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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 FORMINGREGIONSByTakashi SatoB. Sc. (Physics & Astronomy) University of British Columbia, 1986M. Sc. (Astronomy) University of British Columbia , 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1995© Takashi Sato, 1995In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.Department of PhysicsThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1Z1D ate:23AbstractTwo sets of protostellar objects have been studied using the James Clerk Maxwell Telescope as the main observational facility.The first set is a selection of sources from the IRAS Point Source Catalog, originallyobserved as part of a survey of protostellar candidates. In this present work, the observational database has been extended to include the (sub)millimetre continuum andJ = 3 —* 2 and 2 —* 1 lines of CO, ‘3C0 and C’70, and J = 7 — 6 and 5 —‘ 4 linesof CS and C345. The continuum mapping was able to resolve each source in addition tomaking flux measurements. The analysis of these flux values using dust emission modelsis reported in a separate paper. The molecular lines have been analysed using radiativetransfer models in the Large Velocity Gradient (LVG) approximation. Molecular hydrogen densities have been derived for most of the sources studied and have been found tocluster around n 105cm3.No apparent correlations are seen among the observed andderived parameters.NGC 6334 I and NGC 6334 I(North) comprise the second set of objects and arelocated at the northern end of the molecular cloud complex NGC 6334. This region hasbeen observed using the same lines, and in particular, mapped in CO (J = 3 —* 2) and CS(J = 7 — 6). “Extreme High Velocity” (V ‘-s kmr’) wings of CO are seen aroundNGC 6334 I and the outflow is found to be bipolar. The outfiowing material has beenshown using radiative transfer models to contain gas at a density of ii “-‘ x 103cm for atotal mass of 2.5M0 in the wings. This corresponds to a mass flow rate of 8 x104M® yr’and a mechanical luminosity of 89 L0. A neutral H I wind ejected at high velocity fromthe star is inferred to be driving this molecular flow. The implied stellar mass loss rate11is 4 x 104M® yr1. The CO line wings at peak I(North) are much less prominent, with20 km 5—1, although significant wings are present. They are not, however, in theform of bipolar lobes. Another feature, an extension 30 arcseconds to the northwest ofI, has been newly identified. LVG model analysis has been used to derive H2 densitiesat a large number of beam positions. This yields n ‘—s 1.3 x l07cm3for peak I whilefor I(North) the gas density is only n-I 4.5 x 105cm3. This contrast in gas density,combined with the lack of a luminous thermonuclear source detected around I, supportsthe suggestion that NOC 6334 is a very young stellar object bnt that I(North) is an evenyounger one. A lower limit of n. 3000 yr for the age difference between the two systemsis inferred from the time scales of the bipolar outflow at NOC 6334 I.111Table of ContentsAbstract iiTable of Contents ivList of Tables ixList of Figures xAcknowledgement xii1 Introduction 11.1 The Star Forming Environment 21.2 Current Issues in Star Formation Research 51.3 Objects Studied in This Work; Background and Review 61.3.1 IRAS Selected Protostellar Candidates 71.3.2 NOC 6334 101.4 Radiative Transfer Model/Code and Applications of its Results 141.5 The Objectives 162 The Radiative Line E&ansfer Model: The Physics and The Computing 172.1 Introduction 172.2 The Model Basics 182.3 The Detailed Picture 222.3.1 Optical Depth 22iv2.3.2 Transition Probabilities. . 222.4 The Algorithm: An Outline 242.5 Structure of the Code 252.5.1 Array Structure 252.5.2 Initial Conditions 282.5.3 Iteration and Convergence 292.6 Sample Output 312.7 Validity of the Models 342.7.1 Is the Code OK? 342.7.2 Is the Model Representative2 372.8 Internal Checks 382.8.1 Grid Resolution 382.8.2 Initial Values 392.9 External Checks. . 402.9.1 Tests Against Expected Behaviour or Analytical Solutions in Limiting Cases . 402.9.2 Tests Against LVG Solutions 413 Observations3.1 The James Clerk Maxwell Telescope3.1.1 Physical Description of the JCMT3.1.2 Signal Paths and Receivers for the JCMT3.2 Observations of IRAS Selected Protostellar Sources with the JCMT .3.3 Observations of NGC 6334 with the JCMT3.4 Calibration3.4.1 Calibration of Continuum Data4444444548525353v4 The IRAS Selected Protostellar Candidates4.1 Continuum Data4.1.1 Results from Continuum Data4.1.2 Dust Models4.2 Line Data4.2.1 Results from Line Data4.2.2 Column Densities4.3 Possible Trends and Patterns4.4 Future Work4.5 Individual Sources5 NGC 6334 I & I(North)5.1 Observed Data; Overview5.2 CO Spectra at I and I(North)5.3 Molecular Line Maps5.4 The Mystery of NGC 6334 I(North)5.5 LVG Models5.5.1 Model Results5.5.2 C34S J = 7— 6 Anomaly at Peak I5.6 Derived Parameters: The Bipolar Outflow at NGC 6334 I5.7 Discussion5.7.1 Relative Ages5.7.2 Are EHV Outflows a Common Phenomenon73.4.2 Calibration of Line Data3.5 Telescope Pointing3.6 Transport of Observed Data55565758585961626267697273787878829192939799104104104vi5.7.3 Neutral Hydrogen Wind in NGC 6334 J? 1076 Conclusions 1086.1 The IRAS Selected Protostellar Candidates 1086.2 Northern End of the NGC 6334 Complex 1096.3 General Conclusions 1106.4 Summary of Suggested New Observations 110Bibliography 112Appendices 117A Other Discussion 117A.1 IRAS Protostellar Candidates Revisited 117A.1.1 Artifacts in the LVG Model7 117A.1.2 FutureWork 118A.2 In general 118A.2.1 Potential for Problems with the LVG Analysis 118A.2.2 Line Transfer Model 120A.2.3 Additional Lines for Observation/Modelling 121B Data Transport 123B.1 Spectra 123B.2 Continuum Maps 126C Figures in Series: IRAS Protostellar Candidates 128D Figures in Series: NGC 6334 I & I(North) 160viiE Astronomical Units and Constants 167F Abbreviations and Symbols; A Glossary 168viiiList of Tables1.1 Protostellar Cloud Conditions 21.2 Protostellar Candidates from IRAS PSC 92.1 Models in the High Density Limit . 402.2 Models in the Low Density Limit . 412.3 IViodels in the LVG Limit 423.1 Spectral Lines Observed 483.2 Log of Observations for the MDPS IRAS Sources 493.3 TJKT14 On-The-Fly Mapping Parameters. 513.4 Log of Observations for NGC 6334 I a I(North) 523.5 JCMT Calibration for Continuum Mapping 554.1 Integrated Continuum Fluxes 604.2 Source Angular Size and Position Angle 614.3 Molecular Abundances 644.4 LVG Model Results 664.5 Masses of the Molecular Component 674.6 C’70 Column Densities 685.1 LVG Model Results over NGC 6334 945.2 Physical Parameters for the Outflow in NGC 6334 I 100ix5.15.25.35.45.55.65.75.8List of Figures193132353647657079818384868990961241271292.1 Model Geometry2.2 Iterating Towards Convergence2.3 Sample Output Spectra2.4 Self Absorbed Profile2.5 Exploring the Effects of a Temperature Gradient3.1 Signal Path to the JCMT Spectrometer4.1 Example of LVG solutions4.2 Patterns in our SampleSample CO J = 3 —f 2 SpectraSpectra Centred on NGC 6334 IMap of Velocity Integrated CO EmissionMap of Velocity Integrated CS EmissionOverlay of Near IR and Other Compact ObjectsCO 3 —* 2 Wing EmissionR.A. — Velocity Diagram for Peak IDerived Gas Densities over NGC 6334B.1 Data flow for Line ObservationsB.2 Data flow for Continuum ObservationsC.1 Continuum Data on the MDPS IRAS Objects . . .xC.2 Molecular Line Data for the MDP•S IRAS Objects 139D.1 Beam Positions for Each Line Observed 161D.2 Velocity Slices of CO Emission 162D.3 Velocity Slices of CS Emission 165xiAcknowledgementThis thesis represents much of my contributions towards two ongoing projects. I thankmy collaborators, Drs. W.H. McCutcheon, P.E. Dewdney and C.R. Pnrton, for the IRASselected protostellar candidates programme, and Drs. W.H. McCutcheon, T.B.H. Kuiperand 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 receiverconstructed 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 ‘showingme the ropes’ during my countless visits, both personal and electronic.The export software package from DRAO was used to perform some of the analysisand to prepare most of the figures presented in this work. I wish to thank Dr. L.A. Higgsfor making the software available and for his unending guidance during the installationprocess.Finally, I hope all readers appreciate my gratitude to Dr. L.W. Avery who kindlyprovided the LVG code used in this study although I may appear to criticise it at certainpoints in the text.xiiChapter 1IntroductionAstrophysics, if we take the literal meaning of the word, is the branch of physics concerned 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 formedstars, from the quiescent main sequence stage of hydrogen burning in the core throughthe 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 observeddata can he used to determine composition, age, temperature, luminosity, etc. for individual stars or groups (e.g. Sato et al.3 1989). By comparison, the formation process ofstars is very poorly understood. Observational evidence tells us that stars must somehowform inside dense molecular clouds by the gravitational collapse of interstellar gas anddust, and that the remaining material is blown away once the star becomes sufficientlyluminous. The quantitative details of the exact physical processes, however, are poorlyknown (but see the list of review articles at the end of Section 1.2 for current state ofthe art.). This lag in development in star formation research compared to other areas ofastrophysics 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 tomake a contribution to this field of research.1Chapter 1. Introduction 2Property “Standard” ProtostellarCloud & CircumstellarGas Density H + H2 (cm3) 10 1010Size (pc) 10 iO 10_i (or 1 104a.u.)Gas Temp., TkI (K) 70 10 1000Visual Extinction, Av (mag) 0.1 opaqueMass (Me) 300 0.01 100Free Fall Time (yr) not bound ioTable 1.1: Protostellar cloud conditions. Some parameters describing protostellar cloudsare compared with “typical” conditions found in interstellar clouds. [Taken from Table2 of the review article by Zuckermann and Palmer (1974).] These numbers are here toserve only as rough guides to help develop an intuition for the star forming environment.1.1 The Star Forming EnvironmentIviolecular clouds, which have been identified as sites of star formation, are simply cloudsin interstellar space consisting of dust and molecular gas. Normally, in the interstellarmedium, 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, theouter (or circumstellar) regions, which still consist of atomic and ionised gas, can beeffective in shielding the central material. Thus, the ambient radiation field or radiationfrom stars nearby (or within) is prevented from dissociating the molecules. The range oftypical gas densities found in such clouds are n = (10 1010) cm3. The gas kinetictemperatures can be few tens to lOOK but as high as 1000K near the protostar (See alsoTable 1.1). The most abundant molecular species is H2, followed by CO. The primaryreason molecular clouds are identified as regions of star formation is that we see luminousChapter 1. Introduction 3OB stars’ and H II regions2 associated with them (e.g. see Lada 1980).Triggered by external influence (e.g. galactic density waves or supernova winds, theexact 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 anddust start to collect within the molecular clouds aided by self gravitation and perhapsthe local magnetic field. Eventually, these grow into star forming regions which arethought to be in states of general collapse. Such a cloud then releases energy by radiativemeans. This “cooling” permits further contraction. Thus the system is gravitationallyunstable 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. Theinfalling material is heated by release of gravitational energy and also by such processes asmolecule formation. It cools by radiating in the infrared continuum as well as in spectrallines of constituent molecules. The infrared radiation is due to the dust component andthis can be used to study not only the properties of the dust itself but also the couplingbetween the dust and the molecular component. The radiative transfer of line radiationdepends very much on the spatial velocity structure since the large optical depths ofCO (the dominant molecular species of interest, as we shall see below) and some of theother high abundance molecules imply that, in order to evade reabsorption and thus beavailable to be observed by us here on Earth, a photon from one region within a cloudmust be Doppler-shifted out of the line in an adjacent region. This requires a significantvelocity gradient within the cloud. A comprehensive modelling of a star forming cloudmust therefore solve simultaneously equations describing the radiative processes locally1Stars of spectral types 0 and B are those with the greatest masses. They are also the most short-lived.This combined with their observed kinematics imply that OB stars could not have formed elsewhere andthen travelled to their present locations for they would have evolved past the main sequence during thejourney. Thus, if one sees OB stars in association with molecular clouds, it is reasonable to suppose theywere formed there.ii regions are those regions of interstellar clouds in which the gas is ionised by the high energyradiation from the stars within.Chapter 1. Introduction 4as well as those describing the coupling between the regions.Owing to the cosmic elemental abundances, the most abundant molecule by far in theinterstellar medium is H2. Due to its symmetry, however, this molecule lacks a permanentelectric dipole moment. This attribute makes the H2 molecule unobservable by means ofits 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 thehigher J levels. Thus, in this study, the observational and modelling efforts begin withthe lines of CO.The rotational transition lines of CO have proven to be the primary workhorse indelineating molecular structures in our galaxy (see, for example, Williams 1985, Polk etal. 1988 or Liszt 1982). It is particularly useful in the study of dense clouds and regionsof forming stars where, traditionally, observations consisted only of optical work. Bytheir dusty and nebulous nature and associated high extinction, these regions could notbe penetrated beyond the outer skin by optical observations. Thus, the description oftheir 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 majorcomponent of the cloud directly, rather than relying on some starlight to illuminate (andinteract with) it. Although some difficulties arise with 12C6O observations due to theoften excessively high optical depth caused by its high abundance, this effect can bemodelled in the manner outlined below. In addition, we have used observations of lessabundant isotopic species of CO as well as CS in order to minimise or avoid problemsassociated with high optical depths.Chapter 1. Introduction 51.2 Current Issues in Star Formation ResearchOn the observational side, the accessibility of a great deal of data on the molecular gascomponent has now been established for some time, in the form of molecular rotationaltransitions observable using millimetre-wave and, more recently, submillimetre-wave telescopes. However, while we have been able to measure global characteristics of the circumstellar matter, these do relatively little to probe the stellar component directly.With the emergence of far infrared and submillimetre technology, we are now gainingaccess to this component. These wavelengths are proving useful since the peak in thecontinuum emission from protostellar sources occurs in this region, characteristic of theirwarm temperatures. As well, the lower opacity in this band makes it possible to penetratedeeper into the circumstellar cloud. If only in this way, new submillimetre telescopes suchas 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 databaseis in the form of an all-sky survey has made IRAS that much more invaluable. This accessto the far infrared sky afforded by IRAS will continue to be exploited by astronomers foryears to come, even though the telescope itself has terminated operations years ago.On the theoretical side, the strictly “stellar” component, has been well understood forsome time. This includes not only the main sequence and subsequent evolution but alsothe pre-main sequence activity as characterised by Hayashi (1966) and Larson (1972).Current efforts seem to focus on the circumstellar component and its interaction withthe protostar. This includes the gas and dust in the circumstellar nebula, a disk, ifany, and associated questions of angular momentum. Behind all this is the origin andnature of the molecular bipolar outflow (BPO) so ubiquitously observed. As the reviewby Bachiller and Cómez-González (1992) indicates, there are now more than 200 suchBPOs known in the galaxy, always found in association with active sites of star formation.Chapter 1. Introduction 6There also appears to be an emerging new class of Extreme High Velocity (EHV) outflowswith 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, alsoLizano et ci 1988, Koo 1989, Margulis and Snell 1989, RodrIguez et ci 1990 and Bachillerand Cernicharo, 1990.] The problem is in putting the observed properties together withthe 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 cursorymanner, many of these issues have been addressed in review articles by Znckermann andPalmer (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 ReviewThe objects studied here are separated into two categories: the IRAS selected protostellarcandidates 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 employingmuch 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 formingmolecular clouds. After the sources are introduced in this chapter, observations for bothprojects are described together in Chapter 3. The results are then described separatelyfor the IRAS sources and NGC 6334 in Chapters 4 and 5, respectively.Chapter 1. Introduction 71.3.1 IRAS Selected Protostellar CandidatesA sample of 39 protostellar candidates was initially selected based on their characteristicsas they appear in the IRAS Point Source Catalog.3 This process has been described indetail elsewhere [McCutcheon, Dewdney, Purton and Sato (1991), hereafter MDPS].Briefly, these sources represent cool galactic sources with star forming cores but withoutprevious optical identification. The purpose then was to identify previously undiscoveredobjects 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 furtherstudy.Our previous observations as described in the first paper were made at various wavelengths with numerous telescope facilities. They have formed the basis of the first phaseof the project and are described in detail in MDPS. The data there include, for each of the39 sources, the original IRAS broad-band measurements, both Low Resolution Spectraalso from IRAS, J = 1 —* 0 rotational transition lines of CO, ‘3C0 and C’80 obtainedat the NRAO “ 12 meter telescope, as well as C-configuration VLA observations at6cm. The optical image from the Palomar Observatory Sky Survey (POSS) E print isalso shown.The majority of our sources was found to have very wide (V 10 kms at T0.2 K)6’7 CO lines, many consistent with strong outflow activity. Eleven were classified to5lnfrared Astronomy Satellite (IRAS), among its many tasks, made an all-sky survey at 12, 25, 60and 100 pm bands. The Point Source Catalog (PSC) is one of the chief data products available fromthis project.National Radio Astronomy Observatory is operated by Associated Universities, Inc., under contractwith the National Science Foundation.The Very Large Array, operated by NRAO is a dedicated aperture synthesis telescope capable ofsubarcsecond resolution and working at wavelengths now down to 7 mm.6zXV: In “radio” astronomical spectroscopy, frequency shifts of spectral lines are often expressed interms of the velocity that would cause that shift via the Doppler effect. In the same manner, line widthsare expressed in velocity units.see definition, p.55.Chapter 1. Introduction 8be pre-main sequence objects; another four may also belong to this list. Among our higherluminosity sources, those with strong molecular outflows were generally associated withpre-main sequence objects whereas the sources in our narrow line category appeared tohave 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 somehowceases or perhaps is disrupted on the high luminosity sources before they reach the mainsequence.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), Beichmanet at. (1986), Snell et at. (1988), Snell et at. (1990), and Carpenter et at. (1990).] Ofthese, the work of Wilking et at. (1989) is perhaps most similar to our own, albeit anindependent effort (and unknown to us at the time). Indeed, the search criteria throughthe IRAS PSC bears close resemblance to our own. As one might expect, our two surveyscontain 13 objects in common. The majority of their sources was found to be associatedwith 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 weredetected from a large fraction of their objects. Two classes of dust clouds emerge in thisstudy; one small and dense, the other more diffuse.Moriarty-Schieven et at. (1992) have made a CO J = 3 —* 2 survey of a similar classof objects within the Taurus cloud complex. They too found outflow in many of theirsources. However, their source list does not overlap with ours, as we happen not to haveany sources in the Taurus region.In the stage of this research programme described here, new observations have beenChapter 1. Introduction 9Source IRAS-PSC Coordinates (1950) Pre-MainNo. Name R.A. Declination Sequence?# 01 18134 — 1942 18h3m24s6 —19°42’25” maybe# 02 18151 — 1208 18509s• —12°08’34” yes# 04 18162 — 2048 18h6m2s•8 —20°48’51” yes# 05 18258 — 0737 182551 —07°37’30” no# 06 18265 — 1517 gh26m32s9 —15°17’Sl” maybe# 07 18316 — 0602 18h3190 —06°02’08” yes# 09 18517 -I- 0437 1851m45s +04°37’42” yes# 13 20178 + 4046 20h1753s•0 +40°47’OO” maybe# 14 20188 + 3928 2018m57 +39°28’18” maybe#15 20216 +4107 20h137s6 +41°07’56” yes# 18 20286 + 4105 208rm4 +41°05’39” don’t know# 21 21334 + 5039 21h334s0 +50°39’43” yes# 22 22272 + 6358A 227m199 +63°58’21” don’t know# 23 23545 + 6508 23h543s +65°08’29” no# 25 00338 + 6312 0033m53s.3 +63°12’32” don’t know# 26 00420 + 5530 00h42m5s +55°30’54” yes# 31 03235 + 5808 03231 +58°08’56” no# 36 05553 + 1631 05h5m20s +16°31’46” don’t know# 38 06103 + 1523 061023s• +15°23’28” yes# 39 07427 — 2400 07h42m5 —24°00’22” yesTable 1.2: Protostellar candidates from IRAS PSC. The original list of MDPS contains 39sources. Sources investigated in this study form a subset of the original 39. Observationalcoverage varies from source to source due to practical considerations.Chapter 1. Introduction 10made using the JCMT5 in both the continuum and molecular line emission in the millimetre to submillimetre wavelength region. The continuum observations were designedto probe the dust density distribution and to measure the far infrared luminosity of eachsource. The molecular lines were used to determine the density and the dynamics of thegas cloud. In later sections, these are compared with theoretical predictions as well aswith each other. Of the original 39, a number have been dropped from the list for furtherstudy as constraints are placed by the available telescope time. In particular, our continuum 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-Russelldiagram, on and off (pre-) the main sequence, for the line observations. Table 1.2 showsthe sources targeted in this phase of the study.1.3.2 NGC 6334This giant molecular cloud complex is an optically prominent object in the southerngalactic plane. The complex, with coordinates R.A. = l7hhl8m, Dec. = —35°42’, islocated at a distance of 1.74 + 0.31 kpc (Neckel 1978) in the Sagittarius arm. In thisstudy, we wish to investigate the nature of the molecular material in the northern endof 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 atdifferent 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 numberof previous investigations, as described below, focusing on far and near infrared, radiocontinuum or molecular line (including maser) emissions. For this reason, NGC 63345The James Clerk Maxwell Telescope is operated by the Observatories on behalf of the ParticlePhysics and Astrophysics Research Council of the United Kingdom, the Netherlands Organisation forScientific Research and the National Research Council of Canada.Chapter 1. Introduction 11is also a region exceptionally rich in nomenclature. In this work, attention is focusedon NGC 6334 I [nominally, a = 17hm32s6 = —35°44’07”] and NGC 6334 I(North)[a = 17hm35s, 6 = —35°42’17”j.The entire NOC 6334 complex was mapped in the 1.0 mm continuum by Cheung etci. (1978). A succession of bright peaks (I through IV, in their numbering scheme) withregular angular separation is revealed in this map and a suggestion of an age sequence ismade with our source I(North) being the youngest member. I(North) is also the brightestfeature 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 IIof 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 oneof the authors of the former paper, in order to avoid future confusion with the McBreenci ci. numbering scheme.] In Gezari (1982), a 400 pm map of the NGC 6334 complexis presented. Their dust models show T = 33 + 5 K for peak I and T = 19 + 5 K forpeak J(North). For I(North), an inferred gas density of 3 x 105cm3 is given. SourceJ(North) remains faint at the shorter JR wavelengths in that it is undetected in the firsttwo (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 resultsin their near and far infrared mapping work of the NGC 6334 complex employing threedifferent telescopes. The map of Emerson ci ci. (1973) over a 40—350 pm band shows thebrightest peak at the position of I but shows no counterpart at J(North). Although themaps 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 theother hand, the maps clearly show emission peaks at 2.2, 10 and 20 pm at the position9There may be some extended emission indicated in their maps at 71 pm over this position.Chapter 1. Introduction 12of NOC 6334 I. This source is found to be quite confined in the 10 pm and 20 pm mapswith diameters less than 1 arcsecond in each case. The IRAS Point Source 17175 — 3544corresponds to NGC 6334 I. No counterpart to I(North) is listed in the Point SourceCatalog or the Small Extended Source Catalog. As Moran and RodrIguez (1980) pointout, 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 objectsyet established. In this pure accretion phase, they continue, diffuse heating is providedby 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 NH3(1, 1) main hyperfine line.Two lobes of emission are seen and their dynamics have been modelled as a rotatingmolecular disk of 30 M®, diameter 0.3 pc, thickness 0.1 pc with gas density of r-J l05cm3around a 31 M® central star. An integrated line emission map of J = 2 —* 1 C150together with the 1300 pm continuum map was made by Schwartz et at. (1989) usingthe NRAO 12 meter. Both peaks are clearly seen in both maps with their 30 arcsecondbeam. More along the lines of our own work (but unknown to us at the time), Bachillerand Cernicharo (1990) have mapped the high velocity wings of CO J = 2 —+ 1, SiOJ = 3 —k 2 and J = 2 —* 1, and HC3N J = 17 —÷ 16 lines around peak I using the IRAM30m telescope. As described in Chapter 5, the wings of the CO J = 2 —* 1 line observedby Bachiller and Cernicharo, including the bipolar nature, are similar to our J = 2 —÷ 1and J = 3 —* 2 data. The velocity structure seen previously by Jackson et at. (1988)is reproduced in their HC3N data and they offer an alternate explanation in which thelow velocity gas motion is a companion feature to the high velocity gas. A host of otherlines 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 13Straw and Hyland (1989B) present a map of shocked molecular hydrogen emission inthe 2.12 pm v = 1—, 0 5(1) line. Here, I(North) is again undetected while I is a distinctfeature. Straw, Hyland and McGregor (1989) and Straw and Hyland (1989A) presentresults from extensive near infrared mapping in J, H and K bands.1° Extended emission,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) althoughthe 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 maseremission. 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. TheOH maser observations of Clegg and Cordes (1991) on source I show variability in theirdynamic 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 arcsecondbeam at 2 arcminute grid spacing] to be the brightest NH3 maser in their southern skysurvey and derive some physical parameters: the resulting gas kinetic temperature isc-i 30 K and the H2 density is c-s 7 x io cm3, and for a source diameter of 1 pc, themass is inferred to be e-i 103M®. The survey of Moran and RodrIguez (1980) for H20masers in the NGC 6334 complex detected maser emission at both I and I(North) alongwith 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 sourceis observed near I(North). However, a featureless “source E” is found between I andI(North). The 1.95cm map of Schraml and Mezger (1969) shows no peaks discerniblewith the 2 arcminute beam of the 140 ft telescope at either position, although the limit10 j, H and K are three of the standard wavelength bands, or filters, in the near infrared usedfor 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 14of the extended emission appears to lie between I and I(North).In the present work, observations of CO and CS in their rotational transition linesare described. These submillimetre wavelength lines were observed nsing the JCMT.One immediate result from these new observations is the vast improvement in angularresolution. The JCMT beam can be as fine as 7 arcseconds wide, compared to the 48 and65 arcsecond beams nsed for the 400 pm and 1.0 mm maps. Thus we can attempt to revealfiner features such as the structure of the cores. Since the observations are of spectrallines, we have also been able to extract valuable dynamical information. As well, thestructures 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 employingsimultaneously the many lines observed in order to deduce the physical parameters ofthese regions. Of particular interest is the molecular gas density.1.4 Radiative Transfer Model/Code and Applications of its ResultsWhile observations using molecular rotational transition lines constitute the primaryprobe into molecular clouds, their interpretation is too seldom straight forward. This isbecause the observed line is sensitive to changes in the density, temperature and dynamicswithin the clouds, often in a very non-linear fashion. Thus, numerical modelling plays akey 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 lineradiation (such as the equations of statistical equilibrium and radiative transfer) to compute the profiles of the CO emission lines and those of other molecules. By following theapproach of Goldreich and Kwan (1974) and de Jong et al. (1975) for example, one canChapter 1. Introduction 15attempt to reproduce our observed line profiles and line intensity ratios among the various isotopic species as well as among different transitions. Here, the velocity structureis of particular importance, especially for‘2C160, since the high optical depths wouldquickly saturate these lines if all parts of the cloud were at the same velocity. (Eventhen, the‘2C’60line can still he optically thick.) Thus, we appeal to the Large VelocityGradient (LVG) model (first investigated by Sobolev, 1957) in which the difference invelocities between spatially separated parts of the same cloud is significantly greater thanthe combined local thermal and turbulent line widths (which represent the only important mechanisms for line broadening on the local scale) so that CO is coupled radiativelyonly 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 denseregions of molecular clouds, such as those under study here, line saturation is still noteliminated 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 whichphysical 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 prioriassumptions or “conclusions.” In this thesis, the former approach is taken using an existing code (Avery, private communications) while a new code was prepared to undertakethe latter. The physics incorporated into the new code is described in Chapter 2, togetherwith the details of the associated computing. The usefulness of this code is hoped to belong-lived, extending well beyond this thesis.These models must, of course, be consistent with other observed data. While I havenot, at present, made any specific provisions in the computational code to ensure uniqueness in our models, constraining data from other wavelengths are expected to go a longway toward this purpose, in addition to using sensible initial guesses (solutions are foundChapter 1. Introduction 16iteratively). For instance, the kinetic temperature and dust density must be consistentwith the JR emission. Where ambiguities persist, model predictions have enabled us tosuggest 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 observationspointed out in Sections 3.2 and A.2.3.1.5 The ObjectivesTo 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 formingregions in CO, CS and their isotopes and in the (sub)millimetre continuum. Next, theseobservations are interpreted in the context of radiative transfer models, in the hopes ofenhancing 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 objectsfor which we have already considerable amounts of observed and derived informationavailable. In our first paper, this resulted in placing our objects on a Hertzprung-Russelldiagram and identifying main sequence and pre-main sequence objects. In a similarvein, we wish to undertake further examination of our sample, with regard to some newparameters.The NOC 6334 portion of this work provides an opportunity to study the cloudstructure by high resolution line mapping across the complex in combination with modelanalysis. The detailed information assembled allows us to study features of the twopeaks 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 theyare observed in the same manner, and because they are at the same distance, renderthemselves well to systematic comparison.Chapter 2The Radiative Line Transfer Model: The Physics and The ComputingThis chapter describes the multi-level line trausfer model code prepared as a tool to beused in the work to follow, within this thesis and beyond. As such, the nature of thediscussiou in many sections leans toward that of computer documentation, rather thanoriginal scientific research. It is included here for completeness but readers may wish toskim or skip this chapter on first reading.2.1 IntroductionThe primary tool available to us in probing molecular clouds is their molecular lineemission. However, interpretation of the observed line is complicated as it depends onthe density, temperature, dynamics and the radiation field inside the cloud, often insensitive and non-linear manners. Fortunately, the physics describing the formation andtransfer of the line formation is relatively well understood in terms of the individualsteps (although the choice between line broadening mechanisms remains a question.)To understand the collective effect of these mechanisms operating simultaneously, oneresorts to numerical modelling.Following the approach of de Jong, et al. (1975), Leung (1978), Bernes (1979) andCabrit and Bertout (1986), to name only a few, we start by examining the equationsdescribing the radiative transfer of line radiation within a molecular clond. Our goalhere will he to predict the observed line shape and intensity when physical and dynamicalconditions in the cloud are specified. In this way, we can postulate models of the cloud17Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 18and 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 thesystem, which would then be incorporated analytically into the model. While beingmore costly in a computational sense, we preserve a great deal of generality by nsingthis approach. By keeping the physical problem in its general form, input models canbe 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 codeto produce realistic results for each input case is a separate matter. Tests for somespecific cases are discussed later in this chapter.] The computational powers requiredin this approach are quite modest by current standards. It was decided to pursue thisapproach to supplement (or complement) the model code already made available to usby Dr. L. Avery (private communications). This latter code uses simplifying analyticalapproximations, rather than numerical brute force, to help arrive at the solution.2.2 The Model BasicsWe start the construction of our model with its one major assumption, that regarding itsgeometry. We assume that the observed molecular cloud can reasonably be representedby a series of slabs (or a “stack”), infinite in the tangential direction and individuallyhomogeneous (c.f. Figure 2.1). As we shall see below, the advantages of this method aremany-fold.First, since the molecular clouds of interest to us are generally large and smoothcompared to the beam sizes of modern submillimetre wavelength telescopes, we can seeintuitively that the infinite extents of our slabs do not present a large problem. Thispoint is again examined in Section 2.7.2. Second, since we are now able to specify, withthis model construction, the physical and dynamical parameters of the layers at will, to—/(cosmic)\backgroundIradiation1_./observedemissionmolecularcloudmodelledaslayersofslabs(IDobseerFigure2.1:Modelgeometry.Thisschematicdiagramillustrateshowthemodelcloudisconstructedandusedtopredicttheobservedemission.Seetextformoredetails.flN,VN,TNflN-1,VN-i,TN-1nvT32ni,Vi,TiChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 20any functional or tabulated form, the model allows us to examine “new” effects such asself-absorption or outfiowing wind.However, the greatest advantage of this method by far is the fact that it has essentiallythe same geometry and mathematical structure as the “plane parallel atmosphere.” Theplane parallel atmosphere has been studied extensively in the first half of this centuryby scientists who made the pioneering investigations into the theory of radiative transferin 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 resultsin 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 byits optical depth r, and the equation of radiative transfer can be written as1IV(rV) = IV(0)e + JT (T’T)d (2.1)where IV(TV) is the specific intensity of the radiation, IV(0) represents the radiation entering the cloud [for an isolated cloud, IV(0) = B(v, Tbg), the specific intensity of ablackbody at the temperature of the cosmic background], and j(= SV) is the ratio ofemission 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 (2.2)for complete redistribution. Here, gi is the statistical weight, given by gi = 2i + 1, andn is the molecular gas density for the ith rotational state. To find n, the equations of1llere. we adopt the notation in standard texts (e.g., Chandrasekhar, 1950, Bowers and Deeming,1984) in which a v-subscript denotes a function of frequency and its absence specifies the integral overfrequency, except that the integration extends only over the line and not from zero to infinity. Forexample,= June Idv.Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 21statistical 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 byA + BJ3(r) + C(r), i > jFj1(r)=- (2.4)I. B1Jij(r) + C1(r), i <jwhere and are the Einstein coefficients 2 for spontaneous and induced transitions,and C1 are collision induced transition probabilities from the ith to the jth rotationalstate. (Note that are also functions of position due to the positional dependencies ofn and T.)Though we have not yet specified the value, form or physics3 of or ‘r(r), we cansee that we have come full circle back to Equation 2.1 via the mean intensity. Thus, wesee that it may be possible to solve this system of equations numerically by a series ofiterations 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. Thiscan then be used in Equation 2.4 to determine the transition probabilities between therotational levels. These can in turn be applied to find new densities (Equation 2.3, butalso see Section 2.5.3) which will be the starting point of the next iteration. In thefollowing section, I shall discuss the physics and the subtleties of evaluating the opticaldepth function.2Here, as in de Jong, et al. (1975), I have defined the Einstein coefficients in terms of the meanintensity instead of the customary energy density. This introduces a factor of 4w/c in some equations.(See Section 2.3.2, Transition Probabilities.)31n fact, in order to preserve generality in these models, I have purposely not specified any form for,or structure in, n(r), v(r) or Tkfl(r) all of which influence r(r).“ Local Thermodynamic Equilibrium. In this context, the term LTE is used to describe a conditionwhere locally, the relative populations among the rotational states of the molecule of interest can bedescribed by Boltzmann factors of a single, common temperature. = ThIn)Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 222.3 The Detailed Picture2.3.1 Optical DepthIn any radiative transfer investigation, a fundamental quantity of interest is the opticaldepth. Consider first, ‘j(r, v — v0(r)), the normalised, local line shape. This is theshape with which the lines are emitted or absorbed at some particular region in thecloud. Note that ii, the frequency of the line centre, is a function of position, as weexpect to use significant velocity gradients throughout the cloud. This will shift the linecentre via the Doppler effect. In the models thus far computed, I have used Gaussianfunctions 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 raisedin Section A.2.2.) The two widths are combined in quadrature.Next we consider the absorption coefficient,k0jj(r)=[nj(r)Bj — n(r)B13j. (2.5)The optical depth can now be expressed simply asr(v, r)= j 1.66k0q(r’)(r’, v —v0(r’))dr’ (2.6)for the i—> j transition. This integrand represents the probability of the photon beingabsorbed 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 overdirections. It results from the exponential integral that arises under the plane parallelgeometry (see, for example, Chandrasekhar 1950).2.3.2 Transition ProbabilitiesIn order to proceed with computations, one needs to evaluate the transition coefficientsA1, and The Einstein coefficients, and are normally available fromChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 23any 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) B1 in termsof the mean intensity. The customary definition involves u,, the specific energy densityof the radiation. This departure from custom results in the relationship between andgiven by,B = 23A (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)andA1 = 64rv2 (2.9)where the rotational dipole moment for the i —* i — 1 transition is given byp_ 2 = 2( (2.10)Values for the dipole constant p for simple molecules can be found in the standardliterature (e.g. Lang, 1980). For example, p = 0.112 Debye for CO, and 1.98 Debye forCs.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 atransition being induced by a collision.”) In my models, I simply use the probabilitiescomputed by Green and Thaddeus (1976) and Green and Chapman (1978). These values are based on “extensive theoretical calculations using methods of known reliability”.Although experimental confirmation of these values by direct measurement is not generally 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 24Cabrit and Bertont (1986), Bernes (1979), Lenng (1978).]. As the authors point out,the same extreme physical conditions found in interstellar space that make experimentalmeasurements difficult facilitate theoretical determinations of collisional rates.2.4 The Algorithm: An OutlineIn developing this theory into computer code, the basic principle of keeping the algorithmand the code as general as practical has been followed. As such, the only constraints involved are those required by the geometry. The equations of radiative transfer can beeasily applied to plane parallel slabs. It is also a simple task to propose analytical expressions 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. Goldreich and Kwan, 1974, de Jong, et al., 1975, Cabrit and Bertout 1986). However, I havedeliberately stayed away from this approach in this investigation. My approach maycost extra computing time, but saves us from oversimplifying the problem or having tomake a priori judgements on the models. Also, it renders itself to flexibility and futuremodifications or extensions.For each run, I propose a model, described by arrays containing n-j2, TM and Vjsr foreach layer. [At the risk of overemphasising the point with a comment, we note that wedo 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 theoryand much of the work can be done analytically. This means that the equations to besolved can be tailored so as to make the numerical problem much simpler and less costlyto solve. In recent times, however, computational cost of this magnitude is no longer thelimiting factor. With this new model, I can (and do) recreate velocities whose gradientsChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 25happen 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 staticmodels which would represent the opposite extreme from the models in the large velocitygradient limit.] A solution is obtained iteratively for populations at each rotational levelin 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 CodeIn this section, discussion is made of some specific details describing how the physicsalready outlined has been encoded into a numerical form. In addition, methods used tofind solutions to the physical equations are outlined.2.5.1 Array StructureAs described earlier, and as depicted in Figure 2.1, our model is constructed with a seriesof plane parallel layers or “slabs.” Admittedly, specifying this, or any other geometry,restricts the generality of the model to some extent. However, the celebrated generalityof this model arises from the following.The input physical parameters (density ri, temperature T & velocity v) are specifiedusing arrays, where each element represents the value for a particular slab. (i.e., thereis 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 elementsare assigned values using a subroutine for this specific purpose, as part of the programinitialisation. The powerful point of this design is that by making simple changes tothat subroutine, the investigator has complete freedom to assign any value to any arrayelement. In many existing applications, specific functional forms are assumed for theChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 26physical parameters, often accompanied by specific relationships between the differentparameters. In many cases, this can greatly simplify the numerical problem and shortenexecution 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 capabilitiesfor doing so. In this application, the investigator can choose any functional or tabulatedform for the input physical parameters.For the purposes of the above discussion, the density array was shown with a singleindex. In fact, the density array is further subdivided into another dimension, J, therotational 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 willbe the chief output product to be compared to observations. The total density (as afunction of space), n = nj, is assigned values as described above and is fixed for theduration of the model run. Physically, this means zero net matter flow, consistent withthe quasi-steady state assumption. Of course, the distribution among the J levels willbe solved for a steady state solution.Introducing a third dimension, that representing frequency, allows us to define anintensity array, ‘ijk Here, the k index refers to frequency across the line. For fixed i and, ‘k is a spectrnm for the J = j + 1 —* j transition line at the it’ layer. In fact, there aretwo arrays, 1k and 1k’ representing the two directions (‘streams’) required to describeintensity function under the plane parallel assumption.In gridding the variables (which are inherently continuous) into discrete array elements, care has been taken to ensure that both resolution and width of coverage aresufficient 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, themost rapidly varying parameter at its most rapidly varying location is still well behavedChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 27numerically (i.e., layer to layer changes are small and smooth). Tests to ensure sufficientspatial resolution were performed as discussed in Section 2.8. The approach describedhere might be argued to be wasteful of computing resources, since spatial resolution ismuch 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 interms of the optical depth. However, this is not always straight forward when the inputphysical parameters (which are described in spatial terms) do not have a fixed or evenan analytical form. Rather than programming a spatial to optical depth transformationfacility, 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 profilesat the local level. This is to ensure that the radiative flux is numerically well characterisedin 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 besuch that the local line profiles (which are dominated by turbulent velocity effects) aresampled by many grid points. Typically, “channel spacings” equivalent to 0.05km sare used. Tests for these effects also are discussed further in Section 2.8. At the sametime, we require a wide coverage in frequency since the lines to be modelled are often verywide. Thus, a large number of frequency elements are required in the arrays. Again, thiscalls for much more computational resources than is customary for this type of work.However, we specifically ignore this concern. At this level of demand, computationalpower is now plentiful enough that the astrophysicist should concern himself with theeffective use of his time rather than that of the computer.We note also, that questions regarding spatial and frequency resolutions are coupledby way of the velocity gradient. That is, the line centre can shift from one layer to thenext. Therefore, care is taken that (1) layer thickness is not so large that this shift is aChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 28significant fraction of the local line width and (2) the frequency resolution is sufficient torecognise this shift.Unlike the variables for space and freqnency, the rotation levels are quantised andthere is no concern over choosing sufficient resolution. It is sufficient to ensure thatthe highest rotation level included in the computation (Jmax) is taken high enough thatpopulations iu states above Jmax are too small to influence the (lower) transitions understudy. Tests for this effect are straight forward but, in practice, our choice of Jmaxis strongly influenced by the values of Cq available to us as tabulated by Green andChapman (1978).2.5.2 Initial ConditionsThe only parameters in this code requiring initial values are contained in the densityarray nq described in Section 2.5.1.The values for n (= > n) are prescribed as part of the iuput and only the distribution among the J levels is left to be decided.Obviously, some choices of initial conditions will allow for faster convergence to astable solution. However, there is no one, all-encompassing rule for choosing this distribution. In a manner of speaking, knowledge of such a rule would itself represent thesolution to this entire numerical exercise.One example of a start-up distribution is to assume LTE. At the low densities ofthe interstellar medium, it is reasonable to expect the populations in the higher J levelswould 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 betested in Section 2.8.Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 292.5.3 Iteration and ConvergenceThe iterative method used to find a steady state solution to the numerical problem mayresemble how real systems move to steady states by time evolution or relaxation.Each step in the iteration involves the following. First, the current density populationsare 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. Themean integrated intensity is then computed and used in Equation 2.4 to find the transitionproabilities between the J levels for each layer. The probabilities are used with the currentn array and a (initially small) time step to find new values for the density-populationarray. Thus we have allowed the system to evolve over that time step.Under numerically well behaved situations, the physics of the transitions ensures thatthe populations move toward the steady state. For example, if the ith rotational levelis somehow overpopulated, the products riPj are elevated until the excess populationis transferred out of that level. This method has certain advantages over solving theequations of statistical equilibrium (Equation 2.3) using standard algorithms such as theNewton-Raphson method. The Newton-Raphson method requires knowledge of the partial derivatives of Pq in order to steer the parameters toward convergence. Unfortunately,the complexity of the stimulated emission term in (involving space and frequency integrals) makes differentiation non-trivial. The observant reader may have noticed thatEquation 2.3 has the form of an eigenvalue problem. Again, the complexity and thenon-linearity of P hinders an approach of this type.In any iterative application for solving a system of equations, the criteria for stoppingthe iteration can he somewhat arbitrary. In some cases, it is clear when one has reachedsome precision limit and the solution starts oscillating about some mean. In other instances, we simply satisfy ourselves when solutions from one iteration to the next varyChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 30by less than some small amount, determined perhaps arbitrarily. In this application, thelatter is used to decide when to stop the iteration, although the former condition is oftensatisfied as well.Specifically, the stopping criteria are chosen based on the following observationalprinciple. In the observational work described in this thesis, there have been a numberof cases in which a particular source has been observed in one session, to be repeatedin another, perhaps a year or more later. In such cases, we invariably see no significantchanges in the observed spectra. Thus, we can say for the computed models that theymust be stable under time evolution over periods of order one year within limits ofdetection. In the code, convergence is declared when the population densities change byless than a specified small (for practical reasons, adjustable) percentage over a simulatedtime period of one year. The number of iterations required, or the execution time inthe computer, clearly depends strongly on the array sizes and complexity of the inputphysical parameters and often their specific values. It also depends on the machineused for computations, its speed and memory capacity. While there is no one, all-encompassing answer, often when execution times exceed a few hours, array sizes aredecreased or convergence criteria are relaxed, to the level indicated to be appropriate bythe test cases (Section 2.8).Figure 2.2 shows a sample (CO) case of population densities for the four lowest rotation levels approaching the steady-state values by iteration. The J = 3 level illustrateshow the high energy states (J 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 theJ = 3 curve is due to the J 4 populations stepping through this rotational state ontheir way to lower levels. The example shown is at a low density (n 400 cm3) andis slow to converge, providing a good demonstration of the convergence mechanism. Atvery high densities where we expect frequent collisions to thermalise the populations,Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 310.0080.006I.,S0>.0.0040.0020.0001000Figure 2.2: Iterating towards convergence. This figure illustrates the CO populationdensities for J levels 0, 1, 2 and 3 approaching the steady-state values at the centre ofa low density model cloud. In this slowly converging example, the different rotationallevels 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 theiteration process is trivial.2.6 Sample OutputIn order to demonstrate the effects of the model computations under discussion, two examples 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 microscale turbulence hut no structured velocities. The line profile is the main form of outputand is computed as=[I - Bv(Tbg)j0 200 400 600 800Iteration NumberChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 325040II / \ ‘\II I \ ‘\1 I \ ‘\II I \ ‘.‘/: / \i; I \ ‘I I \ ‘>%,20 IC IssoC II I’— IsIs 510 ,5 5IsI,I,0—10—5 0 5 10Velocity (km/c)50/—S40ISI, III I‘:1Is,SII- Ij>‘ IIIIL20CS I10 ‘5/I’Isjii0—10—5 0 5 10Velocity (km/c)Figure 2.3: Sample output spectra. (a) Top panel. A sample microturbulent model cloudCO 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 isshown in the same lines. See text for details.Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 33where I is the emergent intensity at the cloud surface. (See also definition of T,p.55.) The kinetic temperature and H2 density are both constant throughout the cloudat Tlth = 50K and nn2 = 104cm3. There is no velocity gradient or structure (v = 0everywhere), but there is a turbulent component of VtUrb = 6.3 km s, as well as a smallthermal contribution to the line width. The cloud is 2 pc in thickness and the H2 columndensity is 6 x 1022cm.For each transition, we see the line reaches a maximum intensity approaching thekinetic 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 expected, the line widths are consistent with the turbulence velocity. Although a series ofruns 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 Section 1.4). That is, a cloud with an assumed structure that obeys the restrictions of ourLVO code (except that it is not spherical). It is homogeneous in density (nil2 = 105cm3),isothermal (TkI = 50K), and has a velocity gradient of 20 km r’pc’ over a total cloudthickness of 0.75 pc. Although we do not expect to find interstellar clouds fitting thishighly idealised description, it is useful to compute models in this limit because the resultscan 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 totalwidth to be given approximately by (cloud thickness) x (velocity gradient). The widthof this ‘rectangular’ line reflects the range in radial velocity across the cloud, as eachlocalised region emits the line in its own rest frame. The intensity of the line is governedby 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 canarise when the spatial gridding is insufficient (see Sections 2.5.1 and 2.8.1). Each rippleChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 34represents 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 areretained here for demonstration purposes but normally care is taken to avoid this andother numerical artifacts.2.7 Validity of the ModelsThere are two questions one needs to ask when considering the validity of numericalmodels and the results obtained through them. Of operational interest is the question:does the code solve the mathematical problem correctly? On the astrophysical side, weneed 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 thiscomplexity is functioning as intended, there are a number of tests that can be performedto help answer this question.One way to test this model code is to compute solutions in certain limiting casesof 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 intensityeasily predicted from the gas kinetic temperature which would also be the excitationtemperature. Since we have an established LVO model code, model solutions can becomputed in the LVG limit (together with homogeneous and isothermal assumptions)such that a direct comparison of the results is possible. Tests have been performed inthese limits and their results were found to be in good agreement, except for the effectsof artificially sharp boundaries. (See Section 2.9.)In addition to the quantitative tests, qualitative behaviour of changes to the computedChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 3550.040.030.0I’*I20.00C4)C10.00.0—10.0—20.0 40.0Figure 2.4: Self absorbed profile. A numerically generated CO J = 2 —, 1 line profilewith a self reversal feature (thick dashed line) is compared to an observed spectrum (thinsolid line) of IRAS 18162—2048 (see Chapter 4). In the model cloud, the line core featureshave 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, onecan introduce a dense, cold foreground layer of gas and see if a self absorbed line profile results. One can also look for variations in the predicted line profile as the gas temperatureor density structure is varied. Tests of this nature have been quite successful in attainingthe expected results in a qualitative sense, giving some confidence in using the quantitative results. Some examples of this model applied to observed data demonstrating theseeffects are shown in Figures 2.4 and 2.5.0.0 20.0Velocity (km/c)Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 3650.040.030,0*20.010.00.0—10.0—10.0Velocfty (km/s)Figure 2.5: Exploring the effects of a temperature gradient. Molecular lines observedin the ISM are often sharply peaked, as opposed to the rounded peaks of Gaussianprofiles, for example. One way to produce a sharp peak in the computed line is tointroduce a temperature gradient in the input model. The observed J = 3 —* 2 COline 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 Gaussianprofile. When a temperature structure is introduced, a sharp-peaked emission line can beobtained due to a number of mechanisms. In the example shown (thick dashed line), thegas kinetic temperature decreases roughly as r0’7, effectively creating foreground layersof colder, absorbing gas which affects one side of the line.—5.0 0.0 5.0 10.0Chapter 2. The Radiative Line Transfer Model: The Physics and The Cornputing 372.7.2 Is the Model Representative?In order to answer this question, I shall will start by examining the underlying theoryemployed in the modelling. Fortunately, these are generally well understood. The equations of radiative transfer, statistical equilibrium and others, as laid out earlier in thischapter, individually are well established and involve no exotic physics. Of more concernare the rates for collisionally induced transitions. As mentioned earlier, these have beentaken from the works of Green and his collaborators. Since the details of their calculations 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 theart in collisional (de-)excitation theory. They have been successfully applied in predicting molecular emission in the interstellar medium (c.f. Section 2.3.2). In addition, othermethods 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 ofslabs reminiscent of the ‘plane parallel atmosphere’. While our LVG models assume aspherical 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 iswell modelled by either a planar or a spherical geometry. This is a departure from thecommon practice in the earlier, pioneering works in molecular cloud model studies whichtended to assume that their spherical clouds fit within the telescope beam. This is nolonger an appropriate assumption as telescope beams have become smaller with increasesin both frequency and antenna size. I have also improved on our LVG model by allowingfor variations in density and temperature through the cloud. This is a much neededfeature since effects such as self absorption cannot be reproduced under the restrictiveassumptions of the LVG version (which, incidentally, does not generate a line profile).Chapter 2. The Radiative Line Transfer Model: The Physics and The Cornputing 38This feature also allows comparisous of lines of various species that may be generatedover regions of varying extents (section A.2.1). As well, the implicit LVG assumption hasbeen removed. While we can specify the infall/outfiow velocity structures such that thevelocity gradients are indeed large, this is not a required part of my models. Althoughthe 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 asmicroturbulence.In summary, the model as described here is believed to be a fair representation ofastrophysical clouds. These geometrical generalities do require greater computationalresources 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 someparameters) a number of effects.2.8 Internal ChecksThis section addresses concerns regarding numerical artifacts. One primary area of concern is the grid resolution, both in space and in frequency. The number of rotation levelsto be included in the computations should also be considered. Finally, we must ensurethat the computed results are independent of the exact choice of initial conditions. Thesepoints are now addressed individually.2.8.1 Grid ResolutionOne way to describe the resolution of the space and frequency gridding is in terms of theoptical depth function, r3(v, r). The array representing this function must be smooth inboth dimensions. The reasons for, and the consequences of violating this condition havealready been discussed in 2.5.1.Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 39As a starting point, we take Av and r such that both EAv and are small.Numerically, when one such model run is completed, we compute a solution for the samemodel 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 andstop 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 occurredduring development. For example, there was one early case in which the spatial griddingwas too coarse, and the emitted line was narrower than the velocity gap between adjacentlayers. The effect was to decouple the layers radiatively, allowing each to emit its lineunattenuated by the foregronnd layers. The “observed” spectrum resembled a picketfence.2.8.2 Initial ValuesSince the solutions here are derived iteratively, it is possible that the final result towhich the model converges may depend on our choice of initial values. However, thisonly occurs for start-up values outside some bounds (Press et al., 1986), so that forall “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 wouldseem to be reasonable. Since our iterations are analogous to time evolution, any excessor deficiency in a population density element can be expected to be rectified by theappropriate transitions as dictated by the equations.Numerically, this has been confirmed by a number of trials. In all cases, the convergedsolutions agree within the specified tolerance (the value that defines “convergence”).Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 40H2 Tki Texc (K)(cm3) (K) 1—>0 2—*1 3—*2iO 30.00000 30.00007 30.00003 30.00000iO 30.00000 30.00002 30.00000 30.00001iO 30.00000 30.00017 29.99998 30.00003106 30.00000 30.00168 29.99978 30.00027Table 2.1: Models in the high density limit (> 103cm). The computed excitation temperatures 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, collisions dominate the transitions and cause Texc to approach Tk1, as verified here withinthe convergence tolerance.2.9 External Checks2.9.1 Tests Against Expected Behaviour or Analytical Solutions in LimitingCasesUnder some conditions, quantitative results of computations can be predicted from anunderstanding 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 andde-excitation processes. It follows that the excitation temperature approaches the kinetictemperature throughout such a region for all transitions. Table 2.1 shows a comparisonof 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 cloudhave little roles to play. The radiation field inside a low density (low r) molecular cloudis dominated by the comic background radiation (CBR) since it is able to penetratethroughout the cloud, and the molecules will he found in radiative equilibrium withthe CBR. Thus, we expect Texc = Tbg or 2.8 K for all transitions. Although this isnot precisely the case seen in the examples of Table 2.2, the values of the excitationChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 41T Texc (K)(K) 1—*0 2—÷1 3—210 3.15 2.89 2.8720 3.47 3.12 3.2030 3.65 3.26 3.3950 3.83 3.43 3.59100 4.04 3.63 3.82Table 2.2: Models in the low density limit. The computed excitation temperatures atcloud 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, thecloud has a gas density of H2 = 10 cm3 and is 0.2 pc thick. At this low density,the excitation mechanisms are dominated by the cosmic background radiation so thatTexc — 2.8 K everywhere.temperature can still be seen to approach the cosmic background value. In the limitingcase, no “line” will he observed above the continuum of the CBR. With respect to themodel computations (because the output intensity scale is defined to be T] = 0 whenit reaches the CBR level) whenever a T value of zero is generated, the zero point ofthe intensity scale is verified. This test also applies to intensity array elements near theedge of the spectrum where r 0 [so that T = 0, meaning I, = Bv(Tbg), or that theintensity of the blackbody radiation at the CBR temperature is recovered].2.9.2 Tests Against LVG SolutionsMolecular clouds in the large velocity gradient limit form another class of special casesthat avails itself to easy testing. Since we already have access to an established LVOcode of Avery, we simply use the new code with input models that satisfy the sameconditions such that results from each code can he compared directly. [See the examplein Figure 2.3(h).]Table 2.3 shows some sample cases for comparison. The cloud parameters are typicalChapter 2. The Radiative Line Transfer Model: The Physics and The Computing 42H2 T11 Vel. Grad. Transition T (K)(cm3) (K) kmr1pc’ J = LVG code this work1.0 x 106 20 K 5.0 1 —* 0 16.541 16.4692 —* 1 14.782 14.7543 —* 2 12.792 12.7831.0 x i05 30 K 10.0 1 —* 0 26.481 26.4272 — 1 24.595 24.5863 —+ 2 22.391 22.4113.0 x io 40 K 1.0 1 —> 0 36.427 36.3182 —> 1 36.475 34.5013 —* 2 32.163 32.2223.0 >< l0 50 K 20.0 1 —, 0 46.443 46.3922 —* 1 44.455 44.4503 —* 2 42.089 42.108Table 2.3: Models in the LVG limit. Output from compnted models satisfying the largevelocity 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, themore flexible code, at least in this limit. The computed radiation temperatures for COJ = 1 —* 0, 2 —* 1 and 3 —* 2 transitions are shown for some sample cases as computedwith both codes. The only conceptual difference is the geometry; the LVG-specific codemodels a spherical cloud compared to our slab structure. Other transitions providesimilar confirmation but are not shown here for space considerations.Chapter 2. The Radiative Line Transfer Model: The Physics and The Computing 43for star forming clouds of interest in this thesis. While we do expect some differences inoutput due to the different geometries used (sphere vs. infinite slabs), the table showsthis effect to be minor for the examples calculated.Chapter 3ObservationsThe new observational data for these projects have been acquired using the facilities ofthe James Clerk Maxwell Telescope (JCMT). The following section describes the JCMTfor 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 isvery introductory in nature. The initiated reader may wish to skip to Section 3.2 whereobserving 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 theefforts and techniques used to calibrate the observed data. The transport and exchange ofdata 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 andChapter 5 for the NGC 6334 sources. Continuum maps and spectral line profiles for theIRAS sources and line emission maps for NGC 6334 are presented in Appendices C andD, respectively.3.1 The James Clerk Maxwell Telescope3.1.1 Physical Description of the JCMTLocated on “The Big Island” of Hawaii near the Mauna Kea summit (at elevation4092 m), the JCMT is a (sub)millimetre wavelength “radio” telescope. Its 15 mparaboloid antenna is mounted on an alt-azimuth system inside a rotating carousel.44Chapter 3. Observations 45With surface deviations as small as 25 jtm, the JCMT operates with spectral line, heterodyne receivers working between 200 and 700 0Hz (A = 0.43 ‘- 1.5 mm) and continuumbolometers covering wavelengths between 0.35 and 2.0 mm.In the context of the present study, making observations with the JCMT has someimmediate advantages. In contrast to earlier observations (in MDPS) using the NRAO12 meter, the higher frequencies made accessible with the advent of this telescope enableus to study the higher rotational transitions of interstellar molecules. At the same time,observing at shorter wavelengths while maintaining a relatively large aperture gives ushigher angular resolution (21 arcseconds or better).3.1.2 Signal Paths and Receivers for the JCMTThe signal path for the JCMT is more or less a standard one for millimetre and submillimetre wavelength telescopes. Generally speaking, the astronomical signal arrives at theparaholoidal antenna and is reflected to a focus. In the case of the JCMT, the Cassegrainfocus (f/12) is normally used for the heterodyne receivers and the continuum bolometersare mounted at the Nasmyth focus (f/35).For UKT14, the continuum bolometer on the JCMT at the time (of the observationsdescribed 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). Insidethe TJKT14 package, the signal is fed through a variable aperture, a Fabry lens, a filterwheel and a parabolic horn, on its way to the Ge:In:Sb detector element. The entirepackage is cooled to progressively colder, cryogenic, temperatures in order to reduceelectrical noise and thermal emission from TJKT14 itself.At the sophistication level of this discussion, the inner workings of all heterodynereceivers used here are essentially identical. Briefly, the astronomical signal and a localoscillator (LO) signal are fed into a mixer at the front end of the receiver system. TheChapter 3. Observations 46resulting interference signal is the IF (intermediate frequency) signal, which is then amplified and fed to the spectrometer (see Figure 3.1.) Without an additional device suchas a filter, this signal will contain astronomical signals from two frequency hands, thosecentred 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 towhich a particular signal belongs can be identified easily by shifting the local oscillatorfrequency by small amounts. This causes corresponding shifts in the line position at thespectrometer 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 factorsthat set the tone for receiver characteristics and these are now discussed briefly for theinstruments used in the course of this study.Receiver A, now superseded by Receiver A2, was part of the first generation of instruments available on the JCMT. It covered the frequency range 220— 280 0Hz, theso-called “A-Band” at the JCMT. This band includes the 230 0Hz, J = 2 —+ 1 line ofCO, an important molecule in observational interstellar astronomy. It used a Schottkymixer for electrical rectification (actually, one of two, depending on frequency). Schottkydiodes operate as a result of a moderate potential barrier that exists between a conductorand 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 COJ = 3 —* 2 line is among those accessed in this frequency range, the “B-Band.” An SISmixer is built around a Superconductor-Insulator- Superconductor junction and operateson the principle of the Josephson tunnelling effect.Receiver B2 is a Schottky system used briefly at the JCMT as a common-user instrument. It covered the range of 330 — 360 0Hz but has since then been superseded byChapter 3. Observations 47Figure 3.1: Signal Path to the JCMT Spectrometer. The block diagram shows the signalflow from the antenna to the spectrometer through a “typical” heterodyne receiver. Seetext for a further description.AntennMixerLocal OscillatorMainComputer“Receiver”Chapter 3. Observations 48Species Transition Frequency Receiver Beam SizeJ = (GHz) (arcsec)‘2C’60 2 —÷ 1 230.5380 A 21‘2C’60 3 — 2 345.7960 Sutton, B2 14, 16‘3C’60 2 —* 1 220.3987 A 21l316 3 —÷ 2 330.5881 Sutton 14l2l8 2 — 1 219.5603 A 21l2ClrO 2 —* 1 224.7144 A 21121’7O 3 —* 2 337.0611 Sutton, B2 14, 1612325 5 —* 4 244.9357 A 21l232 7 —* 6 342.8833 Sutton, B2 14, 16l2345 7 —* 6 337.3966 Sutton 14Table 3.1: Spectral Lines Observed. Their rest frequencies and the receivers used arealso given. Where more than one receivers were used, beam sizes (half power widths) arelisted in respective order.Receiver B3i, an SIS device.3.2 Observations of IRAS Selected Protostellar Sources with the JCMTThere has been a total of five observing runs at the JCMT for this project. These aresummarised 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 sourcesin the CO J = 2 —* 1 line (Receiver A), J = 3 —÷ 2 line (Receiver B) and in thesubmillimetre continuum emission (UKT14). The unfortunate failure of Receiver B priorto our run precluded the J = 3 —* 2 observations. The continuum observations turnedout to be of limited use due to problems in calibration. Although Receiver A sufferedfrom a calibration problem as well, we were able to overcome this problem and constructfive-point grid maps for sources #09, #14 and #25 in the J = 2 —* 1 line of CO. Some13C0 and C18O lines have been observed as well. However, because its frequency fellChapter 3. Observations 49Date Target Line ReceiverJune 1989 CO, ‘3C0, C180 2 — 1 A 1500 1800KApril 1990 CO, ‘3C0, C170 3 — 2 Sutton 1200KCS, C34S 7 —* 6 SuttonCO, 13C0, C’70 2 —+ 1 A 1100 1500KApril 1991 C’70 2 —* 1 A 1100KCS 5 —* 4 A 1400K, 2700KMay 1991 800, ll00tm UKT14May 1992 450, 800, 1100gm UKT14Table 3.2: Log of Observations for the MDPS IRAS Sources. [The system temperatureis a measure of the total noise including contributions from the receiver and theatmosphere.]slightly below the good, low noise tuning range of Receiver A, C180 observations werenot 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 bythe group led by Sutton. [See Sutton et al. (1990) for a comprehensive description ofthe receiver.] Using this superb receiver, we were able to observe the J = 3 — 2 linesof CO, C170 and ‘3C0. We were also fortunate to be able to observe, simultaneously,J = 7 —* 6 lines of CS and C34S in the image sideband. Also during this run, J = 2 - 1lines of CO, C’70 and ‘3C0 were observed using Receiver A.These data were further supplemented in a run in April 1991. In addition to expandingour coverage using the same lines observed previously, we targeted new observationsusing the J = 5 —f 4 line of CS. These were chosen for observations since preliminarymodelling work suggested that data on another transition of CS molecules could clarifysome ambiguities in the models. (See Section A.2.3.)All of our spectral line observations were made in the position switching1 mode in1When a signal is detected at a high frequency telescope, it is normally dominated by systematicChapter 3. Observations 50order to eliminate much of the background emission. Initially, the “off” positions usedwere those used in our initial survey, as these were confirmed to be lacking in CO emissionin the J = 1 —‘ 0 line with the 1 arcminute beam of the NRAO 12 meter. However, asthese often translated into large slews of the telescope (many arcminutes), we adoptedcloser sky positions for some of our later observations. It is indeed reasonable to expect tofind a suitable blank sky region closer to our sources given the smaller beam sizes (from60 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 againstthe original ones to ensure that they were free from line emission.For all spectral work, the “Canadian” Acousto Optic Spectrometer (AOSC) was usedas the backend instrument. This instrument gives an effective resolution of 330kHz overa bandwidth of 500MHz (normally centred around the target line frequency) sampled bya 2k photodiode array at 250kHz separation. Integration times were typically 10 to 30minutes for each beam position observed.Finally, a run in May 1992 was dedicated to mapping a selection of these sourcesin the submillimetre (and millimetre) continuum. These observations were made usingUKT14, the standard continuum bolometer on the JCMT. “On-the-fly” (OTF) mappingtechniques were used to map nine sources from our list at 1100 iim and 800 çtm. The ninewere selected from our original list of 39 to concentrate our efforts on the younger sourcesbackground 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 thisbackground signal at the time of observation. As a spectrum is taken ‘on source’, another is taken ata 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 areable to correct for various effects (whose contributions may be rapidly changing) without having toknow their exact magnitudes. There are alternative methods such as beam switching and frequencyswitching; the former moves the secondary mirror to access the blank sky whereas the latter uses aline-free region in frequency space. While being potentially more efficient with observing time, beamswitching 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 switchingmode exclusively.Chapter 3. Observations 51Filter A Aperture Beam Width Cell Size Map Size Chopper Throw(pm) (mm) (arcsec) (arcsec) (cells) (arcsec)450 27 8 2.0x2.0 53x37 30.0800 47 14 3.0 x 3.0 39 x 25 42.01100 65 18 5.0 x 5.0 33 x 21 60.0Table 3.3: UKT14 On-The-Fly Mapping Parameters. The apertures chosen correspondto the diffraction limited beam in the focal plane. The cell sizes are the increments inazimuth and elevation as the telescope is scanned.which have yet to reach the main sequence. Practical considerations such as limits onavailable telescope time and Right Ascension range helped to shorten the list as well. Ofthese nine, five sources were also mapped at 450 pm. Observations at this wavelength aremore time consuming in addition to being more difficult due to the reduced transparencyof the atmosphere.“On-the-fly” is a mapping technique used to eliminate some of the overheads associated with performing point-by-point photometry in order to construct a map. Theprimary mirror is scanned across the source while the secondary mirror is chopped in thesame direction. The signal is integrated using a phase sensitive detector, with a positiveor a negative sign depending on the position of the secondary. (i.e., “+“ if the beam ispointed on the source, “—“ if off source.) This chopping is designed to eliminate much ofthe background, ‘sky’ emission, around our source. For example, after performing a fullraster scan with the primary mirror over a point source, one obtains an unprocessed mapwhich 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. map2 is later done in software. More detailed descriptions of this processcan be found elsewhere. [e.g., Matthews (1992), Salter(1985)]2A Right Ascension— Declination display shows the intensity of an object as a function of positionon the celestial sphere.Chapter 3. Observations 52Date Target Line Receiver T55April 1990 CO, C’70 3 —* 2 Sutton 1200KCS, C34S 7 —* 6 SuttonC170 2 —* 1 A 1100 1500KApril 1991 CO, C’70 3 —* 2 B2 2100 3000KCS, C34S 5 —* 4 A 1200 2200KCS 7 — 6 B2 2100 2200K‘3C0 2 — 1 A 3200 3600KTable 3.4: Log of Observations NGC 6334 I & I(North).3.3 Observations of NGC 6334 with the JCMTObservations of NGC 6334 in the context of this work were started at the JCMT duringa run in April of 1990. This run was concurrent with the IRAS/protostellar candidatesprogram session mentioned above. Again, the principal receiver used was the SuttonReceiver in the ‘B window’, supplemented by observations with the common user ReceiverA. The same selection of lines was observed.This set of data was supplemented by another run in April, 1991 using receivers A andB2, a newly commissioned common-user receiver at the JCMT. Again, the J = 5 —p 4lines of CS and C34S were added to the list. These observations are summarised inTable 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 forabout four hours at a time for airmasses3less than 2.0 atmospheres. In particularly goodweather, this can be extended to about six hours by observing the source at elevationsdown to 20° (3 atm.).3The airmass, A, is a measure of the amount of air (in the Earth’s atmosphere) through which anobservation is made and is defined as A = 1 atmosphere in the zenith direction. The airmass is ofconcern at these frequencies, since the atmosphere can attenuate the astronomical signal, as well as emitits own.Chapter 3. Observations 533.4 CalibrationAlthough the photons for line and continuum observations arrive at the telescope in thesame manner, due to different observing techniques used, line data and continuum dataare processed and calibrated in ways that are slightly different. I now proceed to describeeach process separately.3.4.1 Calibration of Continuum DataIn order to calibrate the so called ‘on-the-fly’ maps, I am first required to calibrate thepoint by point ‘photometry’ observations. To explain, I shall first describe how the fluxdensity 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 opticaldepth 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 V0 = SGe_TA, whereo is the effective ‘gain’ of the telescope system including the antenna, filter, receiver, etc.Each observation consists of a measurement of V0 at a known A. On a ‘photometricnight’ when r can be expected to remain low and essentially unchanged for hours at atime, its value as well as the value of the gain can be derived by frequent observationof planets (Mars and Uranus were used) and other, secondary calibrators. The planetsmake ideal primary calibrators since the intrinsic fluxes from them can be predictedaccurately 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 bygraphical means aided by least squares fitting. This is a fairly simple exercise at 1100 jimhut 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 bothChapter 3. Observations 54to measurement errors and time variability which are both facts of life when working atthese freqnencies, limit the precision to which the gain can he measnred. Further, whatmay seem like small errors in r can lead to large uncertainties in the derived value ofO which is affected exponentially by r, or linearly by e6. The factor is not a goodmeasure of the error.] The results are summarised in Table 3.5. The gain values for1100 pm and 800 pm were in line with the nominal values available from the local staffat the Joint Astronomy Centre4 but the 450 pm value was found to exceed the nominalones by as much as a factor of three. At face value, this is indicative of a degradationin the beam quality. Fortunately, (or perhaps unfortunately) the estimated uncertaintieson this value were found to be large enough that any departure from the nominal value,as large as it was, cannot be considered terribly significant.5 Thus the nominal value of16.5Jy/mV for the gain at 450 pm was adopted. While this large uncertainty may seemto render our 450 pm data valueless, we shall see later (e.g. Figure C.1) that errors ofthis magnitude at this wavelength do not influence the results profoundly. Also, becausethe 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 determinedin order to convert the map units into amplifier voltage, a quantity we now know how todeal with, having determined G and r. This can be accomplished by making a map of acalibrator source. For this purpose, “beam-maps” were made at each wavelength band bymapping Mars using the telescope in the same configuration. The total flux is obtainedby integrating the intensity over the entire map and is used to derive a conversion factorbased on the predicted, full aperture flux of this calibration source.The Joint Astronomy Centre (JAC) is the Hawaii local operation centre for the JCMT.5However, there are some indications that the telescope gain may have been mysteriously poor duringthis period. See Annual Report of the JCMT Board, 1992, p21.Chapter 3. Observations 55Wavelength Nominal Gain Derived Gain I(m) (Jy/mV) (Jy/mV)1100 12.5 12.07 + 0.33800 9.5 10.0 + 1.3450 16.5 15 50Table 3.5: JCIVIT Calibration for Continuum Mapping. These valus are derivedby repeated observations of standard sources as described in the text. “Nominal” values are ones derived by observatory staff over time whereas “derived” values are those determined based on observations made during our observing run only.[1 Jy = 1023erg s’cm2Hz’ = 10_26 W m2Hz1]3.4.2 Calibration of Line DataThe calibration of spectral line data at millimetre and submillimetre wavelengths is mucheasier in comparison to that of continuum photometry. All receivers involved in this studyemploy the chopper wheel technique [Penzias and Burrus (1973), see also Ulich and Haas(1976)] to eliminate much of the effects of atmospheric attenuation. The assumptionsrequired for this technique to be effective do break down at large optical depths (Sato1986); however, under those conditions of bad weather, the sky noise would be quite highsuch that it is generally unprofitable to attempt observations.Having eliminated the rA dependence, one simply needs to check the overall intensityscale by observing a few standard sources6 from time to time. Sources used here for thispurpose include S140, 1RC10216, Orion A, G34.3 and DR21. Generally, the line shapesand 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 onthe T scale (Kutner and Ulich, 1981). Briefly, T is defined as the temperature of ablackbody that would emit the same specific intensity as our observed source above the6’Standard sources’ or ‘standard objects’ in astronomy are those objects in the sky with constant andknown intensities. Frequent observations of standards are useful in calibrating the telescope gain as wellas monitoring numerous factors that influence overall data quality.Chapter 3. Observations 56background. It is related to the antenna temperature T) by a factor that corrects for theforward spillover and scattering (i.e., T = T/?]f3).7 In this way, the intensity scale iscorrected for everything except for the actual coupling of the antenna power pattern tothe source. (This last step is not possible to perform without knowledge of the sourcemorphology, even if we were familiar with the the details of the antenna pattern.)3.5 Telescope PointingAnother factor that requires constant monitoring is the quality of telescope pointing.The JCMT operates with a pointing model which automatically corrects for much ofthe pointing shifts caused by known or predictable effects such as antenna flexing andatmospheric refraction related to the aiming of the telescope in different directions. Fromtime to time, however, small offsets need to be measured and used to correct for pointingerrors due to other causes. (These could include, for example, thermal flexing or some yetunknown effects.) Whenever possible, this was done by observing one of the planets in thecontinuum. They are most suitable for this purpose because, in addition to being bright,their positions can be precisely predicted and their morphologies are simple. Secondarypointing sources were used when no planets were available in order to ensure that somecheck of pointing was made once every hour or so. There is also an opportunity to checkpointing performance by repeated observations of our programme sources. Many of oursources have structures on small enough scales that observed spectra can be noticeablydifferent 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 when7This efficiency factor, ?Jfss, was defined by Kutner and Ulich (1981) to denote the fraction of theradiation incident on the antenna from the forward hemisphere that is contained in the primary diffraction beam. It clarifies the relationship between 7 and T, a previously used but sometimes ill-definedterm.Chapter 3. Observations 57updating with the newly measured corrections.3.6 Transport of Observed DataDue to the large number of computers and the variety of operating systems and analysissoftware involved, much care had to be exercised to ensure that our data remained inusable 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 withsoftware facilities of the observatory. In moving the data to our home institution, theUniversity of British Columbia (UBC), and its facilities available to us, many steps hadto 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 concernwas the conversion of data file formats required by the variety of computers and softwareinvolved. This process is described in some detail in Appendix B for the benefit of futureusers of the system at UBC.Chapter 4The IRAS Selected Protostellar CandidatesIn this chapter, we first discuss the continuum data and then the spectral line dataseparately. Figures showing these data are contained in Appendix C. Trends and groupbehaviour among the sources are then investigated in Section 4.3. Finally, some of thesalient features of each source observed are noted in the source-by-source discussion.4.1 Continuum DataData on the continuum emission obtained at the JCMT as described previously arepresented in Figure C.l. For each source observed, maps made at 1100 pm, 800 pmand, if available, 450 pm are displayed. The mean noise levels at each wavelength are0.09, 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 aswell as the four IRAS bands (recall footnote 3, p.7, on the IRAS survey). The IRAS LowResolution Spectra are also shown in the same diagram.The contour maps at a given wavelength are shown using the same contour levels forall sources to facilitate source to source comparison, with the following exceptions. The800 pm emission of source #04 is particularly bright; for this reason, this map is shownwith contours with values five times greater than for the other sources. Also, sources #15and #21 were found to be particularly faint. Here, I have kept the usual contour levelsto avoid confusion. However, they have been supplemented with “dash-dot” contours at58Chapter 4. The IRAS Selected Protostellar Candidates 59intermediate values which allows for finer contouring.4.1.1 Results from Continuum DataThe integrated flux contained in each of the maps has been measured using facilitiescontained in AlPS.’ In integrating emission over the sources with consistency, I havechosen 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 arenot as well delineated as in the 1100 pm and 800 pm maps. This may be due to thespatial smoothing associated with the larger beam size but is more likely attributableto the much higher S/N ratio achievable at these lower frequencies. The resulting fluxvalues in Janskys are tabulated in Table 4.1. They are also plotted as AFA in theSED’s of Figure C.1, in keeping with the practice in MDPS and other works in theliterature. The uncertainties in these values due to uncertainties in atmospheric opacityand 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, aremuch 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 factorgreatly, since it appears as eTA. The uncertainty is estimated2to be a factor of e±.7S or(+110%, —50%) for the 450 pm observations. While these “factor-of-two” errors mightappear 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 somefeatures of source morphology are hinted at. Consequently, two dimensional Gaussians1 Astronomical Image Processing System (AlPS) is a software package developed by and availablefrom the (U.S.) National Radio Astronomy Observatory.2This is a fairly liberal estimate. For example, the results of dust emission model fitting to be reportedin Section 4.1.2 suggest that these errors might be reduced by perhaps a factor of two.Chapter 4. The IRAS Selected Protostellar Candidates 60Source 1100 jim 800 jim 450 jimNo. (Jy) (Jy) (Jy)# 02 2.26 13.9 47# 04 7.90 56.2 78# 06 N 7.63 23.8 —# 06 S 6.68 16.4 —# 07 6.67 20.0 125# 09 4.57 11.2 321# 14 8.99 19.2 51# 15 1.17 2.9 —# 21 1.09 2.6 —# 25 4.73 9.9 —Table 4.1: Integrated continuum fluxes. Source fluxes are integrated over the continuummaps 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 angularsizes 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 appearsto 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 whilethe others remain more or less constant. Also in Table 4.2, the position angles of thefitted Gaussians are listed. As one would expect, the position angles are similar at thethree (or two) wavelengths, except for sources with low ellipticity.Sources #04 and #06 have also been independently observed in the survey work ofWilking et al. (1989). They have been able to estimate source sizes at .\ = 2.7 mmfrom interferometric measurements. They obtain values of 13 + 6 arcseconds and 13 + 4arcseconds for sources #04 and #06, respectively. Although, at first glance, these valuesChapter 4. The IRAS Selected Protostellar Candidates 61Source Size Position AngleSource 1100 pm 800 pm 450 pm 1100 pm 800 pm 450 pmNo. (arcsec) (arcsec) (arcsec) (degree) (degree) (degree)#02 22x7 22x12 20x9 78 69 73#04 28x21 23x17 17x11 91 86 53#06N 39x21 51x14 — 61 38 —#06S 22x18 26x16 — -77 -43 —#07 21x14 22x17 17x11 -47 -21 6#09 23x20 20x18 21x17 66 10 50#14 53x26 50x29 28x23 -8 -2 7#15 35x23 40x26 — -65 -56—#21 24x6 22x14 -77 -84 —#25 34x24 31x22 — -65 -60 —Table 4.2: Source angular size and position angle. Measured by performing two-dimensional Gaussian fits to the reduced maps and removing (“deconvolving”) contributions 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 onJCMT maps, the differences may not be significant as the results of Wilking et al. arenot obtained from full mapping of the sources. One would expect some agreement withsource 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 ModelsThese data shown here are also being studied with dust emission models. The detailsof 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 infraredintensities [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) emissivityChapter 4. The IRAS Selected Protostellar Candidates 62(function), source size, and dust temperature. For all sources modelled, best results wereobtained by fitting a two-component model consisting of a small, hot (- 130K) and alarger, cool (rs? 35K) component. (The median size ratio is 50 for the two components.)4.2 Line DataThe J = 1 —÷ 0 lines of CO, ‘3C0, and C180 have already been published separately inanother paper (MDPS) along with the VLA and IRAS data. Subsequent observationsmade at higher frequencies using the JCMT are shown here in Figure C.2. Each sourceis presented on its own page. The five point maps of CO J = 3 —÷ 2 and CS J = 7 —* 6are made with 7 arcsecond beam separation so as to cover a similar area as the ReceiverA beam which is used for the lower transitions. This provides for useful comparisonslater in our modelling work. Spectra taken of various isotopic lines are also shown inseparate panels.4.2.1 Results from Line DataA cursory look at the new line data tells us that the 12C6O lines of many of our sourcesare quite prominent. This immediately gives us a lower limit on the gas densities sincea minimum density of approximately io cm3 is necessary to excite the CO J = 3 —‘ 2line, We see also that none of our sources shows a C34S J = 7—, 6 line detected clearlyabove the level of the noise. This gives us an upper limit in density l06cm3at ourtypical noise levels). In addition, the fact that we do detect lines of C32S whose abundanceis only a factor of 20 above C34S (see Table 4.3) immediately places constraints on thedensity estimates.In order to extract more quantitative information from our observations, an analysisusing a simple LVG model has been performed. The code used in this study assumes aChapter 4. The IRAS Selected Protostellar Candidates 63homogeneous, isothermal cloud under uniform collapse (Avery, private communications).It is used to predict TR* given the density, n, and kinetic temperature, Tk1, of the gasalong with the velocity gradient, , in the cloud.The procedure used can be described in the following way. First, the gas kinetictemperature is fixed by using a line that is expected to he optically thick. Normally,our choice is ‘2C’60 J = 2 —, 1 or J = 3 — 2 line. Since r is very large at the highdensities expected for these protostellar clouds, TR* is insensitive to anything but Tk1under the assumptions of this model. That is, the line acts as a good thermometer.3Theoptically thick assumption can be checked at the end but is seldom necessary due to thehigh densities concerned and the high abundance of CO. Complications to this use of COlines arise when the peak of the line is affected by self-absorption. However, peak valuescan he estimated using techniques such as the fitting of Gaussian profiles. Next, for eachobserved line, a series of (n, ) pairs of solutions which represent the observed TR* iscomputed. In order to perform the computations, some knowledge of the abundancesof each molecular and isotopic species is required. Obviously, the choice of values forabundances affects our results at a fundamental level, especially in comparing data ondifferent species. For this study, abundance ratios have been compiled from the literatureand the adopted values are listed in Table 4.3. The LVG solutions are next plotted as3This thermometer effect can be understood in the following way. In a simplified picture of a homogeneous cloud, the excess radiation temperature one observes above the background can be expressedas= T0 [ eTa/Tx— I — eTa/Tog— i] (i— er)where T = hv/k-, Tb9 corresponds to the cosmic background radiation, r is the optical thickness of thecloud 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 athigh densities, r — co thus we haveT —oeTa/Tkjn— 1 + const.which is a function only ofChapter 4. The IRAS Selected Protostellar Candidates 64Molecule Abundance Reference‘2C160 3.0 x 10 adopted by de Jong et al. (1975)‘3C’60 3.4 x iO adopted by de Jong et al. (1975)1218 9.0 x 10—8 from 160/180 ratio of Wannier (1980)l2l7 1.5 x 108 from 180/170 ratio of ‘ATannier (1980)12325 3.0 x i0 Walrnsley (1988)1234 1.5 >< 10_b Walrnsley (1988)Table 4.3: Molecular abundances. Adopted values from the literature for abundances ofmolecules observed in this study are given relative to the abundance of H2. The referencescited 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 curvescross, 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, whenour “error-bands” are considered, our solutions give us cause for much confidence andoptimism. 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 dusttemperatures, Td,t, obtained for the large/cool component (McCutcheon et al 1995 andSection 4.1.2, this work), have been compared with these values which describe themolecular gas component. They are generally found to agree within reasonable errorestimates. This agreement suggests that the molecular gas and the dust are co-extensivein our sources. That is, frequent and wide-spread collisions between the gas and dustparticles 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 latercalculations relating to the molecular matter.There appears to be a clustering of derived densities around n 105cm3.This effectappears not to be an artifact of the LVG analysis, as discussed in Appendix A.1.1. Thedisagreement with the higher densities one might expect in a protostellar cloud may beio7E0>(0C1)U,oChapter 4. The IRAS Selected Protostellar Candidates 65iog108 C170 2—1C170 3—213C0 3—2C34S 7—6/CS 5—4/ CS 7—6////_____________solution in this regionI ...,.... I1 10 102 io51Velocity Gradient (km spc’)Figure 4.1: Example of LVG solutions. The curves shown here are for Source #14. Thedashed lines are upper limits in density derived from lines not clearly detected above thenoise. See text for a full description.Chapter 4. The IRAS Selected Protostellar Candidates 66Source Density Veloc. GradientNo. (K) (10cm3) (km s1 pc’)Nominal Range Nominal Range# 01 44 15 4 50 17 0.04 100#02 50 4 2 8 6 3’15# 04 37 15 3 100 9 3 300# 06 36 13 6 20 9 3 30# 07 34 11 3 20 15 2 75# 09 42 13 5 40 7 3 37#13 44 6 4-’ 7 5 3’10# 14 31 14 9 18 8 5 ‘ 12#15 26 6 4’-.’ 10 5 3’--’lO# 18 29 15 3 50 7 1 30#21 19 11 — 9 —# 22 20 25 15 60 26 10 75# 25 39 66 15 120 70 10 100#39 41 42 — 53 —Table 4.4: LVG model results. The total gas density and velocity gradient for each sourceis presented with the adopted, ‘nominal’ value, as well as a range of values reflectingthe agreement between various combinations of lines modelled. T1 is the gas kinetictemperature determined as described in the text.Chapter 4. The IRAS Selected Protostellar Candidates 67Source MolecularNo. Mass#02 22M®#04 23M®#06 26M®#07 82M®#09 64M®#14 307M®#25 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 derivedusing the ranges of density given there. For Source #06, the mass represents both Northand South components.indicating the presence of other effects such as the beam filling factor.4 This would beimportant 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 componentof each source. For sources with well measured sizes from the continuum maps, thishas been possible, assuming spherical geometry to obtain the third dimension. Since wealready 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 theparent molecular cloud for each of the protostars in our list.4.2.2 Column DensitiesSince the density ranges derived in the above were disappointingly wide, another measureof the cloud gas density was computed in order to guide us in the process of physicalinterpretation.4The filling factor represents the ratio of source size to the telescope beam size and quantifies thedilution of the source signal when its value is less than unity (e.g., when the beam is larger than thesource or when the source is clumpy).Chapter 4. The IRAS Selected Protostellar Candidates 68Source Nc170No. (cm2)# 01 3.7 x 1015# 02 4.8 x i0# 04 1.4 x 10’s# 05 7.9 x 10’s# 06 1.1 x 1016# 07 6.8 x 1015# 09 6.1 x 1015# 13 7.7 x 1015# 14 6.9 x 1015# 15 4.1 x i0’# 18 6.5 x iO’# 21 3.9 x 1015# 22 4.2 x 1015# 23 2.6 x 1015# 25 7.4 x 1015# 26 8.1 x i0’TaMe 4.6: C170 Column Densities.Chapter 4. The IRAS Selected Protostellar Candidates 69Values for column densities5 for the C’TO molecule, Ncl7o, were computed using itsJ = 3 —, 2 line and are listed in Table 4.6. This can be accomplished with standardtechniques using the C’TO intensity integrated over the line (f TAdv) and assuming thatthe line is optically thin. This assumption can be verified by examining the values of rcomputed during the LVG analysis already performed, to see if the line is indeed opticallythin. The excitation temperature is assumed equal to the ‘2C0 excitation temperatureand is listed in Table 4.4 asIn giving up any information about the third dimension, we have been able to reducethe random component of the uncertainty significantly. Estimated random errors of+10% in each of Tk1 and f Tdv result in 6Ncl7o of only +12% when combined inquadrature. These values can be converted to Nn2 by scaling by the molecular abundancelisted in Table 4.3 or by using the relation given by Frerking et al. (1982).4.3 Possible Trends and PatternsOne of the original aims of this project was to search for any patterns that might exist in alarge sample of protostellar objects. In our first paper (MDPS), for example, we were ableto 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 havebeen observed or derived and can now be examined, particularly for correlations withcharacteristic parameters of the emerging main sequence object.Figure 4.2 shows the gas density plotted against Tea, the effective temperature ofthe stars, derived in MDPS, for all sources modelled. Teff is a measure of the zero5Column density is a two-dimensional density obtained from the three-dimensional space density ofparticles projected to the celestial sphere and has units of number per unit area. It measures the numberof particles (in this case C170 molecules) in the region sampled by the telescope beam, which resemblesa “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 706__________________________________________________________________________________________________10 I I I.‘I,E0Cio5Cl)CID00io4 I4.5 4.4 4.3 4.2 4.1log T0ffFigure 4.2: Patterns in our sample. Densities derived from modelling the observed linedata are plotted against the stellar effective temperature in search of correlations. Thefilled squares indicate sources confirmed to be pre-main sequence (PMS) in MDPS. Theopen 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 inthe effective temperature are difficult to estimate and are perhaps large. However, asdescribed in MDPS, many of the steps that contribute errors to the final value of Teaare systematic in nature. Therefore, for the purposes of the present discussion, whilethe overall scale might be affected, we do not believe the scatter to be affected to such adegree as to mask an inherent correlation in the data.] Unfortunately, inspection of thisdiagram reveals no striking correlation. In any event, the sizes of the error bars comparedto any variations seen suggest no trend can be found in this set of data. Other pairs fromour list of parameters (including Nciro, molecular mass and spectral type) haveChapter 4. The IRAS Selected Protostellar Candidates 71also been plotted in search for a correlation. No obvious trend has been found. A similarconclusion was reached in our investigation of the continuum map data and derived dustmodel 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 alreadybeen discussed and is almost certainly a factor. Unfortunately, improving the precisionsignificantly is not straight forward without some fundamental change in our methods.Nonetheless, this was the reason for which C’70 column densities were calculated. Inforgoing any information on the third dimension, the random part of the errors has beenreduced to +12%. While the sizes of individual error bars have been reduced, the degreeof scatter seems unaffected.If there is truly no underlying pattern here, we will be faced with some differentpossibilities. 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 theMDPS catalogue from the IRAS PSC. Figure 4.2 shows that our sources span a zX log Teffof only 0.35, or ZAMS spectral types between 08 and B3.5 only. Thus, differences in theobserved and derived quantities due to differences in the main sequence stellar mass maynot 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, thenwe reach another conclusion; the range of evolutionary stages represented by sources thatmeet 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 theoreticalwork 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 timeprotostellar accretion has ended.” Our sources fall into this category according to themass range of 10 r’.’ 25 M® inferred from the spectraltypes (Mihalas and Binney, 1981).Chapter 4. The IRAS Selected Protostellar Candidates 72This is short-lived indeed and the stellar component may not have sufficient time toinfluence the observed properties of the parent cloud.One last limitation of note concerns our principle of quantifying the properties of theparent molecular cloud iu order to learn abont the emerging protostar. If the characteristics of the protostar are subject to many other (often external) factors that influencethe star forming environment, then there will not be a simple, well defined correlationbetween the molecular properties and the properties of the embedded protostar.In any event, our sample of star forming clouds appears homogeneous in the parameters investigated to the best of our abilities.4.4 Future WorkCertainly, there is much sense in following up the work already described by modellingthe molecular lines in increased detail. For the most part, such a project would requireno additional observations. The line data already available, particularly in CO, showmuch structure and contain much mysteries to be examined. The results and insightsgained through the LVG analysis are expected to form an invaluable starting point forthis phase of the ongoing investigation.From the outset of this survey, we have concentrated on star forming objects of highluminosity. It may be of interest to make a companion survey of low luminosity starforming regions for a number of reasons. For example, compilation of the same type ofdata for two classes of objects may reveal some distinguishing characteristics (other thanthe luminosity). However, to a large extent, this has already been accomplished by otherinvestigators such as in the works referred to in Section 5.6. Although the observationsthere cannot be compared directly to those presented in this work, in that the focus andinstrumentation are not identical (as would be the case for a companion work specificallyChapter 4. The IRAS Selected Protostellar Candidates 73designed for comparison purposes), they do constitute a useful database for comparison.As already mentioned, for example, the low and high-luminosity star forming sources dodisplay differences in the dynamical parameters. [l4nax, K.E., and Lmech are all smallerfor low-luminosity protostars, r is larger.]4.5 Individual SourcesDuring the course of this study, some features of the individual sources have been notedand are discussed here briefly. Also, some results from MDPS are given inside squarebrackets. (Where ambiguities exist for kinematic distances, D1±,6 the preferred valuesas described in MDPS are shown here as Dne or Dias.) In addition to the data alreadydiscussed, a fraction of our 39 sources has been mapped in the J = 1 —* 0 lines of COand ‘3CO 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 waythough it has not been observed with the JCMT.)Source #01; IRAS 18134 — 1942 : [Compact H II region. Close to, or on mainsequence B2. Dnear = 1.5 kpc.] The CO peak at v e’-’ 22 km s appears to be aseparate cloud and is also seen in CO J = 1 —* 0 data. The absorption feature in COcoincides in velocity with the main peaks of ‘3CO spectra. (i.e., self absorption.) It isnot seen as distinctly in CO J = 1 — 0 spectra, most likely due to beam dilution. Thatis, the self absorption appears to be confined to a small region. A CO J = 1 —> 0 map isavailable.6 Kinematic distance, or is perhaps the primary method for estimating distances to spectralline sources within the galaxy. It is derived from the observed radial velocity of the source and anestablished kinematic model of galactic rotation. The latter describes the velocity of objects in orbitabout the galactic centre as a function of galactocentric distance. X’Vith some simple geometry, a radialvelocity— 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 74Source #02; IRAS 18151 — 1208 : [Pre-main sequence BO. Dnear = 2.8 kpc.]Enhanced wing on the positive velocity side of line peak. Molecular mass 22 M®.Source #04; IRAS 18162 — 2048 : [Compact H II region. Probably on mainsequence B0. 10 pm absorption feature. Dnear = 1.7 kpc.] Emission at 800 pm isexceptionally bright. This is the only source for which the far—infrared source angularsize varies with wavelength in a significant way. (Size decreases with decreasing A.) Thisis not an artifact of the differing beam sizes, as this effect has been specifically accountedfor (and is not manifested in other sources). Self absorption in CO lines. Molecular mass23 Al®. Wilking et al. (1989) report a continuum source size of 13 + 6 arcsecondsbased 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 areall coincident, within the IRAS position centroid. However, the 450 pm peak is displacedby 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 simpleand conducive to good modelling.)Source #06; IRAS 18265 — 1517 : [Compact H H region. Close to or on mainsequence B2. Dnear = 1.6 kpc.] The continuum maps show two components. Theyhave been labelled #06N and #06S or North and South. This causes problems in dustmodelling since the IRAS data have insufficient angular resolution to enable us to studythe two components separately. Wilking et at’. (1989) report a continuum source sizeof 13 + 4 arcseconds based on 2.7 mm interferometric measurements, somewhat smallerthan our maps indicate.Source #07; IRAS 18316 — 0602 : [Compact H II region. Probably pre-mainsequence ‘- 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 75Source #09; IRAS 18517 + 0437 : [Pre-main sequence r’ B1. 12 pm absorptionfeature. Dnear = 2.6 kpc.] There is a CO J = 1 —* 0 feature at v ‘-S’ 32 km seenperhaps also in CO J = 2 —, 1 but not in other lines. (Line shapes are simple andconducive to good modelling.) Molecular mass e-’ 64 M®.Source #13; IRAS 20178 + 4046 [Compact H II region. Close to or on mainsequence c- 09. 10 pm absorption feature. Df = 3.1 kpc.] Line shapes are simple andconducive to good modelling. CO J = 1 —* 0 map is available.Source #14; IRAS 20188 + 3928 : [Compact H H region. Probably on mainsequence BO. D1 = 3.2 kpc.] The appearance of‘2C’60 J = 1 —* 0 and J = 3 —* 2are quite different, with J = 2 —, 1 line taking what is perhaps an intermediate lineshape (as would be expected with its intermediate excitation and beam size). Molecularmass s 307 M®. This is our highest value, due to its large angular size and distance. Gasdensity 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 thecontinuum maps have been supplemented with intermediate ones (dash—dot contours).The CO feature at v ‘ 11 km s seen in J = 1 —i 0 line can also be seen here but it islikely a separate cloud. A CO J = I —* 0 map is available.Source #18; IRAS 20286 + 4105 [Main sequence ‘—‘ B0 and extended H Hregion if associated with the radio continuum object. If not associated, object moves offthe main sequence to the right. 12 pm absorption feature. Dkj = 3.5 kpc.j The fivespectra of CO J = 3 —> 2 are supplemental, “service” style, observations made in 1992using Receiver B3i and replace the one spectrum at (0,0) taken originally with the SuttonReceiver. 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 Suttonreceiver.Chapter 4. The IRAS Selected Protostellar Candidates 76Source #21; IRAS 21334 + 5039 : [Compact H II region. Probably main sequence BO. D1r.j = 5.0 kpc.] This source is relatively faint in its submillimetre emission. The contours in the continuum maps have been supplemented with intermediateones (dash—dot contours). A CO J = 1 —* 0 map is available.Source #22; IRAS 22272 + 6358A : [On main sequence B3.5, or pre-mainsequence. Probably won’t produce H II region. Dk1 = 0.8 kpc.]Source #23; IRAS 23545 + 6508 : [Compact H II region. On main sequenceB2. Possible 10 um absorption feature. Small Extended Source IRAS X2354 + 651is associated. = 1.2 kpc.] The CO J = 3 —* 2 line appears to suffer from a lot ofself absorption, as opposed to showing two separate components. A CO J = 1 —* 0 mapis 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-mainsequence hut may have a weak radio continuum source in which case it is a compact H Hregion and on the main sequence. D = 1.1 kpc.] Self absorption in ‘3C0 J = 3 —* 2indicates a high gas density, which is confirmed by the modelling, as it yields our highestdensity of 6.6 x 105crn3. Molecular mass 42 M®. LRS 1 and 2 are noisy hut areshown for completeness. A CO J = 1 —* 0 map is available. This source has also beenmapped in the CO J = 1 —* 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 bipolaroutflow. Carpenter et cii. report that no 6cm continuum source is detected in associationwith 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.JSource #31; IRAS 03235 + 5308 : [Compact H II region. Probably on mainsequence BO. 10 im absorption feature. Dkj = 6.0 kpc.jChapter 4. The IRAS Selected Protostellar Candidates 77Source #36; IRAS 05553 + 1631 : [Compact H II region. Probably on mainsequence ‘ B3. 8.5 zm emission feature. = 0.8 kpc.] The CO J = 1 —. 0 emissionhas been studied extensively in earlier efforts (MDPS and McCutcheon, Sato, Purtonand Dewdney, unpublished) and found to be a bipolar outflow. The CO J = 1 —> 0line 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 (byassociating the source with the 5254—5258 complex of H II regions) in contrast to ourkinematic 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 ‘3C0 line suggests a high gas density for this source.Unfortunately, the high noise in the CS data prevents us from improving on the upperlimit in gas density of 106cm3.Source #39; IRAS 07427 — 2400 [Compact H II region. Probably pre-mainsequence 08. Dk = 7.7 kpc.] Strong ‘3C0 lines including self-absorption in J = 2 —1 indicate a high density, as is shown by the model work, yielding the second highestdensity in our list.Chapter 5NGC 6334 I & I(North)5.1 Observed Data; OverviewMolecular line spectra have been observed at a large number of beam positions aroundthe northern end of NOC 6334 encompassing peaks I and I(North). The observed positions are summarised in Figure D.1. The coverage varies for each line due to practicalconsiderations during the observing runs. In addition, the lines observed using ReceiverA are subject to coarser sampling reflecting the larger beam size. That is, the grid positions for Receiver A lines are separated by 20 arcseconds while the B-band lines havegrid intervals of 10 arcseconds. In both cases, the beam spacing is less than twice theinterval 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 COJ = 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 extendingalmost 100 km s wide. While the raw spectra are not shown here, it should be notedthat the quality (in particular, the flatness) of the baselines is excellent throughout thespectrometer 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 ofemission. Figure 5.1 clearly shows the enormously wide wings at NGC 6334 I while the78Chapter 5. NGC 6334 I St I(North) 7940.-*ct L,SJ )AA M (40ri10)F-20(—30,—i 10)10 ---(—20,—iou)0—100—50 0 50 100Velocity (km/s)Figure 5.1: Sample CO J = 3 —> 2 spectra. CO line profiles from beam positionscorresponding 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 themap reference position (a = 17h1m348,98 S = —35°42’17”). For I, spectra from threepositions are shown to illustrate the bipolar wing structure.Chapter 5. NGC 6334 I & 1(North) 80line at the I(North) peak is “quiescent” by comparison, although by normal interstellarstandards, this line would itself be regarded as a wide one (L\Vj’wHM ‘- 20 km s andAl4wzI 80 km -1).12 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 = 3 —* 2 line on peak I is remarkable. (SeeFigure 5.2 which also shows the C170 — C345 spectrum.) In addition to the enormouswidth of the CO line, there are a number of other lines (identified and unidentified) seenin both sidehands, suggesting either a very high gas density or a high temperature, orboth, 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 butclumps of CO at different velocities. The existence of such fast moving CO “bullets” hasbeen established in other outflows (Bachiller and Gómez-González, 1992). Before thishypothesis can be confirmed, however, the suspected lines must be found to be (1) in thesame sideband as the main CO feature and (2) at the same velocity in another transitionof CO or in some other species. In our case, the J = 3 —* 2 transition of C170 is availablealthough we would prefer to examine the J = 2 —, 1 spectrum of 12C0 at this positionif one were available (since the abundance of C170 is a factor of 2000 lower). There areno spectral features that clearly satisfy both these criteria, thus favouring the originaltheory of high density/temperature and rich chemistry.The sharp “absorption” feature at vi = +6.5 km s appears to be very much real,as it remained with the main features when we retuned the receiver to slightly differentfrequencies to determine which of the features were in the image sideband. As we usedthe same “off” position in position switching throughout the entire map, which itselfhas been checked against another blank sky position, it can also be argued that the‘FWHM: Full Width at Half Maximum.2 FWZI: Full Width at Zero Intensity. In practice, “zero intensity” means one follows the signal untilit is indistinguishable from the noise.Chapter 5. NGC 6334 I & I(North) 81*3020(LsB)345.5 345.6 345.7 345.8 345.9 346.0(usB)(LsB)3020*0(usB)Frequency (GHz)Figure 5.2: Spectra centred on NGC 6334 I. Each panel shows two frequency scalescorresponding to the upper and lower sidebands, labelled USB and LSB. The top panelincludes 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. Thebottom panel includes the C’70 J = 3 — 2 (337.06 0Hz, USB) and C34S J = 7 —* 6(337.40 GHz, USB) lines. A host of other lines can be seen in the bandpass in additionto the target lines.337.0 337.1 337.2 337.3 337.4 337.5Chapter 5. NGC 6334 I & I(North) 82absorption featnre is not due to the presence of a CO line in that reference position.The same feature was also present in spectra taken a year later using a different receiver.The CO J = 2 —* 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 absorptionfeature in their spectrum appears to be only one channel wide, although that is the widthwe would expect. [We measure SV c 1.5 km s (7 channels) from our spectrum, whereasthe Bachiller and Cernicharo spectrum has a resolution of 1.3 km s per channel.] Oncloser examination, this “absorption” feature is visible at the same velocity in spectra atother beam positions. (It is not as prominent perhaps because there is less backgroundradiation to be absorbed at this frequency.) A plausible explanation is that we areobserving the entire cloud through another, foreground CO cloud.5.3 Molecular Line MapsUsing the two spatially well sampled lines, CO J = 3 —÷ 2 and CS J = 7 —i 6, a numberof contour maps have been constructed. Figures 5.3 and 5.4 show the integrated lineemission. The CS map clearly shows the two peaks, I and I(North), with the southerncomponent being the brighter at its peak by a factor of two. In the CO map, I appearswith 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 30arcseconds to the northwest of I. It is also recognizable as a lobe or an extension fromthe main source in the map of integrated CS emission, although not as prominently. [Forfuture reference, this feature is designated NGC 6334 I(NWX) or simply NWX. Thisfeature is not to be confused with the features to the northwest of I mentioned in HarveyChapter 5. NGC 6334 I & I(North)30 -35° 42 00 -I I8330 -—35° 43 00” -30350 44 oc”350 44 3Q17” l7m 4O 38sFigure 5.3: Map of velocity integrated CO emission. The CO J = 3 —* 2 line emissionintegrated over the velocity range —50— +50 km s1. The first contour and the contourinterval are both 50 K• km s1.I I I I0LO0)z0z-JC-)036 34S 32 30 28 26RIGHT ASCENSION (B1950)Chapter 5. NGC 6334 I & I(North)3035° 42 00”30010a)z2_° 43• 00”2-J0uJ030_350 44 00” -350 44 3017h 17m 4O 38 36RIGHT ASCENSION (B1950)84Figure 5.4: Map of velocity integrated CS emission. Similar to the CO map but thevelocity interval is —35—+ +25 km s1 as the line emission does not significantly extendbeyond this range. Contour levels are multiples of 10 K . km s1.I I I • I34S 328Chapter 5. NGC 6334 1 & I(North) 85and Gatley (1983). The authors refer to two such extensions or lobes but these correspond in position to their IRS—1—2 (6 arcseconds away from IRS—I—i) and the H H regionNGC 6334 E (1 arcminute from IRS—I—i).]Figure 5.5 shows the positions of the compact near infrared objects from the JHKphotometry (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. Thepositions of the H II regions E and F from Rodriguez et al. (1989) [marked in the figureas “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 Harveyand Gatley; the radio source E is 20 arcseconds in diameter.) We see that indeed the nearinfrared objects appear to form a cluster around peak I while their distribution is rathersparse toward I(North). In particular, there are no near infrared objects detected in theimmediate 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 emissionfrom source I. This object is also coincident with NGC 6334 I / IRS 1 of Becklin andNeugebauer (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 lesscoincident with this CO peak. Also in this area is IRS-I-i of Harvey and Gatley. Theobserved and derived parameters from these studies are discussed in Section 5.6 with ourown results.We see no significant molecular feature centred on the position of F. However, NGC6334 E [size — 20 arcseconds] is situated on the edge of the northwest molecular extension of I. In Straw et a!. (1989), the authors attempt to associate their IRS 20 withChapter 5. NGC 6334 I & I(North)—35° 42 00” -30 -_350 43 QQ -30 -+SHM3O ÷SHM2986—35° 44 00”—35° 44 30+ SHM 130(81950)Figure 5.5: Overlay of near JR and other compact objects. Locations of compact objectsin 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 andRCM F are VLA H II regions from Rodrfguez et al. (1989). The object marked IRASis 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.)30I I I • I I • I0U)O)z0z-JC-)LU017h 17m 4O 38+ SHM 2I • I I • I36RIGHT ASCENSIONChapter 5. NGC 6334 I St I(North) 87NGC 6334 E, with some problems in positional coincidence. IRS—I—4 of Harvey andGatley (1983) is found to be closer in position. However, it is interesting that we find nosigns of significant molecular activity at the positions of these objects. In the context ofthis work, the Straw et al. IRS 17 can he seen associated with our NWX, the northwestmolecular extension (Fig 5.5). Figure 4 of Straw et al. (1989), a (K, J — K) diagram,shows IRS 17 to be an A6 (or later) star, with A = 10 mag or more. In this light, NWXappears to he a separate centre of star formation activity. It pales in comparison to (themain 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 requiredangular 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 COand D.3 for CS. We see immediately the high velocity wing emission of CO from sourceI throughout all slices. The emission from source I(North) is more or less confined tobetween —25 and +15 km s. The northwest extension to peak I, seen in the integratedCO map but not obvious in the CS version, can be seen prominently in CO slices withvelocities between —25 and +15 km s1, same as those occupied by I(North). We seethat the I(North) peak appears in the velocity integrated maps due to the lines beingbroader 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 accountfor the increased line width) is unclear if there is indeed a lack of a luminous object atthe core of I(North). However, in the context of collapse velocities toward the core, it isreasonable to expect this trend in line widths as it simply reflects the range in projectedinfall velocities at different projected distances from the core. That is, at lines of sightaway from the projected core, much of the infall (or outflow) motion would be tangentialto the line of sight, while our observations are sensitive only to radial velocities.Chapter 5. NOV 6334 I & I(North) 88It is perhaps more instructive to examine the CS slices; the northwest extensionfeature is even brighter than peak I(North) in the sixth slice [vlsr = —10 —* —5 km s9but is conspicuously absent in the adjacent slices. The individual spectra show thepresence of enhanced emission on the blue side of the line centre.The wing emission is perhaps best summarised in Figure 5.6. This diagram showsmaps 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 aroundpeak I with the peaks of blue and red shifted emission separated by ‘- 22 arcminutes.The H H 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 thisoutflow motion and likely refer to the same object. This wind, as well as the material inthe northwest extension must represent a great deal of mass and momentum. This pointwill be examined further with model studies.An unfortunate consequence of these lines being so wide is that we cannot see, asclearly, 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 about3 km s1 making it too small to extract from our wide and complex lines of CO. Nonetheless, with the CS data, a R.A. — velocity diagram has been made (Figure 5.7). The CSJ = 7 —* 6 data were chosen because the lines are relatively narrow in addition to beingwell sampled. Unlike the ammonia data of Jackson et at. which contains no emissionfrom the centre of the source, the CS emission is peaked in the centre. Thus we do notsee two islands of emission, in this type of diagram, as seen by Jackson et at. in theirFigure 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 seensuperposed 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 wingsChapter 5. NGC 6334 I I(North) 89I I I I30” -//_/\N35° 42 00”//N/ N30 -/00)Na /z /o _350 43 00 -,- \ NNI \/z——--o-—LU0/ \If”N_350 44 00 - I\ N/_350 44 30” -I I Il7’ 1 7m 40s 348 32 3O 28RIGHT ASCENSION (B1950)Figure 5.6: CO 3 —* 2 wing emission. The CO line emission is averaged over velocityintervals (—40 km s1 —* —15 km s1) (dashed contours) and (+5 km s1 —* -1-30 km s’)(solid contours) to bring out the blue and red shifted wings, respectively. The contourlevels 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) 905.0000.000-—5.000-—10000—15.000I I I I17h 17m 408 36 328RIGHT ASCENSION (B1950)Figure 5.7: R.A. — velocity diagram for peak I. The CS J = 7 —* 6 data for declinationsbelow —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.>(1)-jC’,EC-)0-juJ>Chapter 5. NGC 6334 I & I(North) 91seen in Figure 5.6 are indeed coincident in angular position. One is left to explain thedifference in the velocities of these systems which spans more than an order of magnitude,(AV 100 km s1 for CO, LIV 2.5 km r’ for NH3) although the signs of the velocitiesare in agreement. As Bachiller and Cernicharo (1990) point ont, the system is surely nota molecular disk in Keplerian orbit around the centre of peak I as originally proposed byJackson et al. In light of our data as well as those of Bachiller and Cernicharo showingthe molecular outflows, we would not expect the disk material to be aligned with theoutflow axis and be of comparable size as the outflow. In the standard theories, (see, forexample, Shu at al., 1987) one predicts the axis of the disk to be aligned to the outflowwhich will also be much more extended than the disk. In any event, a disk would verylikely be disrupted by this high velocity flow. These authors suggest further that theslower outflow delineated by their own HC3N data as well as the NH3 data of Jackson atal. are generated by the presence of the fast CO outflow. The exact mechanism for thiscoupling between the high and low velocity flows remains unspecified, although there isample mechanical energy available (see Section 5.6). However, if the low velocity flowis being ‘dragged out’ by the high velocity material, one might expect more turbulencethan is evident from the HC3N and NH3 lines. An alternative explanation is offered inSection 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 toits many remarkable features. However, as highlighted below, we can see that sourceI(North) is very remarkable in itself.In the first place, we have already taken note of the widened lines, indicating thepresence of outflow activity. However, it does not display a beautiful bipolarity as inChapter 5. NOC 6334 I & I(North) 92the case of I. Rather, the outflow appears “isotropic.” We do not see separate, spatiallydistinct, blue and red shifted lobes in our maps. Of course, this could simply be due toa chance alignment of the outflow axis with the line of sight. Nonetheless, the outflowregion covers an angular extent of ‘-.‘ 35 arcseconds (corresponding to -‘ 0.3 pc), comparedto our 14 arcsecond beam, and represents many map grid positions. If there is trulysuch an extended outflow around a core so little evolved (as also seen by the lowerdensity/temperature and simpler chemistry) that there is not yet a thermonuclear energysource, then we must also ask ourselves what is driving this flow. The obvious sourceof energy is the collapse itself but then there must be some mechanism which imparts agreater share of the infall energy to a small fraction of the mass in order to arrange thisoutflow.Perhaps the CO wings we observe are not due to outfiowing of the gas but to theinfall itself. The question of infall vs. outflow can, to some extent, be settled using theconclusions of Leung and Brown (1977) based on line profiles computed specifically toaddress this point. In particular, the similarity between the line shapes of 12CO and13C0 favour arguments for outflow. Also, the required mass of the central, gravitatingobject(s) to cause this infall would be extraordinarily high (e.g. Zuckermann et aL, 1976).5.5 LVG ModelsBy running a simple LVG program, the core component of the observed lines (i.e. notincluding the wings) at each beam position has been modelled as a separate, spherical andhomogeneous cloud. This choice of geometry, which came with the LVG code, may bejustified to first order if we consider it in the following way. While the region sampled bythe telescope beam resembles one of many contiguous columns through a large cloud, theobserved emission from within a specific column is likely dominated by that from someChapter 5. NOC 6334 I & I(North) 93central (in the radial direction) region which in itself might resemble a homogeneoussphere. The procedure used is essentially the same as that used for the IRAS sourceswhich has been described in Section 4.2.1. The results from this modelling are listed inTable 5.1. A contour map of the derived densities is shown in Fignre 5.8.5.5.1 Model ResultsAs entries in the table indicate, and as expected from the initial examination in Section 5.2, there is indeed a disparity in densities between I and I(North) [1.3 x 107cm3and 3 x 105cm3 respectively.] In the context of the evolutionary sequence suggestedacross the NGC 6334 complex, in which peak I corresponds to a very young object andI(North) an even younger one (e.g. Moran and Rodrfguez, 1980), the lower density derived for I(North) is perfectly expected. That is, one would expect I(North) not to haveyet 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 densitywith other parameters (Chapter 4), this may appear to be an outdated expectation. Thispoint is discussed further in Section 5.7.2 and shown not to be a concern here.] The highdensity at peak I, together with its higher gas temperature [T11 = 44 K, compared to33 K for I(North)] would tend to explain the host of lines observed at this position.We note that this density above 107cm3appears only at one grid position. Ratherthan attributing this to an error, we believe it is a reflection of the small size of the highdensity 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 discussedfor the IRAS sources. They are based on the range of solutions as given by differentcombinations of observed lines and similar error bounds apply here. In addition, Table 5.1Chapter 5. NGC 6334 1 & I(’North) 94Position flH2 CommentsOffset (“) (K) (cm)(—80, —80) 34 1.6 x io 4 lines only(—60, —60) 29 3.4 x i05(—60, —50) 30 4.4 >< i0 4 lines oniy(—60, —20) 24 2.0 x i05 4 lines oniy(—60, 0) 23 4.0 >< iO(—60, +20) 26 6.0 x iU 4 lines oniy(—60, -1-40) 29 8.0 x iO 3 lines only, Tk guessed(—50, —120) 39 3.0 x i05(—50, —110) 40 5.0 x iO(—50, —100) 39 5.0 x iO(—50, —60) 35 3.0 x iO 4 lines only(—40, —40) 26 1.6 x iO(—40, —20) 26 5.0 x iO(—40,0) 25 1.4 x i0(—40, -1-20) 24 1.7 x iO 4 lines only(—40, +60) 31 2.5 x iO 3 lines only(—30, —120) 39 4.0 x iO(—30,—hO) 44 L3x107 Ipeak(—30, —100) 35 1.3 x 106 I peak(—30, —10) 33 1.8 x i05 3 lines only(—30, 0) 33 2.3 x 1O 3 lines only(—30, +10) 28 3.0 x iO 3 lines only(—20, —100) 33 4.0 x i0(—20, —40) 28 1.0 x iO(—20, —20) 31 1.3 x ho5(—20, —10) 37 2.2 x iO 3 lines only(—20, 0) 33 4.5 x iO(—20, +10) 31 4.1 x iO 3 lines only(—20, +20) 33 8.5 x iO(—20, +40) 25 4.5 x i0_______________________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 notedas the derived densities are expected to suffer from greater uncertainty. Other positionshave five or more lines observed.Chapter 5. NGC 6334 I I(North) 95Position Tk1 nH2 CommentsOffset (“) (K) (cm3)(—10,—b) 34 1.3x105 3linesonly(—10,0) 34 3.0 x iO 3 lines only(—10, +10) 33 3.4 x iO 3 lines only(0, —80) 32 1.3 x iO 4 lines only(0, —60) 27 2.0 x iO(0, —20) 33 1.2 x iO 4 lines only(0,0) 33 3.0 x io I(North) peak(0, +20) 27 1.6 x i0 4 lines only(0, +40) 24 4.0 x iO 4 lines only(+20, —60) 28 1.0 x i0 4 lines only(+20, —20) 28 1.3 x(-1-20,0) 28 1.2 x iO 4 lines only(+20, +20) 28 9.0 x iO(+20, +60) 24 3.2 x i0 3 lines only(+40, —60) 28 2.0 x iO 4 lines only(+40, 0) 26 6.0 x iO 4 lines only(+40,+20) 23 1.0 xTable 5.1: LVG model results over NGC 6334, continued.Chapter 5. NGC 6334 I & I(North) 96I I I I I • I • I30”_350 42’ 00”2 35° 43’ 00”Z_5°M’30”.I I I17h 17m 4Q5 38 36 345 32 28 26RIGHT ASCENSION (81950)Figure 5.8: Derived gas densities over NOC 6334. The contour values are (4, 12, 20, 28,36, 60, 100, 1000) x104cm3. See caution in the text regarding numerical artifacts.Chapter 5. NGC 6334 I & I(North) 97notes map grid positions where the number of observed lines is four or less, indicating thedegree 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 theerrors are expected to be systematic in nature, spurious noise features are not generallyexpected in this map. Unfortunately however, it is not free from numerical artifacts, particularly those inherent to the process (and algorithms) of drawing contour lines throughirregularly sampled data. Features at the periphery of the mapped area such as the sharpridge in the southeast corner and the manner in which the lowest contours seem to fillthe 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 numericalartifact as described above. We note that since these densities are derived by modellingthe cores of the lines, there is no corresponding distinct peak for NWX which is a featureconspicuous by its wing emission (and is distinguished from Tin that way).5.5.2 C34S J = 7 —* 6 Anomaly at Peak IIn running these LVG models it became apparent that interpretation of the high intensityof the C345 J = 7 —* 6 line at peak I is less than straight forward. While the line is notdetected in T(North), it appears as a = 8 K line at the southern peak. Applying thestandard analysis yields a wide gap between solutions obtained using CS (but withoutC345) and that obtained with C345 (ignoring CS). That is, while the CS J = 7 —* 6line observed as = 18 K indicates (in conjunction with the CO lines) a gas density of6 x 105cm3,the C34S line favours ii ‘- l07cm3.One possible explanation is that, for some reason, the 345 isotope is overabundant inChapter 5. NOC 6334 I & I(North) 98this object. Under this hypothesis, one finds a 325/345 ratio of about 5 from our observedintensity 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 C34S J = 7 —÷ 6 line indicates andthat the CS lines have become optically thick, or that the transition has thermalised, andin either case are insensitive to the exact value of the density. This is expected to occurat densities above 7 x 106cm3(Mnndy 1984 and Snell et al. 1984), a value consistentwith our C345 derived densities. It would also tend to explain another anomaly, that theratio IA[C34S 7 — 6]/lj[C3455 — 4] has a value of 1.5 where one would normally expecta value not exceeding unity [since lines of molecules as rare as this are normally foundoptically thin.] That is, perhaps observations of the J = 5 —÷ 4 transition of C345 alsosuffers from the non-linear effects of optical thickness.In order to resolve this question, a proposal was submitted for “Canadian” serviceobserving at the JCMT . We requested observations of the ‘3C5 molecule in the J =5 —* 4 and J = 7 —* 6 transitions. Since this molecule is expected to be 3 to 18 timesless abundant than the C345 molecule (depending on the latter’s ‘yet to be determined’abundance), we expect neither transition of that molecule to he influenced by the effectsof high or intermediate optical depths. Further, the interpretation requires no knowledgeof the 325/4S ratio. In fact, our data would have enabled us to assign a value for thisratio. The proposal had been approved and scheduled for observations. Unfortunately,they were not carried through due to unsuitable weather conditions. We currently planto re-submit the proposal at a later opportunity.The related question of the line ratio between the J = 5 —+ 4 and 7 —÷ 6 transitions ofC345 might he a simple matter of beam size mismatch. That is, the telescope beam forthe lower transition observations samples a larger area of the sky. A proper comparison3Service observing is one in which a set of observations with a telescope is made by someone otherthan the proposers of the observations, usually a member of the observatory staff. It is most useful forshort programmes with straight forward observational requirements.Chapter 5. NOC 6334 I St I(North) 99might most easily be made if we can simulate the larger beam for the 7 —> 6 data. OurC34S data base, unfortunately, is insufficient to resolve this question withont additionalobservations. (We do not have observations at all grid points.) The sampling of the C34S7 —* 6 line around peak I that we do have suggests that it is quite possible that emissionaveraged over the area of the J = 5 —* 4 beam would bring the line ratio closer tounity. An alternative explanation, that the line intensities for these different transitionsmeasured using different receivers have been miscalibrated in such a way as to give rise tothis (erroneous) line ratio seems implausible since we have exercised some care during thecalibration process (and with particular regard to this possibility). Additionally, similarline ratios would also be expected to be found with other molecules. One should notforget, however, that whatever the resolution to this problem, the question of sulphurisotopic ratios remains unanswered.For the present, the density of 1.3 x 107cm3 as indicated by C34S J = 7 —, 6 line(the most optically thin line available) is adopted.5.6 Derived Parameters: The Bipolar Outflow at NGC 6334 IAs described in Section 1.4 and Chapter 2, a new computer code was developed to modelthe radiative transfer of molecular line emission with fewer restrictions than are requiredfor the LVG code already in use. One of the prime applications of this new code has beento model the wide wings of the CO J = 3 —* 2 line around peak I. The new model codedeveloped is particularly useful here, since the old model of a homogeneous cloud underuniform collapse seems not to represent precisely the case at hand. In addition to thegeometry, 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 thatthe velocity gradient is not large, but, for example, it must be everywhere large comparedChapter 5. NGC 6334 I & I(North) 100Size, d 0.2 pcGas Density, n 5 x l0cm3Mass, M 2.5M®Max. Velocity, 1/max 65 km s’Kin. Energy, E 1.8>< lO46ergMomentum, F 82 M®km 51Mass Flow Rate, M 8 x 104M® yr1Outflow Lifetime, rfi0 3.2 x io yrKinematic Timescale, rij 3.0 x io yrMechanical Luminosity, Lmech 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 thecost of increased computing resources, my method specifically refrains from making theseassumptions. In any event, our LVG code is not capable of predicting line shapes whichare of primary interest here.The best models of the line core and outflow wings yield densities of n.’ 5>< 103cmover 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 103cm)x (0.2pc)3x m0i= 2.5M®with a kinetic energy of M < V2 >= 1.8 x l046erg, where mmol is the mean particlemass (= 2.0 InH), < V2 >= (37 km s’)2 is the second moment of the velocity, andthe factor of two accounts for the number of lobes. In units that are perhaps morefamiliar, 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 across-sectional surface A is M = AnVmax = 8 x 104M® yrt The outflow lifetimecan then be estimated as Tfiow = M/M = 3.2 x io yr. A second timescale can hederived 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 canChapter 5. NGC 6334 I St I(North) 101be calculated as = 0.2pc/65 km s = 3.0 >< l0 yr, in agreement with Tifow. Themechanical luminosity4 ascribed to this flow is Lmech = < V2 >= 89 L®. [Thesevalues are summarised in Table 5.2.]The reader is cautioned that these values are derived ignoring the effects of velocityprojection to the line of sight. However, since the positive and negative velocity lobespartially overlap in the maps, the flow direction is likely not far from the line of sightand the projection effect can be expected to be very small. Further, if the line of sightlies 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 needfor corrections. If corrections are needed, however, they come into play as cor1 e for Fand M, cor2 e for E, and sin 9 cor3 9 for Lmech, where 9 is the angle between the flowaxis and the line of sight [for a detailed discussion, see Cabrit and Bertout (1990)]. For9 as large as 45°, the correction factors are only 1.4, 2.0, and 2.0, respectively. Thus, wedo not expect projection ambiguities to be the dominant source of error. However, aftersome analysis, Cabrit and Bertout (1990) argue that the best estimates for momentumand 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 Cernicharo (1990). They found M = 2.3 M®, F = 92 M®km s1, M = 10 x 104M® yr’,E = 4.3 x lO46erg, and Lmech = 170L®. Although Jackson et al. (1988) foundn i0 crn3 in the NH3 lobes, these were estimates based on the kinematics of amolecular disk in a Keplerian orbit. Since this interpretation is no longer supported, weneed not concern ourselves with the density discrepancy.Harvey and Gatley (1983) estimate the far infrared luminosity of this source, theirIRS—I—i, to be 8 x 104L®. This is based on the observed combined flux of IRS—I—i,Mechanical Luminosity output per unit time of kinetic energy through the outfiowing gas.Chapter 5. NCTC 6334 I & I(North) 1022 & 3 and an estimate of their relative contributions to the total flux. We see that thefar infrared, radiative luminosity is much greater than the mechanical luminosity in theoutflow (kin > Lmech), or that the outflow represents only a small fraction of the totalenergy budget.We can estimate some dynamical parameters of the system following the approachof Lizano et al. (1988). In their investigation of HR 7—11, they propose a model inwhich an Extreme High Velocity (EHV) neutral H I wind is ejected in two opposingstreams from a stellar source. When the atomic wind comes in contact with the ambientmolecular cloud and becomes entrained in it, momentum is transferred to that part ofthe cloud, thus driving the molecular bipolar outflow. The bipolar structure of the H Iflow 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 stellarmass loss rate. On initial contact, the H I is moving at the speed of the fastest movingCO observed, approximately 65 km r’. As the two components interact, momentum istransferred. To account for the molecular momentum derived above, the required mass ofthe accumulated mass from the H I flow is = (82 M® km s’)/(65 km s_1) = 1.3 M®.This is then the total mass ejected from the protostar (or its disk). The rate of mass lossis then, roughly, 1l/I = 1.3 M® / 3200 yr = 3.9 x 104M® yr1. The truevalues for i1I and are possibly higher since the present calculation assumes 100%efficiency in momentum transfer. An implied efficiency in the transfer of kinetic energyis 33%. This is obtained by comparing the kinetic energies of the molecular outflowand the assumed EHV H I wind. Key to this discussion is this assumption that such aneutral wind actually exists in the NUC 6334 I system. This has yet to be confirmedobservationally. Direct observation of the EHV H I emission is certainly desired beforeproceeding much further with this analysis.However, this model does offer an explanation for the low velocity NH3 (Jackson et al.,Chapter 5. NGC 6334 I & I(North) 1031988). HC3N (Bachiller and Cernicharo 1990) and CS (this work) lobes seen at the sameposition as the CO outflow. It is reasonable to expect to find these molecules in greatestconcentration at the frontiers of the swept-np material (or the “working surfaces”). Theseare the locations where the outflow enconnters the ambient molecular cloud (shock), theswept-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 expectedif, as we argue, the outflow direction is almost coincident with the line of sight. The lowervelocity 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 molecularoutflows (associated with Herbig-Haro objects). Our values for the outflow timescale rfor NGC 6334 I ranks among the smallest of the entries in their Table 2. The kineticenergy for NGC 6334 I is a full order of magnitude greater than the largest values foundin their list. (Median values from the list of Edwards and Snell are = 25 km s1, r =3 x lO4yr, E = 2.5 x lO44erg.) More recently, Morgan et al. (1991) mapped and analysednine outflows from their survey of low luminosity (> 220L®) young stellar objects inthe L1641 region. Typical values of Lmech from this sample are two or three ordersof magnitude lower than our value for NGC 6334 I. Dynamical parameters derived byBachiller 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) havemapped and compiled similar parameters for outflows near more massive young stellarobjects and found M 0.3— 100 M®, V 10 — 50 km r’, and ‘r lO4yr, typically.Our values for the outflow in NGC 6334 I are in line with those of this group of highmass star forming regions.It should be noted that the attributes of this outflow that make it so unusual orperhaps even unique can all be traced to the unusually high velocities of the outflowing matter. As will be discussed in Section 5.7.2, if wide wings such as these seen atChapter 5. NGC 6334 I & I(North) 104NGC 6334 I turn out to be common, then some aspects of the implied relative youth ofthis system may need to he questioned.5.7 Discussion5.7.1 Relative AgesIn one of the earliest investigations on NGC 6334, Cheung et al. (1978) suggested thatthe complex displays evidence of sequential star formation across the region, since theemission peaks were located in succession with regular spacing. While we cannot comment on star formation sites elsewhere in the NGC 6334 complex, the relative ages ofpeaks 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 themore 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 inI(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 toexpand and accumulate material since its initiation. From the age of this outflow alone,we expect AAge 3 x lO3yr between I and I(North).5.7.2 Are EHV Outflows a Common Phenomenon?In light of the above discussion on NOC 6334 I and the detection of EHV molecularoutflows 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 theChapter 5. NGC 6334 I & I(North) 105following questions. Are these EHV outflows more common than previously believed?Have we systematically missed detecting them in the past by observing with insufficientbaseline and resolution? Do we need only to look with the appropriate, newly available 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 Iso prominent in J = 2 —+ 1 (Bachiller and Cernicharo, 1990) and in J = 3 —> 2 (thiswork) were not reported in the J 1—, 0 line by Dickel et aL (1977) who mappedthe entire NOt 6334 complex in CO. One may point to theoretical arguments favouringwing formation in the higher J transitions (e.g., Mitchell, 1993). However, more carefulinspection of the Dickel et al. observing parameters yields an explanation which as muchas ensures that, present or not, the J = 1 —* 0 counterparts of these wings would nothave been detected. Not only do they suffer from beam dilution due to the 70 arcsecondbeam of the NRAO 11 m but their observations were made in the frequency switchingmode. The 20 MHz shift used corresponds to L\V = 52 km s, restricting the likehoodof noticing the very wide, but relatively flat, wings.Even in this present work, if the receiver system had not given such a confidence inspiring, 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 preprocessing, 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 specificallylooking 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 andSnell (1984). The FCRAO 14 m telescope in the CO J = 1—÷ 0 line gave a heamwidthof 45 arcseconds and allowed a maximum bandpass corresponding to 333 km s. HHChapter 5. NGC 6334 1 & I(North) 1067—11 was included in this work but the EHV flow had to wait for discovery by Bachillerand Cernicharo (1990). The Bell Laboratories 7 m used by Bally and Lada (1983) fortheir CO J = 1 —, 0 survey used a filterhank capable of AV = 1300 km but its largebeam biased against the detection of such confined features.A campaign to this end has already been undertaken by Koo (1989) and Margulisand Snell (1989) using a technique slightly different from the one suggested here. Theyobserved known outflow sources in principally the CO J = 1 —* 0 line with moderateresolution. [NRAO 12 m (Koo 1989) and FCRAO 14 m (Margulis and Snell 1989)]. Theydetected EHV features in a handful of sources in their lists by making very low noiseobservations (Ia noise as low as 3 and 8 mK, respectively).Of course, we have already a wealth of useful observational data on known outflows inour MDPS sample. Except for the declination limit, the IRAS source at NGC 6334 I doeshave the required characteristics to he included in the MDPS list. Since we have seen noEHV 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 issueis a complex one and we need to address at least the following points. First, with theangular resolution involved, detection of wide wings is dependent on the exact directionto which the telescope is pointed. If we had observed NGC 6334 I only at the positionof the IRAS object, the EHV wings may not have been discovered. There is only thered shifted wing at relatively low levels. Without an expectation of finding the wing, thefeature 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 morphologyand 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) 1075.7.3 Neutral Hydrogen Wind in NGC 6334 I?In Section 5.6 we made some simple calculations based on the assumption that an EHVneutral 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 Iobservations 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 theArecibo 300 m telescope. This is the very instrument used to measure the H 1 spectrumat HH 7—11. It offers the spatial resolution and sensitivity of a large, filled-aperturetelescope, and is equipped with a good wide-band, high-resolution spectrometer. Unfortunately, it cannot he steered to the declination of NGC 6334 (—36°).One may, however, use the Arecibo telescope to conduct a systematic search forH I winds in the other known bipolar outflows accessible from it. This will he a goodcounterpart the the CO programme eluded to in Section 5.7.2.Chapter 6Conclusions6.1 The IRAS Selected Protostellar CandidatesFrom the original list of 39 sources, (sub)millimetre continuum maps have been madeusing the JCMT for nine of them. In all cases, the maps show the source to be resolved bythe telescope beam. Continuum fluxes have been measured from each map. A separatestudy using the same data with dust emission models has shown that each of our sourcesconsists of two components: hot & small and cool & large. The latter is identified withthe 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 C345 line hasnot been clearly detected in any of our sources. This molecular emission has been studiedusing LVG models with resulting gas densities of the order of 105cm3 for all sourcesinvestigated. These gas densities, as well as other derived quantities (including columndensity, stellar effective temperature, spectral type and molecular cloud mass), have beenexamined for patterns and correlations, perhaps a manifestation of the main sequence butnone has been found. Thus, the well observed portion of our sample appears to constitutea homogeneous collection of protostars, within the limitations of our precision.108Chapter 6. Conclusions 1096.2 Northern End of the NOC 6334 ComplexThe northern end of the NGC 6334 complex encompassing peaks I and I(North) hasbeen mapped extensively with CO J = 3 —* 2 and CS J = 7 —* 6 lines and with otherlines 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 highvelocities approaching 65 km/s accompanied by a low velocity flow. An extension topeak I, 30 arcseconds to the northwest, has been identified in the velocity integratedline maps due to increased line width at this location. LVG models indicate densities inexcess of 107cm3for peak I while the results for I(North) show a much lower value of4.5 x 105cm3. AU observed and derived parameters are consistent with the suggestionof 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 using a general radiative transfer model. The best models yield outflow densities of5 x 103cm for each wing, corresponding to an outfiowing mass of 2.5M®. Values forphysical/dynamical parameters have been derived (Table 5.2) and are seen to be in linewith those of other high luminosity protostars. The one exception is the extremely highCO velocities in the wings. The BPO has been compared to that of the HR 7—il systemwhose EHV molecular outflow is thought to be driven by a H I wind. The proposed H Iwind for the NGC 6334 I system is estimated to have accumulated 1.3M0 of stellar ejectaover a lifetime of — 3000 yr, at a mass loss rate of 4 x 1V4M®/yr. This is a parameterof the forming star, rather than of the parent molecular cloud, thus providing a checkfor, or a connection to, stellar formation theory. The age of the outflow, since it is welldeveloped in I but not in I(North), sets a lower limit on their age difference at r’j 3000years.Chapter 6. Conclusions 110Model studies also indicate that there may be an anomalously high abundance of the345 isotope at the position of peak I, perhaps indicative of some stellar activity.6.3 General ConclusionsWith 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 usefulinsights, even though many of the implicit assumptions were challenged (by myself) orpushed to the limit in this current application. When increased amount of information isavailable, or when the increased effort is warranted, the line transfer model code developedfor this study has been used. In particular, the wide CO wings at NGC 6334 I wasmodelled using this tool.On the observational side, the importance of fully mapping star forming molecularclouds has been recognised, if one is to detect and recognise some subtle features ofsignificance. A single pointed observation at the IRAS position appears not always to besufficient.6.4 Summary of Suggested New ObservationsIn various parts throughout this thesis, suggestions for desirable future observations havebeen made. In this section, a brief summary is made of these suggestions.Already proposed are the 13CS 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, likelyexplanations for the anomalous C345 line intensities at this location.Also regarding NGC 6334 I, obtaining direct evidence for the presence of an atomicwind by measuring its H I spectrum has been discussed in Section 5.7.3. 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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. InfraredMillimeter 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 andM. 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 AOther DiscussionMuch discussion on the data and results has been made in Chapters 4 and 5. Some pointsof discussion of a more general or parenthetical nature but nonetheless worthy of note arenow addressed. More importantly, some discussion relating to the MDPS sources havebeen reserved for this chapter since it builds on experience from the NGC 6334 portionof this thesis.A.1 TRAS Protostellar Candidates RevisitedThe following points concerning the MDPS objects have been reserved until now as theymake 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—’ 10cm3.Originally, this was cause for some concern in that our LVG code might have some built—inlimitations that constrain the range of possible solutions. However, the results obtainedusing the same code for NGC 6334 indicate that the code (and my own application ofit) is indeed capable of arriving at solutions at both higher and lower densities, givenappropriate observed parameters. Also, the lack of a detected C345 J = 7 —, 6 line inany of these sources supports the idea of an upper limit to density. Thus, we could nowlook for an astrophysical explanation for this common density with some confidence thatwe are not suffering from a model artifact.117Appendix A. Other Discussion 118A.1.2 Future WorkIn the NOC 6334 portions of this thesis, we learned of the advantages of mapping amolecular cloud. The discovery and subsequent investigation of the bipolar outflow is aprime example. Since we believe this BPO may have gone nnnoticed if we had observedit only at the coordinates in the IRAS catalogue, it is possible that there are moreinteresting and/or complex features in our IRAS sources yet to be discovered. Maps ofour IRAS sources similar to the NGC 6334 maps (CO/CS combination) may prove veryprofitable. This discussion is also examined from another point of view in Section 5.7.2.A.2 In generalIn addition to topics raised with respect to one or the other of the two projects, thereare some points common to both efforts. These matters are now discussed.A.2.1 Potential for Problems with the LVG AnalysisThe LVG code used in this study has been tested by its author and used to producereasonable and insightful results (e.g. Richardson et al. 1985). In addition, our owntests and examinations indicate it is performing properly within the assumptions of themodel. (See for example, Section A.1.1. Also, models have been computed in certainlimiting cases where analytical solutions are possible.) We must now consider whetheror not there are problems with the way in which the code has been applied. That is, “isthe use of these LVG models appropriate here?”It seems generally safe to assume there are no significant problems with our methodfor determining the gas kinetic temperature from the ‘2C0 lines (recall section 4.2.1).That is, the temperature of the gas is well represented by 12C0 emission. This opticallythick line, as stated earlier, is a good thermometer since it is insensitive to all otherAppendix A. Other Discussion 119parameters. While it is true that self absorption is sometimes an impediment, correctionsto the required precision are easily made in practice. However, we might expect problemsas we apply this T1 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 12C0 J = 2 —* 1 line, the gas contributing to the CS J = 7 —* 6line 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. Ifindeed we are sampling different spatial regions (or extents) with different molecules oreven isotopes, results obtained using homogeneous model clouds cannot be accepted atface value.One idea is to separate the CO problem from the CS one and solve for them independently. However, this method is not without its own problems. In addition tohaving fewer independent data, our curves in the (n, ) plane tend to run parallel toeach other (separation is normally within the error bars) over the ‘reasonable’ portionof the parameter space for both the CO-only and CS-only plots. (See Figure 4.1 for anexample.) Thus, it is normally the combination of CO and CS data that yields a solutionin practice. (See also Section A.2.3.) It is also more difficult to obtain a value for Tkusing CS only. The available lines are of intermediate optical thickness such that all threequantities (T1, n and ) have to be solved for simultaneously. In the CS (and C34S)works of Snell et al. (1984) and Mundy et al. (1986) for example, the authors simplymake a priori assumptions for their values of T1. An alternative approach is to dropthe homogeneity assumption. This is discussed again in Appendix 2.7.2.There are other obvious limitations to these models, having to do with the simplifyingassumptions regarding geometry. One is that the cloud size is assumed to match thetelescope beam size (with a fiat response) exactly. While it is difficult to correct forthe contribution due to the gas infall motion having perhaps a significant transverseAppendix A. Other Discussion 120component, the required correction for the (over and under) filling factor can be mademore easily to first order. An assnmption with perhaps a more profonnd consequenceis that of homogeneities in density and temperature. One difficulty arising from thisassumption has already been discussed above. While this assumption can simplify thenumerical problem greatly, it also renders the model incapable of reproducing such effectsas 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 bythese assumptions since we generally expect dense and hot cores to be located in starforming clouds. However, the results from dust modelling of the continuum maps doesprovide 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. Sincethe two components individually are homogeneous ones (in density and in temperature)and one of them (large & cool component) represents the same material modelled herewith the PVC gas model, then it can be argned that the gas can also be approximatedas homogeneous.A.2.2 Line Transfer ModelIn 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 learningexercise, in that an intimate understanding of all known processes is necessary in orderto express each effect in a quantitative manner as is required to write the computercode. Having a flexible modelling tool allows investigation of a number of astrophysicaleffects. For example, our initial LVG analysis did not allow proper treatment of selfabsorbed lines which are quite common among the sources investigated here. As well,nonuniformities are allowed in the physical quantities, making the model process morerealistic. In addition to simple tapering—off of molecular gas density, this feature hasAppendix A. Other Discussion 121been 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 flexibilityit is designed to allow. Preservation of generality can be its own enemy in some casesin that while the models allow us to investigate many effects, we are, in effect, requiredto investigate all of them. This is the common pitfall of many models that attempt toexplain everything in one giant step. For example, we cannot truly separate the linebroadening mechanisms of turbulence and a large velocity gradient. With this level ofgenerality, one cannot ensure any sort of uniqueness in the solutions, especially in lightof the observational uncertainties. In practice, however, it is not at all difficult to fix thevalue 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 LVGanalysis) and is also not uncommon. The choice of the turbulence parameter can bereviewed by comparing a selection of computed models.A.2.3 Additional Lines for Observation/ModellingOriginally, 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 sessionsthat inclusion of an additional line may prove useful. Model calculations indicated thatthe available data at hand allowed for large ranges of values (for density, etc.) in the solutions consistent with the observed line intensities. It was hoped that the CS J = 5 — 4line, having slightly different excitation characteristics, could serve as that additionalline. We realised it may not be different enough, hut since the line was observable withthe JCMT, it was included in our subsequent proposal. Also, using a different moleculein search of more contrasting excitation characteristics, would require knowledge of additional parameters including its abundance and it was decided to use this conservativeAppendix A. Other Discussion 122approach 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 nowthat the two lines tend not to give independent information in the density range of thesolutions as obtained. In retrospect, a separate initiative such as a programme to observethe 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 BData TransportIt is too often the case in modern astronomy that the astronomer toils over computersfor a significant fraction of the time simply converting data formats as he moves from onesite, 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 ourhome institution in a useful form for analysis are outlined in the following.B.1 SpectraThe flow of observational data for spectral line work is summarised schematically inFigure B.l.Initially, line observations made at the JCMT are recorded into ‘GSD’ data filesaccessible by SPECX,1 the reduction software in common use at the JCMT. SPECX hasbeen used to examine the data at the Mauna Kea summit as they are collected and alsofor first stage reduction (such as baseline and bad channel removal). It runs on VMSplatforms including the computers at JAC.In order to continue the work, it was necessary to transform and transport the datafiles to forms readable by the computers available to us at the University of BritishColumbia (UBC). These are the university main frame computer running under what isknown as the Michigan Terminal System (MTS) and our SUN 4 running UNIX. Originally, the SUN was not available and all post-reduction was done on the MTS platform1 SPECX is written by ft. Padman and has been provided by her for use by the JCMT community.123Appendix B. Data Transport 124/Figure B.1: Data flow for line observations. See text for further description.Appendix B. Data Transport 125using local software systems (called ‘IRApS’ and ‘CLOUDS’) which use data in what Icall the ‘clouds.hig’ format. To put data in this format, it was first necessary to transformthe GSD files of SPECX into a more accessible form. The best way seemed to be to usea SPECX facility to make an ASCII dump of each spectrum. This makes an ASCII tableof channel values preceded by a few lines of header information. Files containing theseASCII 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 theASCII tables to the ‘clouds.big’ format.One of the first software packages we installed on the SUN as it became operationalwas IRAF.2 It has proven quite effective, not only in the presentation of data with itsplotting facilities, but also in basic reduction of the kind once done using SPECX. Toread the data into IRAF, one of two things was done. New data from JCMT/JAC wereput into their ‘FITS’ format before leaving the site and transported to UBC either ontape or by Internet. This, so called ‘FITS’, is not quite the same as the ‘real’ FITS3but lists the data elements in ASCII form; the convention of the header is much thesame. (NRAO 12m data used to come in this form for a time.) Fortunately, IRAF hasa facility for reading data of this form called ‘rtextimage’. In order to combine this newdata 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 providedby the Dominion Radio Astrophysical Observatory (DRAO), namely ‘madr’ and ‘plot’.The DRAO software take data in yet another form. For the spectral line data, anothershort 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 isoperated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperativeagreement with the (U.S.) National Science Foundation.FITS (Flexible Image Transport System, Wells, et al., 1981) is a data format standard designed tofacilitate the exchange of astronomical data among different institutions and computational platforms.Appendix B. Data Transport 126format.B.2 Continuum MapsThe on-the-fly mapping data are stored, as they are collected, into GSD files at theJCMT. The first step in reducing these data is to make R.A.— dec. maps ont of them nsingNOD2.4 This program contains facilities for correcting for atmospheric extinction (whichvaries across a map) and deconvolving the dual beam response pattern. There existstandard 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 tapein (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 datain their own internal formats, have FITS readers for two-dimensional map data as partsof the packages, making this particular step relatively painless.The exchange of continuum data between these systems mentioned here is also shownschematically in Figure B.2.“ NOD2 is a software package that is used at the .JCMT to extract maps out of raw ‘scan’ data byperforming such tasks as deconvolution of the dual-beam response pattern. The program originates fromJodrell Bank and Bonn [see Haslam (1974) for a succinct description of the system and the universalneed to free the astronomer from programming chores which he attempts to satisfy with NOD2] but theversion used at JAC appears to be imported from NRAO.“FITS”on diskz:zzz:hzz*UBC/Physics -- SUN 4/ UNIXAppendix B. Data Transport 127‘Observatory -- VAXNMStelescope& continuuibolometerI;,“UBC-- MTS/Figure B.2: Data flow for continuum observations. See text for further description.Appendix CFigures in Series: IRAS Protostellar CandidatesSome figures in series occupying many pages displaying observed data on the IRASselected protostellar candidates are placed in this appendix.128Appendix C. Figures in Series: BiAS Protostellar Candidates 129Figure 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 continuumemission observed with the JCMT at the wavelengths as shown. Circles showing thehalf-power beamwidths are shown in the upper left corner of each map. The shade andcontour 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 shadeand contour levels for the 800im maps are, similarly, multiples of 0.50 Jy/heam. Theshade and contour levels for the 450jm maps are multiples of 2.5 Jy/beam. There areexceptions to this rule, as follows. The contour levels for the 800gm map for source #04are greater by a factor of five from the other sources. The contours for faint sources, #15and #21, have been supplemented by “dash-dot” contours at intermediate values. Forsource #15 these are 0.0625, 0.1250 and 0.1875 Jy/beam at 1100tm and 0.25 and 0.75Jy/beam at 800gm. For source #21 these are 0.125 and 0.375 Jy/bearn at 1100tm and0.25 and 0.75 Jy/beam at 800tm. The lower right panels are spectral energy distributiondiagrams showing the emission integrated over each source, together with the IRAS broadband fluxes and Low Resolution Spectra.1021 00c;i E 10‘<10-1FigureC.l(i)Source#02.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.TheshadeandcontourlevelsforthellO0im,800gmand450gmmapsaremultiplesof0.25,0.50and2.5Jy/beam,respectively.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.s:.) 0. (b ct Cl, OD 0 0 01100Am08’—12°09’C 0 0 C U SSource#02RAS18151—1208450pmI0-S..0•18h151512°08°RightAscensionC 0 0 C I-) S 0 C 0 0 C C-, 5, 008’—12°09’08’—12°09’C’,’,I18hiSm12°08°RightAscension800AmI,0102,,IRightAscension18h15m12808s10102Wovelength(jim)C 0 0 C2OC 0 020°450pmFigureC.1(ii)Source#04.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap, circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.Theshadeandcontourlevelsforthe1100gm,800gmand450immapsaremultiplesof 0.25,2.5and2.5Jy/beam,respectively.(N.B.Thelevelsforthe800gmmaparehigherthanthestandardvaluesfortheothersources.)Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.48 49’Source#04IRAS18162—2048Noteunusualcontourlevelsfor80Ommap.RightAscension18bJ616RightAscension0, ct OD48’C 0 C—20°49’800#m18i6’16-7<10_1.e- CbiO_2•.‘10210ci,I 2RightAscension10Wavelength(Lm)FigureC.1(iii)Source#06.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.Theshadeandcontourlevelsforthe1100pmand800pmmapsaremultiplesof0.25and0.5Jy/beam,respectively.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.Ct 07 I-..Ct Ct 07Source#06IRAS18265—1517C 0 0 C—15°11a C 0 0—15°RightAscension17’18’o.800pmio’’’’Er.‘.‘,I•‘‘‘“I0IC.C“—I7,1o2/eC.C.I‘<10Iio2•’il8I26m3632RightAscension10102Wavelength(pm)1 0I.C 0 a C C.) .1) OC 0 a C C.) SFigureC.1(iv) Source#07.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.Theshadeandcontourlevelsforthe1100tm,800gmand450ammapsaremultiplesof0.25,0.50and2.5Jy/beam,respectively.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.rJ)Cb Cb CO 0 0 Cl, C) 0 CT.) Cl,1100gmIC.’,’•18”31m40S3SRightAscensionSource#07IRAS18316—06020459gm002—6°03 02—6°0336°026003 1 0 102E‘<10_i10_2C 0 a C 0 S80Om018°31m40°RightAscensionIRightAscension18°31m40°36°1010210’sWavelength(JLm)FigureC.1(v)Source#09.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.Theshadeandcontourlevelsforthe1100am,800amand45Oitmmapsaremultiplesof0.25,0.50and2.5Jy/beam,respectively.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.11OOWnc 0 0 S a0 0 c c) a, a C 0 0 C C, a, a450mjSource#09IRAS18517+04370j 0,.c tf Cr)Cl:,44$(b 0RightAscension384037 384037C,’.is”5;m48s44$RightAscension800LmI0384037 10’10Is10OS D1 10—110—’1851m45$DDciWavelength(pm)18h151m4.5$44$10RightAscensionCr)0 0 Cr, ci10210FigureC.1(vi)Source#14.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED,lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.TheshadeandcontourlevelsforthellOOtim,800irnand450tmmapsaremultiplesof0.25,0.50and2.5Jy/beam,respectively.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.ct Cb iD 0 0 Cb110OmCI.’.Source#14IRAS20188+3928029c 0 0 C S O39028 29C 0 V C C, a, o39028•20”18m524RightAscension800pm.029C 0 0 C C) ‘I, O39028 10E10D1<10_i10_2450gm,020”18’”5248”RightAscension44DD.1Q2Wavelength(ILm)--—---‘T-20”18’”52”48s10RightAscensionC 0 0 C 0 w cFigureC.1(vii)Source#15.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.Theshadeandsolidcontourlevelsforthe1100gmand800tmmapsaremultiplesof0.25and0.5Jy/beam, respectively.Sincethissourceisparticularlyfaint,“dash-dot”contoursat0.0625, 0.1250and0.1875Jy/beamareshownforthe1100gmmap,andat0.25Jy/beamforthe800tmmap, tosupplement theusualsolidcontours.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.1100pmI •,\,I20h21m40s36sRightAscensionSource#15IRAS20216+41070841°07 0841°07C 0 0 C 0 S OSOOjim0.LIi/i03••’•III‘1102D2 1 I <101.D010_2,,..1s:.) ci’ ci’ 0 0 ci’ C) ci,RightAscension20h21m40s36S10102Wovelength(Lm)I.CcIvI,21h33m28240200RightAscension800 0L.‘—0 0 0 Cl)FigureC.1(viii)Source#21.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.Theshadeandsolidcontourlevelsforthe1100gmand800immapsaremultiplesof0.25and0.5Jy/beam,respectively.Sincethissourceisparticularlyfaint,“dash-dot”contoursat0.125and0.375Jy/beamareshownforthe1100ummap,andat0.25and0.75Jy/beamforthe800gmmap,tosupplement theusualsolidcontours.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.1100gmSource#21IRAS21334+5039C 0 0 C 0 0 O C 0 0 C 0 1) 04050039’405003910’10E‘<10_i10_2IIDD I—.Wovelength(pm)21033m28s24020010RightAscension102l0-41100tmISource#25CIRAS00338+6i1213’C 0 0 C 0 S (263°12’ 0h34m005652’43’1RightAscension800mmI__________________________‘III,3‘‘‘‘II10-213’‘10)C2I1063°12’-—110Ct 0)II•I•Ilo_2o34m00$56’52’4810102io3RightAscensionWovelength(pm)FigureCl(ix)Source#25.ThecontinuummapsmadewiththeJCMTaredisplayedheretogetherwithaspectralenergydistributiondiagram(SED, lowerleftpanel)showingtheemissionintegratedoverthesource.AlsoincludedintheSEDaretheIRASbroadbandfluxesandLowResolutionSpectra.Foreachmap,circlesshowingthehalf-powerbeamwidthsareshownintheupperleftcorner.Theshadeandcontourlevelsforthe1100pmand800pmmapsaremultiplesof0.25and0.5Jy/beam,respectively.Seealsothegroupcaptiononp.129andacompletedescriptioninthetext.0D0I.Appendix C. Figures in Series: IRAS Protostellar Candidates 139Figure C.2: Molecular Line Data for the MDPS IRAS Objects. For each panel, thevertical 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 arcsecondsin NSEW directions as indicated. This is used for comparison with the J = 2 —* 1data (centre) and other lines whose beams are larger. Isotopic variations are shown inpanels below. Upper right is the five point map for CS J = 7 —* 6. Below that is C34SI = 7 —* 6 followed by CS J = 5 —k 4. See also the “guide,” next page.SourceIDCS7—6(o,+7”)CS7—6(+T’,o)CS7—6(0,0)CS7—6(—7”,O)CS7—6(0,—?”)axislabelledhereonlyCO2—113C03—213C02—1C34S7—6C1702—1C’703—2CS5—413C03—2c17o3—213C02—1TR* (K)CO3—2#01:18134—1942axislabelledhereonlyVisr(km/s) KCS7—6020406040 30 20 10 0CO 2—120 15 10 503‘II02040 Ao5204’060OVII0c17o 2—10c34s 7—6Cs5—45.o0204060cI2040602’04600204060‘ILlMI’I...ICo 2—1.1.Ji..M02040605111:0:2040,60.0TR* (K)axislabelledhereonly#02:18151—1208CO3—2Visr(km/s) 5 0CS7—6FVI—,,,I,,,I,,,I,..IlIllIlillIllIiiLiiliiili”25 20 15 10 5 0 10 5 0—5013003—2Cl73—20vf’f\t020406010 5 0204060I13co2—1Cl72—1c34s 7—6Cs5—40204060—5 0204060020406040 30 20 10 0.1...I.—I20 15 10 5 0 —2002040(K)___CO3-2axislabelledhereonlyVisr(km/s)#04:18162—2048—IlIlIllIjIlIl—-;id.CS7—6LLn.I.i.iiA I.CO 2—100204040 30 20 10 0 20 15 10 5 03—2,,,I,,,I,,,I,.JI,,55 02—1Cl 2—1C73—2IIC34S 7—6CS 5—4—2002040AfJ0I.1.—200204054—2002040—2002040I-’—2002040-18258—07373—210Co 2—1c17o 2—1v!rnriqyvTJ2040605111204060,,I,,,I,,,I,.—LLI.A*AIi.Ic34s 7—6Cs 5—4R (K)axislabelledhereonly20 10#05:CO3—2Visr(km/s) 5 0I-——CS7—6‘IIIIIIIIIIIIIIII.i2020406010I—--I010 0 5 02—12040600C17o3—25nvIw’qvvv-ç20406020406020406020406080l32—1A____3-2axislabelledhereonly-znI-#07:18316—0602Eh‘Isr(km/s) 5 0liiiIII:.‘I’.’TvCS7—6—,IllilIlIllIll.I,III,,I,—Co 2—1.IIIJ.LI.kaL.1ii’2040608020406080406080204060801015 10 5 0 5 03—2C73—2i5C172—1c34s 7—6CS 5—4V!vWvV.Ir.5.•I,.,I,,,I,,.III2040608020406080150 40 30 20 10 0T*‘R (K)axislabelledhereonlyVisr(km/s)#09:18517+0437CO3—2I•’’I’I,,.iliiiliiiliiiaCS7—600680Co 2—124•)25 20 15 10 5 0 10 5 n50 40 30 20 10 0 25 20 15 10 5 0 10 5 013C03—280C173—2_A.52—180Cl72—120406080—‘IIC34S 7—6CS 5—42040605 I-’‘ri,.II.V.20406080—52040608020406080Cl73—25 013C02—1Cl 2—1#13:20178+4046CS7—6axislabelledhereonlyTR* (K)CO3—240 30 20 10Visr(km/s) 5 U9n13C03—2‘J.20 15 10 5 0—200205-0c10 v-5 0 5 0—20020%%I—20020LC34S 7—6CS 5—4—20020—20020—2002013C03—20173—240 30 20 10 0 20 15 10 5 02—1i“9-I-*(K)axislabelledhereonlyVisr(km/s)#14:20188+3928CO3—25 0,IJ’•I———ICS7—6—,,II,,II,,I,I..,I,’II••I’’—wá_--iIiiiIiiiIiiCo 2—120 15 10 5 0;4;0020.15 0—200200II-200205 0c34s 7—6 CS 5—4017052—1—20020—20020—20020kiIYWCS7—6—20020——20020j.2A4AAA30 20axislabelledhereonlyTR* (K)Co3—2#15:1020216+4107Visr(km/s) 5,,I,,I,,,I,,..IlIlIllIllIll——2002015 10LLkEJ.1LLfl.If‘.vl35-325-00—20020C1O53—2o,k0C34S 7—6CS 5—47••9y’—20020—2002050 40 30 20 10 0—40—2002025 20 15 10 5 0 —4010 5 0L N..p LILaPt1LaaAiI..L...S.,’.,40 30 20.10 0 —40—20020TR*(K)axislabelledhereonlyCO3—2Visr(km/s)II-III#18:20286+41055iflilijüIA11&ihi0CO 2—1CS7—6c34s 7—6CS 5—43—2Cl73—2rwwwiir,,,I,,,I.I.—40—200205III-0—40—200205’I’II0IIIII.102000—5-3-—40—20—40—2020#21:21334+50390—80—60—40—20CO3—220axislabelledhereonlyV.‘.II10Visr(km/s)IIIpIIIIIIIII0;øACS7—620 10CO 2—1010—80—60—40—205J1,.—80—60—40—20A—80—60—40—203—2C17o3—25—80—60—40—205 0C34S 7—6CS 5—4U,’—80—60—40—20—80—60—40—20#22:CS7—6axislabelledhereonlyTR* (K)CO3—210 022272+6358AVisr(km/s) 5 020%4w1010CoiA2—1JuLL0—40—200205 0 4 2 03—2Cl73—2—40—2002025III04MMAVI.I—40—20020.:‘::c34s 7—6Cs5—4I...I...III-)—2—40—20020—40—20020Cl7 3—2Visr(km/s) 5 0I.I...I.c34s 7—6CS 5—4TR* (K)axislabelledhereonly#23:20 10 023545+6508CO3—2CS7—6—,I,,,I,,,),’’,I,,,I,,,I,,,ilIlilIlil‘3co 3—210 5 0 5 n—40—200205,51ST,Irr19,‘—40—20020U’ uJ—40—20020—40—20020T* (K)axislabelledhereonly#25:20 10 0CO3—200338+6312I-ii-i11k1IA1CS7—6A1.1L....L .HAILVisr(km/s)20A110 0—60—40—20013002—113C03—20173—2—60—40—20010-A0L1-<5—60—40—200—60—40—2005c34s 7—6CS 5—40—60—40—200—60—40—200Visr(km/s)T* R (K)axislabelledhereonly#26:00420+55305CO3—2CS7—6c34s 7—6Cs5—45III—80—60—40—20—I.LAIMLJA1LL5 0SI.!‘T’17Ir’‘!v—80—60—40—20—80—60—40—20#31:03235+5808axisTR*labelled(K)hereonlyV(km/s)10______________CO3—2IsrCS7—6.ovi12—1#36:05553+163130 20•1*(K)CO3—2axislabelledhereonlyVisr(km/s)Ihh.hI11..CS7—630AbiilLII.—2002040Co 2—1I —20020 4010 0 —200204010-2002040axislabelledhereonlyT ‘R (K)CO3—220 10#38:06103+1523ItVisr(km/s) 5 0flyTr’rCS7—6L’’20—2002040Co 2—113C02—102040406080100TR* (K)30-20-#39:axislabelledhereonlyVisr(km/s)CO3—207427—240010 0•IATT1II9TVW15 0CS7—6ZJcI406080100•1ts.:40608010015,,10 5-0 4060801002—1‘JiAppendix DFigures in Series: NGC 6334 I & I(North)Some figures in series occupying many pages or panels relating to observed data on NGC6334 are placed in this appendix.160Appendix D. Figures in Series: NGC 6334 I & I(North) 16100)cia0z-JC-)_350++++++++++ + ++ + + + +++++++++++++++++++ + + ++ + + + +÷ + ++ + + + ++ + + ++ + + + + ++ + ++ + + + + ++ + + ++ + + + + + ++++++++ ÷++++++++++++++ ++ ++ + + + ÷++ ++++++++U3LI I++ ++4+++++++4++4 +443’. +4++4+ +4+44’. +4++44+C’70 3—1+44++4+4+ +4+4-4+- ++4+- +++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+44+4+ + ++4+4+4+4+ +4+I +1+ ++ +4+ ++4+4++ +4+4+ +4+ ++4+4++4+4 +4+4+Figure D.1: Beam positions for each line observed. Observed positions are indicated in4’ + ‘4 ‘4 -1-4+4-4+- ++4+- ++4’ + ‘4 I- 4+4 +4243’._350 44’+++++++++4.++4.+++4.+4-+4’42’+++++++I ‘ I ‘ I+++4++‘3Co 2—1I , I , IC17o 2—1+4 ++ +4+4++ +4+4++ +4+4++ +4+4++ +4+4+42’43’_350 44’+++++I I+ +4 ++++c34s 5—4I I+ +4+4+++ +4+ +Cs 5—417h 17m 408 361 32 28° utm 40° 368 328 28° 17m408 36RIGHT ASCENSION (B195O)C345 7—6328 288in separate panels for each molecule, isotope and transition observed.Appendix D. Figures in Series: NGC 6334 I & I(North)4243_350 4442424y -_350 44I IRIGHT ASCENSION (B 1950)162Figure D.2: Velocity slices of CO emission. The velocity averaged CO emission in theJ = 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.(—60,—55) km/sI L(—55,—50) km/s (—50,—45) km/s00)43z-JC-)_350I I(—45,—40) km/s\iN(—4o,—5) km/s (.—35—3o) km/s• III(—30,—25) km/s• •(—25,—20) km/s (—20,—15) km/sI I17h 17m 4QS 35$ 32 28 17m 4QS 36 32’ 2S’ 17m 40’ 36’ 32’ 28’Appendix D. Figures in Series: NGC 6334 I & I(North) 16342’I I I I II43’_350 ,(—15,—la) km/s (—10—5) km/s (—5,0) km/sI I I I I I I I I Io 42’0)z)o 43’zIiC-)350 44(0,5) km/s (5,10) km/s (10,15) km/sI I I I I I I I I I42/____44’(15,20) km/s (20.25) km/s (25,30) km/sI_I I I • I I I I I17” 17T 4O 36 32 28s 17m 4O 36 32 28 17” 40” 36” 32” 28”RIGHT ASCENSION (B195O)Figure D.2 continued.Appendix D. Figures in Series: NGC 6334 I & I(North) 164(35,40) km/sI I I I I I I I I17m 40S 360CDz0z-JC-)_3504243_35° 44(30,35) km/s (40,45) km/s N328 288 17Ifl 4Q8 368 328 28’424344,I —(45,50) km/s17h Utm 408 36’ 32’ 28’RIGHT ASCENSION (B1950)Figure D.2 continued.Appendix D. Figures in Series: NGC 6334 I & I(North) 16542’43’350 44o 42’IC)0)43’z-j0350 444243,350 4417h 17m 4QS 36•IFigure D.3: Velocity slices of CS emission. The velocity averaged CS emission in theJ = 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.32 28 17m 36 32 28 17m 4O 360 32 28RIGHT ASCENSION (B1950)Appendix D. Figures in Series: NOC 6334 I St I(North) 166o 42’0’inzo 43’z-J0._35° 44•I ‘ I ‘ I ‘(10,15)km/s ,I ‘ I ‘(15,20) km/sI ‘ I ‘(20,25) km/sit 17m 4Q8 368 32’ 28’ 17m 408 368 32 28’ 17m 40 368 32’ 288RIGHT ASCENSION (B1950)Figure D.3 continued.Appendix EAstronomical Units and ConstantsValues for some astronomical units used in this thesis are listed here.Debye = 108e.s.u. cmParsec pc = 3.086 x 10’8cmJansky Jy = 1023ergs1cm2HzSolar mass M® = 1.989 x 1033gSolar luminosity L® = 3.862 x lO33erg s167Appendix FAbbreviations and Symbols; A GlossarySome symbols and abbreviations are listed. When a definition is given in the text, theappropriate page reference is given.Abbreviation Description pagea Right Ascension.6 Declination.AlPS Astronomical Image Processing System, developed by NRAO. p.59AOSC Canadian Acousto Optic Spectrometer (at the JCMT). p.50ASCII American Standard Code for Information Interchange.BN a class of objects whose prototype was discovered by Becklin andNengebaner.BPO Bipolar Outflow.CBR Cosmic B ackgronnd Radiation.dec. Declination, the celestial coordinate in the North-South direction.Kinematic Distance. p.73Dnear, Dfar The two solutions (when ambiguous) for kinematic distance. p.73DRAO Dominion Radio Astrophysical Observatory, Penticton, B.C., Canada.EHV Extreme High Velocity. p.6FCRAO Five College Radio Astronomy Observatory, Amherst, MA, USA. The168Appendix F. Abbreviations and Symbols; A Glossary 169observatory operates a 14 metre (aperture) millimetre (wavelength)telescope.FITS Flexible Image Transport System. p.125FWHM Full Width at Half Maximum.FWZI Full Width at Zero Intensity. p.80GBT Green Bank Telescope (of the NRAO), currently under construction.GSD a data file format. p.123H i atomic hydrogen.H II ionised hydrogen.HR diagram Hertzprung-Russell diagram. A graph on which a parameter reflectingstellar luminosity is plotted against a measure of stellar mass.IF Intermediate Frequency. p.45IR Infra-red.IRAF an astronomical software package distributed by NOAO. p.125TRApS Interactive Reduction of Astrophysical Spectra, a locally developed p.125software package.IRAS Infra-red Astronomy Satellite. p.7IRS Infra-red Source, a generic term in object naming.J rotationa.l quantum number.JAC, JACH Joint Astronomy Centre, Hilo, Hawaii, USA. p.54JCMT James Clerk Maxwell Telescope. p.44JHK J, H and K are photometry bands in the near infrared. p.13Jy Jansky, a unit of flux. p.167kpc Kilo-Parsec, a unit of distance. p.167L® Solar Luminosity, the power output of the Sun. p.167Appendix F. Abbreviations and Symbols; A Glossary 170LFIR Far Infra-red Luminosity.Lmech Mechanical Luminosity. p.101LU (frequency of) the Local Oscillator. p.45LRS IRAS LRS, Low Resolution Spectra/Spectrometer.LSB Lower Side-band. p.46LTE Local Thermodynamic Equilibrium p.21LVG Large Velocity Gradient. p.15Solar Mass, mass of the Sun. p.167madr a data manipulation software package from DRAO. p.125MDPS McCutcheon, Dewdney, Purton and Sato, 1991, A.J., 108, 1435.MTS Michigan Terminal System, a computer operating system. p.123NGC New General Catalogue of Nebulae and Clusters of Stars.NOAO (US) National Optical Astronomy Observatory. p.125NOD2 a data reduction software package. p.126NRAO (US) National Radio Astronomy Observatory. p.7NSF (US) National Science Foundation.NWX NGC 6334 I(NWX), the North-West eXtension to NGC 6334 I. p.82OTF On The Fly, a mapping technique. p.50pc Parsec, a unit of distance. p.167plot an astronomy oriented plotting software package from DRAO. p.125PSC IRAS PSC, Point Source Catalog p.7R.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.123Appendix F. Abbreviations and Symbols; A Glossary 171SUN a series of computers manufactured by Sun Microsystems, Inc.Tbg 2.8K, the temperature corresponding to the cosmic backgroundradiation.Teff Effective Temperature (of stellar objects).T Kinetic Temperature (of gas).T a unit of intensity. p.55UBC The University of British Columbia, Canada.UNIX a computer operating system. p.123USB Upper Side-band. p.46VLA Very Large Array. p.7VMS a computer operating system from the Digital Equipment Corporation.ZAMS Zero Age Main Sequence.

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