  —20  CO 3—2  (K)  R  T*  Visr  (km/s)  axis labelled here only  0  5  5  5  —40  I  I.  —20  —80  —60  —40  —20  LAIMLJA1LL v SI. !‘T’ 17 Ir’ ‘!  —  I  —60  I  —80  Cs 5—4  s 3 c 4 7—6  CS 7—6  #26: 00420+5530  10  CO 3—2  (K)  TR*  V Isr (km/s)  axis labelled here only  .o  CS 7—6  #31: 03235+5808  vi  1  20  30  —20 0  20 40  CO 3—2  (K)  •1 *  I  30  —20  0  20  Visr (km/s)  axis labelled here only  40  2—1  Co 2—1  .. 11 Ihh.hI  Ab  iil  L  I  I.  CS 7—6  #36: 05553+ 1631  10  20  —20 0  20 40  CO 3—2  (K)  ‘R  T  10  —20  0  10  20  0  0  Visr  20  20  0  5  (km/s)  axis labelled here only  40  40  C0 13 2—1  Co 2—1  -2002040  L’’  flyTr’ r  It  CS 7—6  #38: 06103+1523  0  10  20  30  •IATT1II  --  40 60  80  ZJc 100  I  1 9TVW  CO 3—2  (K)  TR*  40  0  5-  10  60  80  100  40 100 60 80 15,,  ts.:  0  5  Visr (km/s)  axis labelled here only  2—1  40  60  80  •1  100  CS 7—6  #39: 07427—2400  ‘Ji  Appendix D  Figures in Series: NGC 6334 I & I(North)  Some figures in series occupying many pages or panels relating to observed data on NGC 6334 are placed in this appendix.  160  Appendix D. Figures in Series: NGC 6334 I & I(North)  4-4  4’ + ‘4  + 42  -  + +4 +  43’  -  + +  -1-  ‘4  U3L  +++++++ +++++++ +++++++ + ++ + + + ÷ ++ ++++ ++++  ++  0)  cia  +4  + +4+ +++++ +4+ +4  +4  -J _350  +  +  4.  + +  +  +  +  +  4.  +  +  -  +  +  4-  +  +  + I  ‘  +  +  +4+4+  +  +  +  +4+4  +  +  +  +4+  +  +  +4  +4+4+  +  + +4  I  ‘  I  I  ,  I  +  +4  +  +  o 1 C 7  0 3—1 7 C’ I  +4  43’  +4+  +  +4+ +4 4+  44’.  42’  +  +4+4+4+4+ + +44+ + + + +4+4+4+4+ +44+4+4+ + +4+4+4+4+ 4+4+4+4+ + +4+4+4+4+ +4+4+4+4 + +4+4+4+4+ +4+ +4 + + + + +4+4+ +4+4+4+4 4+4+ + + +4+4+4+4 + +4+ + I +1+  +  ÷  4  +  +  +  C-)  4.  I-  +4  -  +  +4+  z  +4  4’  43’.  0  +  I  I  42’  4’ + ‘4  4+ +++++++++ + + ++ + + + + +++++++++ ++++++++ + + + ++ + + + + ÷ + ++ + + + + + + + ++ + + + + + + + ++ + + + + + + + + ++ + + + + + +  ._350 44’  0  4-4  161  ‘ C 3 o  2—1  2—1 I  I  ,  +  +  +4+4+  +  +  +4+4+  +  +  +4+4+  +  +  +4+4+  +  +  +4+4+  +  +  +4  +  +  +  + 4+  4+ + +4  + +  _350  +44+ +4+4 + +4+  44’  + +  Cs 5—4  s 3 c 4 5—4 I  h 17m 408 17  361  32  28°  +  +4 + 4+ 4+ 5 3 C 4 7—6  I  328 tu m 40° 368 28° RIGHT ASCENSION (B195O)  8 4 m 17 0  36  328  288  Figure D.1: Beam positions for each line observed. Observed positions are indicated in in separate panels for each molecule, isotope and transition observed.  Appendix D. Figures in Series: NGC 6334 I & I(North)  I  162  I  42  43  _350  44  (—60,—55) km/s  (—55,—50) km/s  I I  (—50,—45) km/s  L  I  \  42  0 0)  43  iN  z -J  C-)  _350  (—45,—40) km/s  (—4o,—5) km/s  (.—35—3o) km/s •  I  42  4y  •  -  •  II _350  44  (—30,—25) km/s h 17  17m  4QS  35$  (—25,—20) km/s  (—20,—15) km/s I  32  28  17m  4QS  36  32’  2S’  17m 40’  I  36’  32’  28’  RIGHT ASCENSION (B 1950)  Figure D.2: Velocity slices of CO emission. The velocity averaged CO emission in the J = 3 —* 2 line over intervals as indicated inside each panel. The contour levels are 0.0, 1.040, 2.013, 3.001, 4.041, 5.154, 6.357, 7.665, 9.093, 10.66, 12.37, 14.25, 16.31, 18.57, 21.06, 23.79, 26.79, 30.09, 33.71 and 37.68 K.  Appendix D. Figures in Series: NGC 6334 I & I(North)  I  I  I  I  163  II  42’  43’  _350  ,  (—15,—la) km/s I  I  o  (—10—5) km/s I  I  (—5,0) km/s  I  I  I  I  I  I  42’  0)  z  43’  o  )  z  Ii C-)  350  44  (0,5) km/s  I  (5,10) km/s I  I  I  (10,15) km/s I  I  I  I  I  I  42/  44’  (15,20) km/s  (20.25) km/s  I  17”  17T  4O  36  _I  32  s 28  m 17  4O  (25,30) km/s  I  I  36  32  •  I  28  RIGHT ASCENSION (B195O)  Figure D.2 continued.  I  17” 40”  I  I  I  36”  32”  28”  Appendix D. Figures in Series: NGC 6334 I & I(North)  164  42  43  _35° 44  (30,35) km/s I  I  I I  I  (35,40) km/s I  I  I  42  0 CD  z  43  0  z -J  C-) _350  44,  (45,50) km/s h 17  tm 408 U  36’  32’  28’  RIGHT ASCENSION (B1950)  Figure D.2 continued.  I m 40 17 S  —  (40,45) km/s  N  I  36  328  288  Ifl 17  4Q8  368  328  28’  Appendix D. Figures in Series: NGC 6334 I & I(North)  165  I  42’  43’  350  o IC)  44  42’  0)  43’  z -j  0 350  44  42  43,  350  44  h 17  17m 4QS  36  32  28  m 17  36  32  28  m 4O 17  360  32  28  RIGHT ASCENSION (B1950)  Figure D.3: Velocity slices of CS emission. The velocity averaged CS emission in the J = 7 —+ 6 line over intervals as indicated inside each panel. The contour levels are 0.0, 0.3865, 0.7479, 1.115, 1.502, 1.915, 2.362, 2.848, 3.379, 3.959, 4.595, 5.293, 6.059, 6.901, 7.825, 8.840, 9.955, 11.18, 12.52 and 14.00 K.  Appendix D. Figures in Series: NOC 6334 I St I(North)  I  o  ‘  I  ‘  I  I  ‘  ‘  I  166  I  ‘  ‘  I  ‘  42’  0’ in z  o  43’  z -J  0 ._35° 44•  (10,15)km/s it 17m 4Q 8  368  (15,20) km/s  ,  32’  28’  17m  408  368  (20,25) km/s 32  28’  RIGHT ASCENSION (B1950)  Figure D.3 continued.  17m 40  368  32’  288  Appendix E  Astronomical Units and Constants  Values for some astronomical units used in this thesis are listed here. Debye  =  e.s.u. cm 18 10  Parsec  pc  =  3.086 x 8 10’ c m  Jansky  Jy  =  erg 2 23 10 cm 1 s H z  Solar mass  M®  =  1.989 x 10 g 33  Solar luminosity  L®  =  3.862 x lO erg s 33  167  Appendix F  Abbreviations and Symbols; A Glossary  Some symbols and abbreviations are listed. When a definition is given in the text, the appropriate page reference is given.  Abbreviation  Description  page  a  Right Ascension.  6  Declination.  AlPS  Astronomical Image Processing System, developed by NRAO.  p.59  AOSC  Canadian Acousto Optic Spectrometer (at the JCMT).  p.50  ASCII  American Standard Code for Information Interchange.  BN  a class of objects whose prototype was discovered by Becklin and Nengebaner.  BPO  Bipolar Outflow.  CBR  Cosmic B ackgronnd Radiation.  dec.  Declination, the celestial coordinate in the North-South direction. Kinematic Distance.  p.73  Dnear, Dfar  The two solutions (when ambiguous) for kinematic distance.  p.73  DRAO  Dominion Radio Astrophysical Observatory, Penticton, B.C., Canada.  EHV  Extreme High Velocity.  FCRAO  Five College Radio Astronomy Observatory, Amherst, MA, USA. The  p.6  168  Appendix F. Abbreviations and Symbols; A Glossary  169  observatory operates a 14 metre (aperture) millimetre (wavelength) telescope. FITS  Flexible Image Transport System.  FWHM  Full Width at Half Maximum.  FWZI  Full Width at Zero Intensity.  GBT  Green Bank Telescope (of the NRAO), currently under construction.  GSD  a data file format.  H  i  atomic hydrogen.  H  II  ionised hydrogen.  p.125  p.80 p.123  HR diagram Hertzprung-Russell diagram. A graph on which a parameter reflecting stellar luminosity is plotted against a measure of stellar mass. IF  Intermediate Frequency.  IR  Infra-red.  IRAF  an astronomical software package distributed by NOAO.  TRApS  Interactive Reduction of Astrophysical Spectra, a locally developed p.125  p.45  p.125  software package. IRAS  Infra-red Astronomy Satellite.  IRS  Infra-red Source, a generic term in object naming.  J  rotationa.l quantum number.  p.7  JAC, JACH Joint Astronomy Centre, Hilo, Hawaii, USA.  p.54  JCMT  James Clerk Maxwell Telescope.  p.44  JHK  J, H and K are photometry bands in the near infrared.  p.13  Jy  Jansky, a unit of flux.  p.167  kpc  Kilo-Parsec, a unit of distance.  p.167  L®  Solar Luminosity, the power output of the Sun.  p.167  Appendix F. Abbreviations and Symbols; A Glossary  170  LFIR  Far Infra-red Luminosity.  Lmech  Mechanical Luminosity.  LU  (frequency of) the Local Oscillator.  LRS  IRAS LRS, Low Resolution Spectra/Spectrometer.  LSB  Lower Side-band.  p.46  LTE  Local Thermodynamic Equilibrium  p.21  LVG  Large Velocity Gradient.  p.15  p.101 p.45  Solar Mass, mass of the Sun.  p.167  madr  a data manipulation software package from DRAO.  p.125  MDPS  McCutcheon, Dewdney, Purton and Sato, 1991, A.J., 108, 1435.  MTS  Michigan Terminal System, a computer operating system.  NGC  New General Catalogue of Nebulae and Clusters of Stars.  NOAO  (US) National Optical Astronomy Observatory.  p.125  NOD2  a data reduction software package.  p.126  NRAO  (US) National Radio Astronomy Observatory.  NSF  (US) National Science Foundation.  NWX  NGC 6334 I(NWX), the North-West eXtension to NGC 6334 I.  2 p.8  OTF  On The Fly, a mapping technique.  p.50  pc  Parsec, a unit of distance.  p.167  plot  an astronomy oriented plotting software package from DRAO.  p.125  PSC  IRAS PSC, Point Source Catalog  R.A.  Right Ascension, the celestial coordinate in the East-West direction.  SED  Spectral Energy Distribution.  S/N  Signal to Noise ratio.  SPECX  a data reduction software package.  p.123  p.7  7 p.  p.123  Appendix F. Abbreviations and Symbols; A Glossary  SUN Tbg  171  a series of computers manufactured by Sun Microsystems, Inc. 2.8K, the temperature corresponding to the cosmic background radiation.  Teff  Effective Temperature (of stellar objects).  T  Kinetic Temperature (of gas).  T  a unit of intensity.  UBC  The University of British Columbia, Canada.  UNIX  a computer operating system.  USB  Upper Side-band.  p.46  VLA  Very Large Array.  p.7  VMS  a computer operating system from the Digital Equipment Corporation.  ZAMS  Zero Age Main Sequence.  p.55  p.123  

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