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A multiwavelength study of 170 micron selected sources Sajina, Anna 2002

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A multiwavelength study of 170/im selected sources by Anna Sajina B.Sc , The University of British Columbia, 2000 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Physics and Astronomy) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A October 9, 2002 © Anna Sajina, 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics and Astronomy The University Of British Columbia Vancouver, Canada 11 ABSTRACT We present results from sub-mm observations of sources selected from the ISO F I R B A C K (Far IR BACKground) survey, along with UKIRT near-IR imaging of a sub-sample. This gives valuable insight to the brightest 10% of galaxies which contribute to the Cosmic Infrared Background (CIB). We estimate the photometric redshifts and luminosities of these sources by fitting their Spectral Energy Distributions (SEDs). The data appear to show a bimodal galaxy distribution, with normal star-forming galaxies at z ~ 0, and the z ~ 0.4-0.9 tail of a much more luminous population. These are similar to the ultraluminous infrared galaxies which are found to evolve rapidly with redshift in other surveys. We are biased away from much higher redshift objects by the detectability threshold of F I R B A C K . Nevertheless, the handful of z ~ 0.5 sources which we identify are likely to be the low-2 counterparts of the typically higher-2 sources found in blank field sub-mm observations. The sources we identify here have the virtue of being relatively easy to study in the optical. Hence their detailed investigation could help elucidate the nature of the sub-mm bright galaxies. i i i C O N T E N T S Abstract i i Contents i i i List of Tables v List of Figures v i Acknowledgements x i i 1 Introduction 1 1.1 The Cosmic Infrared Background 1 1.2 The Multiwavelength Approach 5 2 T h e Data 8 2.1 Sample 8 2.2 The instrument 9 2.3 S C U B A sub-mm observations 13 2.4 S C U B A data reduction 16 2.5 U K I R T near-IR observations 21 3 Results & Analysis 25 3.1 Assembling the multiwavelength data 25 3.2 Linear Correlations 29 3.3 Sub-mm/Radio redshifts 37 3.4 Sub-mm vs. near-IR 38 3.5 SED fits 44 iv 3.6 Luminosity and SFR 46 4 A Model 53 5 Summary &: Discussion 63 5.1 Comparison with related studies 67 5.2 Bimodality 68 5.3 Comparison with evolutionary models 69 5.4 Future Direction 72 Bibliography 74 A Photometry with SCUBA 79 B Cosmology 83 V LIST OF TABLES 2.1 Source coordinates 22 2.1 continued 23 2.2 Calibration values 24 3.1 Multiwavelength data for our sample0 26 3.1 continued 27 3.2 Results for the linear fits to the data 31 3.3 The sub-mm/radio spectral indices and derived redshifts . . .- 39 3.3 continued 40 3.4 x 2 _ r a n g e occupancy for various /3 fits 45 3.5 Fit results for fi = 1.5 48 3.5 continued 49 3.6 Fit results for the higher-z sources" 50 3.7 Estimating the Star Formation Rates" 52 LIST OF FIGURES 1.1 This figure [58] is a compilation showing the different extragalactic back-grounds including the CIB (called FIB here for Far-Infrared Background). Notice in particular that the power output in the far-IR spectral region is comparable to that in the optical region 2.1 Shows the V L A coverage of the ELAIS-N1 field where our sample is lo-cated. Here the asterixes show the ISOPHOT pointings while the circles are ~30% sensitivity of their centers for the V L A pointings (the absolute radio sensistivity varies from region to region) [15] 2.2 This roughly estimates the selection cut off of the F I R B A C K survey in (L, z) space. The solid line is the 3cr limis (=135 mJy), the dashed line is the 4a limit (=180 mJy). The thin lines roughly estimate the region of influence of the radio selection. See text for details 2.3 Distribution of the S170/S1.4GHZ ratio. The solid histogram represents all the sources from the F I R B A C K catalogue which have been observed in the radio. The dashed histogram is our sample. The dotted line shows our high-z candidates (discussed in Chapter 3) 2.4 This shows the performance of the new S C U B A wide-band filters measured in the winter of 2000 compared to the old filters. Notice in particular the dramatic improvement in the 450 /im filter (30-40% depending on the weather). The black curve is the atmospheric transmission on Mauna Kea (1 mm PWV=precipitative water vapour). This figure was taken from the J C M T website. The filters were measured by D. Naylor and W. Holland. vii 2.5 The S C U B A arrays (courtesy of the J C M T website ). Here shown is both the physical scale of the arrays (~25mm) as well as the field of view (~2.3 arcmin). Note that the closely packed arrays shown here are misleading -the arrays are in fact highly undersampled. Using the basic jiggle mode of observing requires 64-point jiggles to create a fully sampled map in both bands(the spacing between 2 jiggle points is roughly 2"). The photometry mode, that we use, involves a 9-point jiggle pattern with spacings of 1". This is much more efficient at quickly reaching the desired SNR in a given bolometer, but the other bolometers produce a very undersampled map. . 15 2.6 Relations between optical depths derived from 26 skydip observations in 2001 (note the weighting towards grade 1 weather). The left hand panels show the entire range, while the right hand panels zoom to the grade 1 data (TCSO < 0.05) only. Here the dashed lines are the standard relations [1], while the solid lines are simple linear fits to our data (the same fit is shown in both columns). The two are sufficiently similar overall, considering the uneven weighting, and the inclusion of outliers. However, the relations with the CSO r seem to be shallower for the grade 1 data than the single slope relation, which may be due to the uncertainty in rcso 18 2.7 This shows the percentage error in the flux estimate as a function of optical depth r . Here crosses are 450 /im and stars are 850 jim. data. The airmass is 1.3 (i.e. y-axis scales as ~ A/1.3). The fit is y = -0.58+5.24r-6.97r 2 + 5.56T 3. Notice that our May 2001 data is off the scale here in 450 /im, and that with the above relation a r ~ 3 gives roughly 100% error. This figure is reproduced from [25] 19 3.1 The available U K I R T if-band images - centered on the radio positions. These images are about 15" x 15", or roughly one S C U B A F W H M 850 /an beam size. The exception is Nl-004 where the S C U B A beam is the white circle, as the galaxy itself is larger than this 28 viii 3.2 This figure is meant to illustrate, in their most obvious cases, the system-atic effects that must be kept in mind when trying to interpret the data at hand. Both images are roughly the size of ISO's beam. On the left is N1-004 with the S C U B A 850 /mi beam shown to the side (the 450 ftm one is about half of that). On the right is N1-008 with the positions of the two radio detections indicated. Our observation is for the stronger of the two - a 3.0 mjy radio source. Notice that the other radio detection (0.3 mjy) has a fainter near-IR counterpart which potentially could be a higher-2 source. We will explore this further with upcoming observations 30 3.3 The scatter plots with their fits and ±lcr scatter. The fit parameters are given in Table 3.2. Notice that the order here is: the first column is mainly sensitive to the location of the thermal peak, the second column to the sub-mm slope, and the third column to the trough between the thermal and non-thermal parts of the SED. The error bars are representative for our data 32 3.4 The histogram is the result of 1000 Monte Carlo simulations of the sub-mm fluxes of our sample. The dotted line shows the actual value of x2 for the observations. Only about ~ 2% of the simulations have a value this low (note that the binning is too crude to show that clearly) 34 3.5 The shows the best fit [/3,T/(l + z)\ combined from the 170/450 and 450/850 slopes, which is [1.5,31 K] along with the 68, 90, and 95% con-fidence levels. Notice that /3 is more poorly constrained. We exclude Nl-001, Nl-002, Nl-034, and Nl-059 from the fit due to their discrepant colours 36 ix 3.6 The sub-mm/radio spectral index as a redshift indicator. The thick solid line is the relation based on the SLUGS sample (104 galaxies - I R A S ' selected), with the dashed lines being its ±la envelope. The thin solid line is the standard C Y relation [8] (17 galaxies - IRAS and N R A O selection) with dotted ±1<J envelope. The circles are 5 galaxies from our sample with spectroscopic redshifts 41 3-7 ^850 vs K magnitude for our sample (crosses and circles). The filled squares and if-band upper limits are from the lens survey of Smail et al. [61], while the pentagons are from the U K 8mJy survey [40]. The circles are our high-z candidates which populate a similar region to these S C U B A survey sources. The lines are the results from fitting a model to the 6 sources where zspec is available (see text) and are labelled with redshift. The bottom panel shows the K-z relationship obtained above (solid, for 5850=5mJy) , compared with the Willot et al. [66] relation for radio galaxies (dashed). The error bar in the lower right-hand corner is a representative one for our measurements 43 3.8 The SED fits for our sample with ^ = 1.5. The rc,y-ranges in all panels are the same (shown in the labels), and the sources are arranged with decreasing 170 //m flux. The IRAS 100 //m point is not used in the fit. For the sake of clarity, we rescale the flux via (A/170 /mi) 2 47 4.1 This is the luminosity function used for our models and its evolution with redshift. The dashed line is a non-evolving cold, dusty galaxy population, while the dotted line is an evolving ULIG population - the solid line is the sum of the two. See text for details 55 X 4.2 This shows the cold galaxy template (solid) compared with the starburst galaxy template (dashed) at the same luminosity (~ l O n L 0 ) . These were used in our model, but are shown here also as an illustration of the effect of cold dust on the SED shape. These templates are the work of Guilaine Lagache and are used in her model [45] 57 4.3 This shows the starburst galaxy template for a L ~ 1 O 1 2 L 0 galaxy. The template is evolved with redshift - from top to bottom 2=0.1, 0.5, 1.0, 3.0, and 5.0. Notice that this figure also illustrates the negative /c-correction at 850/xm (see next figure) 58 4.4 Here we plot the 850/xm flux vs. redshift for a 4 x 10 1 2L© starburst (template) galaxy. This serves the double purpose of illustrating the effect of the negative ^-correction at 850 /im, and predicting what our 5 higher-2 sources would look like at different redshifts. We cut the curve at z = 0.5 for scaling purposes 59 4.5 The result of our model for the predicted number counts at 170 fxm with limiting flux of 135 mjy (=3 a for F I R B A C K ) 60 4.6 The result of our model for the predicted number counts at 850 /im with limiting flux of 3.5 mjy (=3cr for our sample) 61 5.1 Here we test the hypothesis of our sample being bimodal by comparing the X2 of a single-line fit for the entire sample (right panel) to a two-line fit to each sub-sample (left panel). The dashed lines are ±1<7 where a is the rms scatter in the y-direction. Notice that, apart from Nl-048, even with the single-line fit to the entire sample, our high-2 candidates are > 2<r away from the best-fit line 70 5.2 One example of redshift contributions to the CIB. Here the dot-dashed line represents normal, starforming galaxies, the dotted line is the ULIGs, and the dashed line is the LIGs (reproduced from Chary & Elbaz 2001 [14]). 71 xi A . l This is an example of the raw bolometer variances which are used to select the bad bolometers. Here, any bolometer above the dashed line (=1.25<rarray)is excluded form the sky calculation. Note that since, the sky level is later estimated as a weighted mean, the effect of the outliers is reduced 80 A . 2 The upper panel shows the extinction-corrected timestream of the central bolometer. The middle panel is the weighted mean of all the bolometers (excluding those containing signal or excessive variance). The lower panel is the residual after subtracting the middle from the top. Notice that the vertical scales are the same in each case 82 B. l The effects of different cosmological models on the luminosity distance estimation. In terms of [f2 t o t, CIA, ^ M ] , the solid line is [1,0.7,0.3], while the dashed line is [1,0,1]. Here # 0 =75kms - 1 Mpc" 1 85 B.2 The volume element 86 X l l Acknowledgements This thesis was done under the supervision of Douglas Scott and with the collabora-tion of (in alphabetical order) Colin Borys, Scott Chapman, Herve Dole, Mark Halpern, and Guilaine Lagache who all contributed to this work with useful discussions, and sug-gestions. In particular thanks go to Scott Chapman who provided the near-IR data (and the section on UKIRT observations), Guilaine Lagache who provided the galaxy tem-plates and whose models inspire most of Chapter 4, and Mark Halpern who pointed out the problem with the sub-mm errors. Special thanks goes to Douglas Scott for his critical reading of the text, which greatly improved this thesis. C H A P T E R 1 I N T R O D U C T I O N i 1.1 The Cosmic Infrared Background What makes up the Cosmic Infrared Background (CIB) (Fig. 1.1) detected from the C O B E - F I R A S data [53, 31,46, 47, 35, 26, 32]? This remains an open question, and details of galaxy types, their redshift distribution, and how they appear in other wavebands, remain sketchy. The F I R B A C K (Far IR BACKground) survey [54, 21] addressed this question by performing some of the deepest blank field ISO surveys near the peak of that radiation at 170 /im. About 200 sources were detected above 3 a (=135 mJy) accounting for about 7% of the background flux. In general far-IR sources such as the F I R B A C K ones sample the low-to-moderate redshift regime, and thus provide a link between the local Universe and high-z sources, such as the SCUBA-bright 'blank-sky' population. Understanding the nature of these sources, their emission mechanisms, and their dust properties is crucial to our under-standing of galaxy formation and evolution from high redshift until today. This in turn informs us about the cosmic background, as well as the nuclear activities, star formation distributions, and the role of dust obscuration in star formation through a large fraction of the history of the Universe. It has become increasingly clear that such questions of global galaxy formation cannot be adequately addressed without turning to IR/sub-mm wavelengths. Much of the star formation history is hidden from us at shorter wavelengths by dust obscuration. The result is that up to a 2/3 contribution to the total integrated light from the U V to the sub-mm is in the FIR/sub-mm region [26, 34]. In order to better understand the sources detected by F I R B A C K we have been carrying out follow-up observations with S C U B A at 450/im and 850/im. Selection from ISO 170/im (S ,i 7 0>135mJy) blank sky surveys, Chapter 1. Introduction 2 means that a strong bias away from high-z objects is present, although we expect to detect objects out to z ~ 1 (see Fig. 2.1). The F I R B A C K galaxies represent the brightest contributors to the CIB, and are a different selection than SCUBA-selected galaxies. 'Blank-sky' sub-mm bright galaxies, although so far accounting for up to 50% of the sub-mm background (e.g.[17]), make up an insignificant fraction of the total CIB which is primarily accounted for by more nearby (z < 1.5) sources [14, 28]. The combination of far-IR and sub-mm observations is thus very powerful in establishing a link between high-z dusty starbursts and their local counterparts. IRAS revealed a new population of heavily dust-obscured galaxies with luminosities as high as 1/J.R > 1 O 1 2 L 0 [62], consistent with high rates of star formation. These are the Ultraluminous Infrared Galaxies (ULIGs) believed to be the interaction/merger of two spiral galaxies (e.g.[55]), with the stage of the merger plausibly being related to the dust temperature and luminosity. Observations reveal a dramatic rise in the relative (to the local Universe) importance of ULIGs in the past, consistent with hierarchical structure formation scenarios (e.g.[48, 3], and references therein). In this sense, a popular scenario involves an evolutionary sequence of duration of order 108 years, involving increasing dust temperature (Ta=20 to 50K), accompanied by rising IR luminosity (10 1 0 to 1 O 1 2 L 0 ) , and with the related phenomenon of the formation of a massive, nuclear black hole. In this scenario, there are two competing heating sources in ULIGs - star formation (~ 100 M 0 y r _ 1 ) , and accretion onto the central black hole (i.e. A G N activity). The second contribution appears to be necessary to explain the highest luminosity ULIGs, which would otherwise require implausibly large (> 1000 M 0 y r _ 1 ) SFRs. However, the fractional contribution of A G N [29, 37, 30] is hard to assess as, if present at all, the majority are likely to be buried in the dust associated with the surrounding starbursting region. Investigations into A G N contributions have involved both observations of nearby ULIGs [19, 39], and searches for X-ray detectability [2]. While the precise fraction is still debated, it is generally accepted that the bulk of the far-IR/sub-mm background is due to the emission by dust principially heated by star formation. The range of temperatures, emissivity indices and how they correlate with luminosity and A G N activity, are still Chapter 1. Introduction 3 open questions. In addition there is the possibility of more than one significant dust component in some galaxies [23]. Using long wavelength data alone, it has been difficult to distinguish between cooler local starbursts and warmer, more luminous sources at higher z. This is because the spectral energy distributions (SEDs), for a fixed emissivity index /5, are degenerate in the parameter combination ( l+z) /T d . There are additional complications of course caused by variations in /3, T d , and luminosity, changing the shape of the SED. A similar degeneracy exists when trying to derive the photometric redshifts from the well-known sub-mm/radio relation [4]. For example a cooler, starforming galaxy will have different thermal and non-thermal spectral indices from a warmer galaxy with an A G N contribution. Blindly applying the same values to both will then make the cooler galaxy look warmer and at higher-z than it is in reality. Fundamenetally, our understanding of dust in extragalactic sources, its properties, and interaction with the radiation field is poor, which is a major impediment in our interpretation of the observational evidence. Our approach to these issues is by detailed multiwavelength studies of samples repre-senting key elements in the above puzzle which will help us better understand the nature of the sources making up the CIB, as well as improving our understanding of galaxy formation and evolution. The data we present here is now a large enough sample, including near-IR, far-IR, sub-mm and radio observations, to be able to tackle some of these issues. We do this through a combination of direct SED fitting, statistical analysis, consistency with other observations and comparison with model predictions, trying to use the minumum number of a priori assumptions. We have thus improved our knowledge of the nature of the sources in our sample, and through them the entire F I R B A C K sample of which ours is representative. Throughout we assume a flat Universe with H0=75 km s _ 1 M p c " 1 , f2M=0.3, and f2A=0.7. Chapter 1. Introduction 4 1000 100 h I a 1000 X(/i,m) 100 10 Figure 1.1: This figure [58] is a compilation showing the different extragalactic back-grounds including the CIB (called FIB here for Far-Infrared Background). Notice in particular that the power output in the far-IR spectral region is comparable to that in the optical region. Chapter 1. Introduction 5 1.2 The Multiwavelength Approach As stated in the previous section, we address the issues at hand via a multiwavlength study of our sample, which helps us infer information about the physical nature of the sources. Thus it is useful to review the sources of emission for each relevant part of the spectrum. Near-IR: The near-IR emission is mostly direct starlight from an old quiescent stellar population. The if-band flux is about 10 x less obscured by dust than the optical flux is. This makes it an almost independent (of the dust obscuration) gauge of the lumi-nosity. However, in extreme conditions, such as exist in ULIGs, the extinction becomes substantial even in the near-IR and thus the stellar emission is attenuated by dust ab-sorption resulting in power-law like spectra. This results in the K magnitude becoming more rapidly faint with increasing luminosity than can be accounted for by the distance dimming alone. Far-IR: In our case this is 170 yum flux. It is due to thermal dust emission characterized by a grey-body spectrum - i.e. the Planck function multiplied by a dust emissivity term which is proportional to v& in the optically thin limit: ScxB(v,Ty , where B(u,T) oc ^ _ . (1.1) In principle the ISM of a galaxy constitutes a spectrum of dust grain sizes with different emissivities and radiating at a range of temperatures, depending among other things on the metallicity, geometry, and radiation field of the galaxy. Exploring these in full is beyond the scope of this work, especially since it means dealing with a lot more free parameters than the available data can tackle. We will assume throughout a simple single dust component (ie. one f3, one Td) which is not unreasonable if we restrict ourselves only to the A >170/fm regime, which we address in a later chapter. The 170/tm data point is particularly important as it is near the peak of the CIB. It is also near enough to the peak of the dust emission for cold dust (larger grains)1 that the ratio with 850 /mi flux ^his can be argued simply by Wien's Law: a T ~ 30K source will peak at A ~100 um, and a T ~ 15K source will peak at A ~200 um. Chapter 1. Introduction 6 has a non-trivial dependence on redshift - by z ~ 1 there already is a significant change in slope (as the curvature near the peak of the SED begins to affect it). This allows us to fit the dust model with more precision than the sub-mm data alone would allow. For higher luminosity sources, the dust emission is primarily the reprocessed UV-light of young, massive stars and thus is correlated with the SFR. For less active galaxies this may be more complicated due to the higher importance of the cirrus component, where the power originates in optically-bright older stars. Since, the estimated total luminosity of the IR/sub-mm spectrum is directly related to the dust mass (assuming the dust is optically thin), we can thus also estimate Md (a lower limit in fact, since we use a single dust component). Sub-mm: Apart from providing extra data points to fit the dust emission spectrum, the 850 /im band is especially important in that it is almost redshift independent, due to the negative ^-correction (discussed in more detail in a later chapter). It is thus primarily a luminosity measure rather than a distance measure. Since it is near the end of the thermal spectrum (the non-thermal spectrum begins to emerge roughly near rest-frame 1mm), it is sensitive to the coldest dust component contributing to it. Using the sub-mm spectral slope in conjunction with the radio spectral index (see next) pin-points the location of the trough between the thermal and non-thermal parts of the SED, which can be used to estimate the redshift of the source (with some dust model dependence). Radio: The radio flux is due to the well known synchrotron radiation caused by charged particles (electrons) gyrating about magnetic field lines. The emission is a power law of the form S oc va. The radio spectral index a is related to the exponent of the energy distribution. The high energy electrons that generate this radiation could originate in A G N , but more commonly in supernovae which come from the death of the most massive stars. Thus the electron flux is also a gauge of the SFR. This is the physical reason behind the radio-IR(sub-mm) correlation since the power for both processes ultimately comes from the same massive stars whose lifetimes are short enough that the probe is almost instantaneous (at lower luminosities this would break down as explained above). At the highest -luminosities, when it is almost certain that an A G N is present, it will contribute Chapter 1. Introduction 7 power to both types of emission, thus the relation also approximately holds. We have insufficient information to explore variations in cx so we assume the canonical -0.75 [6]. 8 CHAPTER 2 THE DATA 2.1 Sample Targets were selected from the F I R B A C K (> 3a) catalogue [21] in the ELAIS N l field. Confusion remains a major issue with the ISO beam size, which is ~90", and work is underway (by others) to address that. Our main selection criterion has been the availability of radio detections [15] inside the ISO beam. These are required for pointing since ISO's beam has roughly the area of the entire S C U B A array. Since the array is under-filled (in S C U B A photometry mode, see next section), targetting is very much less efficient if no better position is available than that determined by ISO. When we subtract from these sources radio-bright A G N , as well as sources with several radio detections per beam, we are left with 41 possible sources to draw from - we have followed up 30 (and additionally one N2 source) - listed in Table. 2.1. Notice that if only the > 4a(=180 mJy) catalogue is considered there are 24 sources with radio detections, of which we have followed up 21. Whereas with our 1999 observations we tried to bias our data toward higher detectability in the sub-mm [57], with the 2001 observations our philosophy was that since too little is known about these sources to be able to reliably select for sub-mm detectability, we would try to diversify our sample, and simply target F I R B A C K sources with radio positions. Fig. 2.1 shows the V L A coverage of the N l field which is the primary source of radio fluxes for this field [15]. This incomplete coverage is the main reason for the lack of radio fluxes for a large fraction of the F I R B A C K sources. Fig. 2.2 shows roughly the relative selection (based on a starburst galaxy template, see Chapter 4) in (L, z) space due to the 170 /im F I R B A C K and the 21 cm V L A observations (assuming a detection limit of 0.15 mJy). The range plotted is meant to cover a range of galaxy properties. It is Chapter 2. The Data 9 estimated via two separate redshift estimators (discussed in detail in Chapter. 3). This plot makes it clear that the requirement that a radio position is available does not bias our sample additionally up to redshift z ~ 1, but is a possible factor for higher redshifts (depending on the specific galaxy properties). Due to the broadness of selection criteria we believe our sample represents a fair cross-section of the F I R B A C K population, rather than focusing on a specific sub-population. This can be seen in Fig. 2.3, where we compare the distribution of Sno/SiAGHz for all 41 possible sources with that of the 30 sources in our sample. We discuss the dotted line in later sections. The close agreement between the shape of the total distribution and that of our sample shows that even though this is a targetted follow-up and not a "blank-field" survey, trends for our sub-sample qualitatively correspond to those in the entire F I R B A C K sample. This is reasonable, since apart from the brightest one or two sources, the 170 /mi fluxes (Table 3.1) span only a range of about a factor of 2. Six of our sources have spectroscopic redshifts - Nl-001 at 2=0.03, Nl-002 at 2=0.07 (Guilaine Lagache, private communication), Nl-008 at 2=0.26 [50], Nl-012 at 2=0.02 [60], Nl-040 at 2=0.45, and Nl-064 at 2=0.91 [11]. 2.2 The instrument Currently the foremost sub-millimetre camera is the Sub-mm Common User Bolometer Array - S C U B A [36] on the James Clerk Maxwell Telescope (JCMT) located on Mauna Kea, Hawaii. At this altitude (~4000m) the telescope is well above most of the water vapor (scale height ~2000 m) which is the principal source of atmospheric opacity in the sub-mm. This leaves windows of transmission at certain wavelengths (see Fig. 2.4) mak-ing ground-based sub-mm astronomy possible. S C U B A consequently has filters designed for these windows at around 350 jum, 450 /mi, 750/mi, and 850 /mi. The instrument consists of a 37-bolometer long-wavelength (typically 850 /mi) array, and 91-bolometer short-wavelength (typically 450 /mi) array which operate simultaneously by means of a dichroic beam-splitter. The whole is cooled to 75 mK to maximize sensitivity (without Chapter 2. The Data 10 10* 08* 04*» 16* 00 m RA Figure 2.1: Shows the V L A coverage of the ELAIS-N1 field where our sample is located. Here the asterixes show the ISOPHOT pointings while the circles are ~30% sensitivity of their centers for the V L A pointings (the absolute radio sensis-tivity varies from region to region) [15]. Chapter 2. The Data 11 redshift Figure 2.2: This roughly estimates, the selection cut off of the F I R B A C K survey in (L, z) space. The solid line is the 3<r limis (=135mJy), the dashed line is the 4a limit (=180 mJy). The thin lines roughly estimate the region of influence of the radio selection. See text for details. Chapter 2. The Data 12 10 ~| I I I I I I i I 1 1 V 8 h W C D o u O 6 W C D 4 3 r i I _i i i_ _i i i_ 200 400 600 800 ^ 1 7 o / ^ l . 1000 . 4 G H z Figure 2.3: Distribution of the 5i7o/5i.4GHz ratio. The solid histogram represents all the sources from the F I R B A C K catalogue which have been observed in the radio. The dashed histogram is our sample. The dotted line shows our high-z candidates (discussed in Chapter 3). Chapter 2. The Data 13 such cooling, thermal emission from the instrument itself would overwhelm the signal). The S C U B A long-wave beam F W H M is ~ 15" whereas the short-wave beam is ~ 8". Most of the sky signal is a " D C " offset, due primarily to sky emission, which is orders of magnitude larger than the astronomic signal. It is removed by chopping with the secondary mirror at a frequency of 7.8 Hz. In addition, nodding is performed every 10-20 s to take out more slowly varying sky gradients, and a huge telescope emission signal. This involves starting from the ON position (usually central bolometer on the source), placing the source onto the O F F position, and then reversing to the other side so that the final sequence is ON-OFF-OFF-ON. Each nod pair is combined by subtracting the signals at the two positions [25] giving a triple-beam (-0.5,4-1.0,-0.5) pattern on the sky. Since this nodding is rather slow, the process still leaves us with a small, but non-zero mean in the non-source bolometers, as well as with some left over correlated sky noise. Thus further sky removal is necessary, which is done at the data reduction stage (see section 2.4 and Appendix A) . 2.3 SCUBA sub-mm observations The observations presented here were taken with S C U B A in March 1999 and in March and May 2001. In order to avoid biasing our data, we attempted to observe each source until a predetermined rms (~ 1.5 mJy) was reached, irrespective of whether the source appeared to be a possible detection or not. The March 2001 data were taken in excep-tional grade 1 weather (r225 ~ 0.041, and as low as 0.02), whereas the 1999 data were taken in a merely 'good' weather (T225 ~ 0.07 or better). The May 2001 data were taken in worse conditions of T225 > 0.1. Throughout we used the 2-bolometer chopping mode. This involves chopping in array coordinates in order to always align one negative beam exactly with a specific off-centre bolometer. Thus the negative beams can be folded in, 1The value of T 2 2 5 (at 225GHz=1.3mm) is taken every 10 min at the Caltech Submillimetre Obser-vatory (CSO), and thus has become a standard weather monitor. It is strongly correlated with r at 850/im and 450 ^m (see next section). Chapter 2. The Data 14 Measured SCUBA filter profiles Wavelength (microns) Figure 2.4: This shows the performance of the new S C U B A wide-band filters measured in the winter of 2000 compared to the old filters. Notice in particular the dramatic improvement in the 450 / im filter (30-40% depending on the weather). The black curve is the atmospheric transmission on Mauna K e a (1mm PWV=prec ip i ta t ive water vapour). This figure was taken from the J C M T website. The filters were measured by D . Naylor and W . Hol land. Chapter 2. The Data 15 SHORT WAVE ARRAY LONG WAVE ARRAY (91 detectors) (37 detectors) 0 5 10 15 SO 25 mm Figure 2.5: The S C U B A arrays (courtesy of the J C M T website ). Here shown is both the physical scale of the arrays (~25 mm) as well as the field of view (~2.3 arcmin). Note that the closely packed arrays shown here are misleading -the arrays are in fact highly undersampled. Using the basic jiggle mode of observing requires 64-point jiggles to create a fully sampled map in both bands(the spacing between 2 jiggle points is roughly 2"). The photometry mode, that we use, involves a 9-point jiggle pattern with spacings of 1". This is much more efficient at quickly reaching the desired SNR in a given bolometer, but the other bolometers produce a very undersampled map. Chapter 2. The Data 16 improving the rms by a factor of yJ2/Z (see Appendix A) . Unfortunately, for our 2001 run, software problems with the new telescope control system resulted in S C U B A not chopping onto another bolometer, making the negative beam unrecoverable. Thus the 2001 data presented here are from the central bolometer only, whereas the 1999 data have the negative beams folded in with the central signal. This is balanced by the exceptional weather conditions during observing. As a result, the 2001 data (March) have slightly higher rms at 850 / i m , but considerably better rms at 450 fxm (due to better weather and the new wide-band filter). The data were taken in photometry mode which involves integrating in a 9-point jiggle pattern (taking ~ 18 s per integration) which is the most efficient way to reach the de-sired rms in a given bolometer, but leaves us with an undersampled map (see Fig. 2.5). However the other bolometers are still valuable for subtracting the residual sky emission. Nightly calibration observations were carried out on Mars, Uranus, CRL618, and CRL2688 (the last two are among the standard calibrator sources for S C U B A ) , typically at the beginning and end of the night (Table 2.2). Pointing checks were done between each change in source (or roughly every (200 x18 s) = lhour). The drift was never greater than a few arcseconds, and usually was on the order of 2". 2.4 SCUBA data reduction The data were reduced using the S C U B A User Reduction Facility - S U R F package [42] for the preliminary stages of the reduction (up to the extinction correction), and custom written software for all subsequent stages. This allows us better control over and understanding of the process, as well as making it computationally more efficient. The extinction correction was performed using skydip observations2 whenever available, 2For 1999 data, the default temperatures (used by the SKYDIP routine in deriving r) were incorrect (the problem was discovered October, 1999). This is particularly severe for 450 pm. data. This is an additional reason requiring some re-reduction of that data. Chapter 2. The Data 17 and with a derived optical depth from the rcso — ^ S C U B A relations otherwise3: T 8 5 0 = 4.02(rC So - 0.001) and r 4 5o = 26.2(rC So - 0.014). (2.1) Our data (Fig. 2.6) seem to suggest that the standard relations given above should not be used in the grade 1 (r225 < 0.05) regime. Thus we prefer to use the S K Y D I P derived opacities for the observations taken in that regime whenever possible. Notice also that in poor weather (high r ) the scatter is considerable. The 450 um data in particular are not reliable, as was already shown by L. Dunne [25]. We reproduce her figure below as it is illustrative for our purposes. Also Archibald et al. [1] find that r 4 5o in grade 4 weather tends to be higher than predicted, which our data support (although not strongly due to small numbers). Thus for most of our March 2001 data where the scatter is small in both bands, the error introduced at this stage is negligible compared to the noise (see next Chapter). For the weather conditions of most of 1999, March 19 and May 14, 2001, the error in the 450 nm fluxes is ~ 5 — 10%(read off figure). For the rest of May, 2001, the 450 jum error is ~ 25 — 100% so derived fluxes should be viewed with greater suspicion (affected are Nl-016, Nl-039, and Nl-041). When calibrating S C U B A data, it is typical to use standard gains - i.e. flux conversion factors between Volts and Janskys. It is clear that using individual calibration observa-tions is not ideal as various factors (such as pointing errors, extended source emission, intrinsic source variability) can introduce significant scatter. However it is also clear that using the same gains for data taken in different instrument and/or atmospheric condi-tions may also be inaccurate. The gains were derived using the J C M T F L U X E S program (standard error ~ 5% ) to obtain the flux of a planet, in Jy, for the time of observation (for non-planetary calibrator fluxes we use the J C M T standard calibrators page), and taking its ratio to the signal in Volts. The standard gains for the post-upgrade 2001 data are 197±13 J y / V at 850pm and 384±82 J y / V at 450/im (from the J C M T website), with 3For the 1999 (taken with the pre-upgrade narrow-band filters) the relations are: Tg5o = 3.99(TCSO ~ 0.004) and r 4 5o = 23.5(rCso - 0.012) Chapter 2. The Data 18 2 h 0 . 2 0 .3 0 .4 T 850 0.5 1 1 1 | I 1 1 1 | 1 D l • ' ^ cP • / - an g -— „ • -B D • — l i l l l l 0 . 0 5 0.1 T c s o 0 .5 0 . 4 O l O CO h 0 .3 0 .2 1 1 1 •' B ^> / / • a • • a • a • -I I I L_ 0 . 0 5 0.1 T c s o i I i I I i i—i—I—I—I—I—I—I—I—i—i—i—r 0 . 0 2 0 . 0 3 0 . 0 4 0 . 0 5 0 . 0 5 0 . 0 2 J i i i_ _i i i i_ 0 . 0 3 0 . 0 4 0 . 0 5 ' CSO Figure 2.6: Relations between optical depths derived from 26 skydip observations in 2001 (note the weighting towards grade 1 weather). The left hand panels show the entire range, while the right hand panels zoom to the grade 1 data (TCSO < 0.05) only. Here the dashed lines are the standard relations [1], while the solid lines are simple linear fits to our data (the same fit is shown in both columns). The two are sufficiently similar overall, considering the uneven weighting, and the inclusion of outliers. However, the relations with the CSO r seem to be shallower for the grade 1 data than the single slope relation, which may be due to the uncertainty in Tcso-Chapter 2. The Data 19 251 20 + + 15 3 1 0 1 c o 01 0.0 I + / + / + -•' + + /+ + + ++ +A + -H+ + y ' + + y+ + + + -H+ + -H-+ 0.5 1.0 . s u b m m zen i th opac i t y T 1.5 2.0 Figure 2.7: This shows the percentage error in the flux estimate as a function of optical depth T. Here crosses are 450 / m i and stars are 850 / m i data. The airmass is 1.3 (i.e. y-axis scales as ~ A/1.3). The fit is y = -0.58 + 5.24r - 6.97r2 + 5.56r3. Notice that our May 2001 data is off the scale here in 450 / m i , and that with the above relation a r ~ 3 gives roughly 100% error. This figure is reproduced from [25]. Chapter 2. The Data 20 roughly 250 J y / V and 800 J y / V for the pre-upgrade 1999 observations (the difference is mostly due to the new wide-band filters - see previous section). The gains we derive are presented in Table 2.3. We estimate the calibration uncertain-ties as the standard deviation from the run mean using all calibration observations in a given month. For March 2001 we obtain average gains of G 4 5 o=371±118 J y / V and G 8 5 0 = 2 10±18 J y / V . For May 2001 G 8 5 0 = 2 3 7 ± 1 5 J y / V ( G 4 5 0 is poorly constrained as described above). For 1999 G 4 5 0 =748±142 J y / V and G , 8 5 0 =237±15 J y / V . These last in-clude all observations; however, we find that Mars calibration observations (total 2) give gains that are far lower: ~220-230Jy/V in 850//m and ~400-600Jy/V at 450/im, while Uranus-derived gains are more consistent with the standards. We are unsure of the cause of this discrepancy, however note that Mars was fairly extended at the time (diameter ~12") which makes modelling the flux/beam from it less certain. If we discard these, we are left for the entire run (6 days) with only 2 Uranus calibration observations that are more trustworthy (one IRC-10216 observation is also dubious as the source is quite extended and variable). The calibration observations do not agree internally, and are too few to feel secure about the uncertainties arising from systematic effects (see above). We therefore, conservatively, decide to use the standard gains for our 1999 run which more-over are consistent with the averages within their uncertainties. Our lesson here is that if calibration is important (as in this study) a sufficient number of calibration observations must be performed and the calibrators must be well matched to the observing mode: for photometry they need to be stable and pointlike for SCUBA's beams. Notice that the values for May 2001 also differ from the standard. This is most likely due to observing being done in grade 3 weather with consequent large uncertainties both in sky opacities (which is the most likely culprit here) and gains. Only three sources (see above) were partially observed at that time, and none are individually detected (<C 2cr signals in both bands). At this stage we have not worried about these apparently exces-sive gains as their impact on our results is negligible. Systematic uncertainties in the opacity and calibration estimates are hard to quantify, but it should be noted in later sections that we will be quoting statistical errors only. Chapter 2. The Data 21 The next step is sky-subtraction, or removal of the average level at each time step, which is well known to be a crucial step in reducing S C U B A data (see previous section). The sky was subtracted as a mean level for the entire array excluding the signal bolometers as well as any bad bolometers, as revealed by excessive noise levels. Appendix A gives some more detail on the process of reducing S C U B A photometry data (specifically as performed by our code). 2.5 UKIRT near-IR observations Most of our S C U B A detected F I R B A C K sources could not be identified in DPOSS im-ages. As the sources are expected to be extinguished by dust and therefore have red spectra, we obtained deep observations in the if-band at UKIRT using the Fast Track Imager (UFTI) for maximum sensitivity to obscured components. The small U F T I field (50"x50") was centered on the source positions taken from the radio /SCUBA identifi-cations. Each source was imaged for a total of 1800s, with individual exposures of 60s each, reaching a limiting magnitude in a 2" diameter aperture of K = 20.4(5<J). The fast tip/tilt , adaptively corrected imaging resulted in seeing better than median conditions at 0.4" F W H M . Data were reduced using the Starlink, U K I R T / U F T I image processing tools under the ORACDR environment [7]. We wrote custom ORACDR scripts to optimize point source sensitivity in our essentially blank field observations, creating flat fields from each 9-point dither, and high signal-to-noise thermal background images from 60 minutes of data centered around the observing period of the given F I R B A C K source. The if-band images for the 12 sources observed in this way are presented in Fig. 3.1. Chapter 2. The Data 22 Table 2.1: Source coordinates Source R A [hh:mm:ss] D E C [dd:mm:ss N l -001 16:07:36.37 53:57:32.72 N l -002t 16:10:05.83 54:10:29.81 N l --004 16:11:09:38 53:58:07.54 N l --007 16:13:31.25 54:16:28.50 N l --008f 16:08:57.98 54:18:16.83 N l --009 16:08:03.89 54:53:02.39 N l --010 16:09:34.91 53:52:23.61 N l --012 16:12:14.35 54:08:32.78 N l --013+ 16:07:41.15 55:01:53.87 N l --015 16:07:24.44 54:12:08.53 N l --016 16:07:38.12 54:46:03.08 N l --024 16:09:37.44 54:12:59.69 N l --029 16:11:17.43 54:16:28.27 N l --031* 16:11:03.74 54:43:19.79 N l --032 16:12:42.34 54:37:38.37 N l --034+ 16:07:19.34 54:43:06.99 N l --039 16:08:48.78 54:51:52.54 N l --040+ 16:09:28.01 54:28:32.56 N l --041 16:08:14.00 54:28:35.92 N l --045 16:08:53.76 54:47:34.71 N l --048f 16:11:02.53 54:23:28.81 N l --056 16:11:43.46 54:16:24.05 Chapter 2. The Data 23 Table 2.1: continued ... Source R A [hh:mm:ss] D E C [dd:mm:ss] N l --059 16:07:58.05 54:23:52.98 N l --064t 16:08:25.33 54:38:09.52 N l --068 16:10:41.36 54:10:29.37 N l --077 16:07:09.46 54:49:24.09 N l --078 16:12:34.96 54:29:17.63 N l --083+ 16:10:19.24 54:21:53.73 N l --101 16:09:45.95 54:21:23.77 N l --153+ 16:09:59.67 54:36:44.83 N2--013 16:34:05.78 40:51:09.80 These sources form the 1999 sample. Chapter 2. The Data 24 Table 2.2: Calibration values Date 850/im gain [Jy/V] 450//m gain [Jy/V] Calibrator 1999 March 18 225(250)° 406(800) Mars March 19 240(250) 670(800) Mars+Uranus March 20 227(250) 608(800) irc_10216 March 21 257(250) 1338(800) Uranus March 22 (250) (800) none March 23 (250) (800) none 2001 March 13 206 343 crl618 March 15 225 374 Mars+crl2688 March 17 198 327 Mars+Uranus March 18 198 340 Mars+Uranus March 19 212 328 Mars+Uranus May 14 (250) (390) none May 22 (250) (390) none May 25 252 361 crl2688 May 26 256 406 Uranus+crl2688 May 28 241 404 Mars+Uranus a The values in brackets are for days with no calibration observations, or the data quality was too poor. When both are given, the value in brackets is used. When more than one calibrator is given, the gain quoted is the average. See text for details, especially on 1999 calibration. CHAPTER 3 RESULTS & ANALYSIS 25 3.1 Assembling the multiwavelength data The 1999 data presented here were previously discussed in Scott et al. (2000)1. However we re-reduced the data again concurrently with the 2001 data in order to ensure unifor-mity (especially as an upgraded version of SURF and a custom-written code was used). We confirm all previously reported detections. The 2001 data have three unambiguous detections at 450/im (Nl-004, Nl-024, Nl-078). This high detection rate at a difficult band is due to the exceptional atmospheric conditions during our observing run as well as the far superior performance of the new wide-band filter (see Fig. 2.2). In addition there are three new detections at 850 /mi (Nl-001, Nl-059, N-078). Note that the few arcsecond pointing uncertainty (see previous) has only a small effect on the long wavelength data, but may be a significant reason for the apparently missing 450 /im flux (where the beam F W H M is only ~7") in sources where one would expect to find some (e.g. Nl-059). The sample as a whole is detected at the 10.6 a level at 850 /im, and at the 9.0 a level at 450/im ( ( S 8 5 0 ) = 2 . 5 ± 0 . 2 m J y and (5 4 5 o)=16.7±1.9mJy) . Our results for the entire sample are presented in Table 3.1, which, in addition to the sub-mm data, includes the near-IR, far-IR, and radio (discussed below). The near-IR data are from the UKIRT observations where available, and from the 2MASS catalogue elsewhere (sources with K ~14-15 were not in the 2MASS catalogue, but we estimated their magnitudes directly from the calibrated catalogue images via aperture photometry in G A I A ) , except for N2-013 since the N2 field was not observed. 1Note that we use the naming scheme of Dole et al. (2001), which differs from the earlier convention used. In particular Nl-038, Nl-061, Nl-063 from Scott et al. (2000) correspond to the new Nl-040, Nl-048, Nl-064. Chapter 3. Results & Analysis Table 3.1: Multiwavelength data for our sample0 Source K <SlOO Sua 5450 5850 5i.4GHz Nl-001 12.4±0.1 430±87 597±72 -3.0±14.0 6.1±1.6 0.74±0.23 Nl-002 12.7±0.1 340±121 544±69 14.4±12.4 4.4±1.1 0.64±0.04 Nl-004 12.4±0.0 300±73 391±58 32.5±7.2 3.6±1.4 0.88±0.13 Nl-007 13.2±0.1 480±73 338±54 23.4±8.1 4.4±1.6 1.04±0.12 Nl-008 14.2±0.1 160±73 335±54 25.9±14.0 1.9±1.1 2.98±0.04 Nl-009 12.0±0.0 310±58 313±52 10.6±7.6 3.5±1.5 1.15±0.11 Nl-010 13.0±0.0 360±99 309±52 15.2±10.8 1.8±1.4 1.05±0.20 Nl-012 13.9±0.2 320±122 302±51 9.2±10.0 1.5±1.6 0.31±0.07 Nl-013 16.8±0.1 350±75 294±51 18.8±9.9 0.0±1.5 0.52±0.15 Nl-015 14.8±0.1 230±41 294±51 -3.4±7.7 1.4±1.6 0.52±0.07 Nl-016 13.2±0.1 470±20 289±50 34.8±16.7 1.5±1.2 1.55±0.13 Nl-024 14.2±0.0 220±69 266±49 32.3±7.5 2.9±1.3 0.75±0.02 Nl-029 14.3±0.1 340±83 229±46 20.0±14.2 0.5±1.7 0.69±0.05 Nl-031 13.5±0.1 110±78 225±46 9.2±13.2 1.9±1.1 0.43±0.06 Nl-032 18.5-19.5 220±53 224±46 14.9±7.7 1.3±1.4 0.21±0.05 Nl-034 19.3±0.8 270±71 221±46 95.1±27.5 1.3±1.3 0.33±0.07 Nl-039 15.8±0.2 230± 0 205±44 10.9±86.8 -0.1±2.3 0.58±0.07 Nl-040 19.4±0.6 0 ± 0 205±44 29.2±20.5 5.4±1.1 0.33±0.03 Nl-041 14.7±0.1 150±55 204±44 20.4±156.7 -0.1±2.5 0.76±0.06 Nl-045 14.4±0.0 280±46 198±44 15.3±8.3 3.0±1.4 0.43±0.06 Nl-048 19.3±0.9 250±51 192±44 15.5±11.6 4.2±1.1 0.37±0.05 Nl-056 15.9±0.2 160±71 179±43 -8.6±8.4 0.0±1.6 0.24±0.02 Chapter 3. Results & Analysis 27 Table 3.1:, continued... Source K <SlOO <Sl70 5 4 5 0 S l . 4 G H z Nl-059 20.4±0.9 230±66 175±42 6.9±34.5 6.4±1.9 0.60±0.06 Nl-064 18.2±0.3 260±79 166±42 35.2±13.9 5.1±1.2 0.23±0.04 Nl-068 15.3±0.1 320±95 165±42 15.1±7.6 2.2±1.4 0.44±0.05 Nl-077 15.5±0.2 200±89 159±41 5.9±7.3 1.1±1.3 0.40±0.10 Nl-078 18.0±0.4 240±63 158±41 35.2±8.7 5.7±1.3 0.24±0.04 Nl-083 15.4±0.2 300±73 150±41 16.2±16.0 0.7±1.2 0.55±0.03 Nl-101 15.2±0.2 210±73 136±40 19.8±7.5 0.9±1.5 0.39±0.05 Nl-153 15.5±0.2 140±58 103±37 9.6±15.3 -0.2±1.0 0.24±0.03 N2-013 O.OiO.O 310±75 244±53 23.5±15.9 3.5±1.4 0.30±0.07 a The K band values are in magnitudes, the other values are in mJy. The errors are lcr. The IRAS fluxes (100 pm here only) were obtained using the XSCANPI facility. We quote them here for the sake of completeness as well as to help in comparison with IRAS galax-ies where the typically quoted detection limit is ~1 Jy. The errors quoted are purely statistical; however, at this faint level systematic errors (including, among other things IR cirrus and mapping artefacts) in estimating the flux dominate to the point of making such estimates of little statistical use. The radio fluxes are from a V L A survey of the field [15] (see Fig. 2.2), as well as from FIRST observations in this region (see [50]) (which also give a highly inhomo-geneous/incomplete coverage). Two possible sources of systematic uncertainty in comparing the far-IR and S C U B A fluxes are: 1) the different sizes of the ISO (about 90") and S C U B A (about 14") beams, and thus the possibility of multiple sources within the beam - this is also complicated by the issue of clustering, and possibly lensing; and 2) the relative proximity of the bulk of our sources and thus the possibility of at least a few being extended beyond the S C U B A beam. This is especially severe for the 450 pm ~ 8" beam - e.g. Nl-001 can be viewed Chapter 3. Results & Analysis 28 Figure 3.1: The available UKIRT /Y-band images - centered on the radio positions. These images are about 15" x 15", or roughly one S C U B A F W H M 850 /im beam size. The exception is Nl-004 where the S C U B A beam is the white circle, as the galaxy itself is larger than this. Chapter 3. Results & Analysis 29 as an ellipse in its 2MASS image with major and minor axes of about 20" and 7", re-spectively. In general, however, other wavelengths images, are insufficient to determine precisely how much flux is being lost in this way, as it is not clear how concentrated the sub-mm emission would be - how it is distributed in comparison with other wavebands. The flux estimate itself is likely to be less accurate in photometry mode if the source size is on the order the beam size. These effects, of course, become more important with increasing Sw Fig. 3.2 shows these effects in some more pronounced cases. 3.2 Linear Correlations Looking at the black-body function (eq-n 3.1), we see that when obseving a redshifted source the term hc/XkT becomes hc(\ + z)/XohsT. So it is immediately apparent that in-terpretations of the far-IR/sub-mm data will be degenerate in the dust model and redshift (mainly the (1 + z)/T^ parameter, with some /3-dependence as well). Essentially cold, nearby sources look similar to warm, far away ones. To a large degree this degeneracy holds for the near-IR, and radio data as well. However, we can still succeed in differen-tiating somewhat among these parameters due to the large size and spectral coverage of our sample. This allows us to look at a variety of projections, allowing some breaking of the degeneracy. Since a fifth of our sample has available spectroscopic redshifts (4 local, and 2 higher z), we can use those as a test for the validity of any conclusions we make. Fig. 3.3 shows a variety of projections for our data from far-IR to radio, where each plot has been treated through the same analysis: a fit is made to all points using a straight line passing through the origin, i.e. y = mx (except when ratios are fitted, when the zero intercept requirement is lifted), excluding the > 2a outliers, then a new fit is made and is plotted along with the 1 a scatter. Table 3.2 shows the results. Notice that for the colour-colour plot we followed a different recipe. There we excluded the outliers (six sources are far outside the boundaries of the plot) by hand, and fit the rest with a standard x2 without forcing a zero intercept. Since in most cases, the errors in the two directions are of comparable size, rather than use the conventional 1-D x2, we minimize Chapter 3. Results & Analysis 30 Figure 3.2: This figure is meant to illustrate, in their most obvious cases, the systematic effects that must be kept in mind when trying to interpret the data at hand. Both images are roughly the size of ISO's beam. On the left is Nl-004 with the SCUBA 850 / m i beam shown to the side (the 450 / i m one is about half of that). On the right is Nl-008 with the positions of the two radio detections indicated. Our observation is for the stronger of the two - a 3.0 mjy radio source. Notice that the other radio detection (0.3 mJy) has a fainter near-IR counterpart which potentially could be a higher-z source. We will explore this further with upcoming observations. Chapter 3. Results & Analysis 31 Table 3.2: Results for the linear fits to the data Relation slope y-intercept" rms 850/im vs. 170/im 0.01 0.00 1.23 18.07 450 /im vs. 850 /an 7.05 0.00 11.74 13.95 850 /im vs. 1.4 GHz 3.66 0.00 2.18 70.76 850/im vs. 850/xm/450/im 20.00 0.00 1.36 7.04 850/im/1.4 GHz vs. 850/im 1.82 0.00 2.46 12.19 a Notice that for all flux-flux fits a y-intercept of zero has been forced the following: N (yi - mxi)2 X20 — X] (3.1) i=l and show the results in Table 3.2. In general, it appears that the typical uncertainties of our sub-mm data points are larger than the 1 a scatter of the fits. This implies that our errors are overestimated. We test this explicitly for the 5450 vs. S&50 plot by estimating the probability of a given X2D y i a Monte Carlo simulations of the data. The procedure followed was to generate random 850 /im fluxes within the range of our data, and find their 450 /im analogues using the best-fit slope of the data (the y-intercept was set to zero). We smear both directions with gaussian errors which we read off the true data in order to make the simulated distributions as close to the true one as possible. We obtain a x2 of 30 when fitting all our data using the above. However if we exclude the clear outliers (Nl-001, Nl-034, and Nl-059 which have highly discrepant colours as we show later) from the analysis we obtain a x2 of 14, whose probability is ~2%. This is shown in Fig. 3.4. At present we do not have an explanation for this. The procedure followed in deriving the fluxes and errors from our code is described in Appendix A; however, note that the same inconsistency is observed when using SURF derived values. This holds also for each of the 1999 and 2001 data separately. We conclude that there is some as yet unidentified source of correlation in the errors which we have not taken into account, or else they are overestimated by a factor of ~ y/2 (which is needed to account for the roughly factor of Chapter 3. Results & Analysis 32 ' 4 6 0 / i m / ^860/ u n ^B60 | t m / ^ 4 6 0 M m ^ 8 6 0 * i m [ m , ' y ] Figure 3.3: The scatter plots with their fits and ±la scatter. The fit parameters are given in Table 3.2. Notice that the order here is: the first column is mainly sensitive to the location of the thermal peak, the second column to the sub-mm slope, and the third column to the trough between the thermal and non-thermal parts of the SED. The error bars are representative for our data. Extreme outliers are not shown for clarity. Chapter 3. Results & Analysis 33 2 discrepancy between the expected and obtained x2)- We will, however, be conservative and leave the errors as they are, since we cannot properly account for the source of the discrepancy. After this cautionary aside, we return to Fig. 3.3. It is organized such that in it, the column order roughly follows the main features of the long wavelength SED: the first column is largely sensitive to the thermal peak, the middle column corresponds to the sub-mm slope, and the last column traces the trough between the thermal and non-thermal emission. First, we will concentrate on the 5s5o v s - 5i70 plot. We immediately notice, that after the above described fitting procedure, a number of sources occupy a locus > 2cr away from the best-fit line. Notice that in the colour-colour plot, these five sources stand out again. Assuming a grey-body, these sources are either at higher redshift or lower temperature than the rest of the 170/mi sources (or a combination of both). To understand which, we turn to the S450 vs. Sgso plot. Here we are mainly exploring the slope of the spectrum in the sub-mm. What we notice in this plot is that there is not a populaiton of outliers like there was in the Ss5o vs. 5 i 7 0 plot (the only outliers are N1-001, Nl-034, and Nl-059 which all have sub-mm slopes which cannot be fit by any sensible dust/redshift combination and thus we assume suffer from some systematic effect such as pointing error - which we discuss more explicitly later. This common distribution implies that a single [/5, Tj(1 + z)\ combination describes the sample reasonably well. The lack of outliers, which were present in the S^o vs. 5170 plot, means that their location in the previous plot is most likely due to somewhat higher z rather than a different SED shape. In addition, their redshift cannot be too high - roughly up to z ~1 as roughly the shift between 170 /im and 450 /mi (a higher redshift, much warmer population would have to be very finely tuned to still fall on the same distribution, which seems improbable). For the benefit of later sections, we present in Fig. 3.5 the combined best-fit and confi-dence levels from both the 5170/5450 and 545o/5s5o slopes. Notice that since there are outliers with discrepant colours, we have somewhat artificially tightened the constraints by using the known best-fit 545o/5g5o slope, and only allowed for the S170/S450 slope to Chapter 3. Results & Analysis 34 200 h W • i-H 100 h X Figure 3.4: The histogram is the result of 1000 Monte Carlo simulations of the sub-mm fluxes of our sample. The dotted line shows the actual value of x2 for the observations. Only about ~ 2% of the simulations have a value this low (note that the binning is too crude to show that clearly). Chapter 3. Results & Analysis 35 be read off the data directly. This was necessary, since (as can be seen in the figure) the ft contours are highly elongated, thus the best-fit value is highly dependent on which sources are included/excluded from the fit. Thus, a more robust approach here is to use our prior knowledge of the best-fit S^o/Ssso slope (Table 3.2).. This only affects the best-fit B value (which is the more uncertain quantity), leaving the best-fit temperature essentially the same. Notice that since the contours in Fig. 3.5 should be regarded with caution, as different choices of including/excluding outliers, using best-fit slopes, or not affect this (partic-ularly the (3 value). When we look at the fits from each slope individually, we notice the same thing - the temperature is usually 30 K , but ranges from 20-50 K depending on various choices (i.e. extremely cold and very warm sources are excluded), but the acceptable /3 range is essentially the entire 1-2 range. It thus seems that Fig. 3.5 roughly represents what we could consider an acceptable range for our sample as a whole. With these caveats in mind, we can assume that it is reasonable to model our data as a single temperature grey body in the limited spectral range considered (i.e. 170 /mi—>-850 /mi) provided we explore the effects of varying the parameters within the accepted range we found here. This model is incorrect in detail for the entire thermal spectrum, as has been shown by several authors (e.g. [23], [4], [63], [44]). In general, any grey-body model, be it one, two, or three temperatures, remains only an approximation to the underlying far more complex dust properties. Thus, at this point, we cannot claim much knowledge of the true state of the dusty ISM of our galaxies, but merely seek the best parameters of an equivalent grey-body describing the far-IR/sub-mm spectrum. We now turn to the third column in Fig. 3.3, where the 5 outliers (except for Nl-059 which has an unusually high radio emission) return as such, confirming that indeed red-shift, rather than dust properties is the main difference between them and the rest of the sample. The tracking of the trough between the thermal and non-thermal emission is commonly used as a redshift indicator (e.g. [8]). We discuss it in the context of our sample in the following section. Chapter 3. Results & Analysis 36 1.8 -1.6 -1.4 -1.2 -J I I I I 1 I I I I I I I I 1 1 I I I I I I L 10 20 30 40 50 T / ( 1 + z ) Figure 3.5: The shows the best fit \B,T/(l + z)] combined from the 170/450 and 450/850 slopes, which is [1.5,31 K] along with the 68, 90, and 95% confidence levels. Notice that /5 is more poorly constrained. We exclude Nl-001, Nl-002, N l -034, and Nl-059 from the fit due to their discrepant colours. Chapter 3. Results & Analysis 37 3.3 Sub-mm/Radio redshifts As described in the introduction, SSSO/SI^GHZ * s a r e d s r u f t indicator [8]. It is, however, degenerate in dust properties for galaxies cooler than ~ 6 0 K [4]. Since we are clearly in that regime (see previous section), here we will look at the relation calibrated on samples with different selections. The Carilli & Yun relation (CY hereafter) is explicitly: af$ = -0.24 - [0.42(a r a d - a s m ) ln( l + z)]t where 350 GHz = 850 pm. (3.2) For the radio spectral index we use -0.75, which is fairly typical for a wide variety of sources (particularly optically thin, star-forming galaxies) [6]. For star-forming galaxies, the Rayleigh-Jeans spectrum tends to be oc v3~~A (e.g. Arp220 with a = 3.4, or M82 with a = 3.0) [8]. From the best fit 450 pm to 850 pm slope of our sample (Table 3.2), we arrive at a s m = 3.1 ± 0.21, although this is based on the mean source, and there are many outliers. Eq-n 3.2 is well parametrized (for the mean galaxy in the C Y sample of 17 which include radio-loud galaxies) by a fourth order polynomial in a (i.e. af5 4°) such that [8]: zCY = 0.050 - 0.308a + 12.4a2 - 23.0a 3 + 14.9a4. (3.3) A different parametrization is derived for the SLUGS (SCUBA Local Universe Galaxy Survey) sample by Dunne, Clements & Eales [24] (DCE hereafter), which selection has more dusty local galaxies, many of which show significant cold dust components [23]. Their result is: ZDCE = 0.551 - 6.652a + 25.57a2 - 30.56a3 + 13.75a4. (3.4) In Fig. 3.4 we compare the two, and overlay 5 of our sources which have spectroscopic redshifts. Notice that Nl-040 (z = 0.45) and Nl-064(z = 0.91) are reasonably well 1The spectral index is denned as a^ i f^ fo / f^ a n d so the associated error is loge(585o/545o)i/(5fO^K^f)2/log(850/450). The values for a?5 4° were found in an analo-gous way. In general we use the convention log = log 1 0 and In = loge. Chapter 3. Results & Analysis 38 described by the D C E relation, but in general, their redshifts are overestimated by the C Y relation. The local galaxies on the other hand, are poorly fit by either relation. This may suggest that the local F I R B A C K selection represents a different population than those selected using IRAS. This is sensible since we have no indication of our local sample being IRAS-bright. In Table 3.3, we explicitly derive the redshifts for our sample using both of these relation, as well as from eq. 3.2 with individual spectral indices for each source. We also list the sub-mm/radio and sub-mm spectral indices as a guide to interpreting some of the derived redshifts. Notice that the D C E relation vastly overestimates the redshift of very low (or negative) a sources. A source such as Nl-002 (z s p e c=0.07) which has a high a value has its redshift poorly estimated by all of these methods (it is even outside the C Y quoted uncertainty of ~ 0.5). D C E quote smaller errors; however, they fail to fit our local galaxies (their sample is local but IRAS-bright and thus may have somewhat different dust properties). We discuss the effects of selection in Chapter 5. We conclude that such relations, although useful in estimating the redshift distribution of sources over larger 2-ranges, provide too weak a constraint locally, due to the large scatter in intrinsic galaxy properties (giving an uncertainty of Az ~ 0.5). However, as a very crude redshift indicator this approach still confirms our prior selection of Nl-040, N1-064, N1-059, N1-078, and probably N1-048 as being at somewhat higher redshifts than the rest of the galaxies in our sample. 3.4 Sub-mm vs. near-IR Here we examine the correlation between the K magnitude and 850 / i m fluxes of our sources. The Ssso A u x density by itself is not a good redshift indicator due to its k-correction behavior. It is however a good luminosity tracer. The K magnitude (in the restframe) is also a luminosity indicator, as it is 10 times less obscured than the optical. The 5850 to K magnitude relation can be used as a redshift indicator [3, 18] because of the rest-frame shorter wavelengths (that are much more dust obscured) moving with Chapter 3. Results & Analysis 39 Table 3.3: The sub-mm/radio spectral indices and derived redshifts Source ,^350 "1.4 our Z D C E ZCY N l --001 0.38±0.07 O.OOiO.OO 0.00 0.34 0.78 N l --002 0.35±0.05 1.85±1.41 0.72 0.26 0.71 N l --004 0.26±0.08 3.46±0.70 0.32 0.07 0.46 N l --007 0.26±0.07 2.62±0.79 0.43 0.08 0.48 N l --008 -0.08±0.10 4.08±1.22 0.08 1.25 0.16 N l --009 0.20±0.08 1.75±1.31 0.52 0.02 0.33 N l --010 0.10±0.14 3.33±1.62 0.22 0.11 0.12 N l --012 0.29±0.20 2.81±2.38 0.43 0.13 0.55 N l --013 O.OOiO.OO 10.12±78.61 -0.06 0.00 0.00 N l --015 0.18±0.21 0.00±0.00 0.00 0.02 0.29 N l --016 -0.01±0.14 4.94±1.44 0.10 0.59 0.05 N l --024 0.25±0.08 3.77±0.79 0.29 0.06 0.44 N l --029 -0.06±0.62 5.77±5.48 0.07 1.00 0.11 N l --031 0.27±0.11 2.48±2.44 0.46 0.09 0.50 N l --032 0.33±0.21 3.84±1.94 0.34 0.21 0.65 N l --034 0.24±0.19 6.80±1.65 0.17 0.06 0.43 N l --039 O.OOiO.OO O.OOiO.OO 0.00 0.00 0.00 N l --040 0.51±0.04 2.66±1.15 0.69 0.68 1.07 N l --041 O.OOiO.OO 0.00±0.00 0.00 0.00 0.00 N l --045 0.36±0.09 2.54±1.12 0.54 0.27 0.71 N l --048 0.44±0.05 2.06±1.25 0.78 0.49 0.92 N l --056 O.OOiO.OO O.OOiO.OO 0.00 0.00 0.00 Chapter 3. Results & Analysis 40 Table 3.3: continued... Source ^350 "1.4 ~a ^our Z D C E 2 C Y N l -•059 0.43±0.06 0.12±7.89 5.30 0.46 0.89 N l --064 0.56±0.05 3.04±0.73 0.66 0.84 1.20 N l --068 0.29±0.12 3.05±1.29 0.40 0.13 0.55 N l --077 0.18±0.22 2.67±2.72 0.34 0.02 0.28 N l --078 0.58±0.05 2.88±0.54 0.71 0.88 1.23 N l --083 0.05±0.29 4.86±2.95 0.13 0.26 0.07 N l --101 0.15±0.31 4.86±2.72 0.18 0.03 0.22 N l --153 O.OOiO.OO O.OOiO.OO 0.00 0.00 0.00 N2--013 0.45±0.08 2.97±1.22 0.56 0.52 0.94 a Derived from the C Y relation (eq. 3.2) using our measured values of a s m and fixing a350=-0.75. 6 Derived from the relation of D C E [24]. c Redshifts derived using the C Y [8] 4th order polynomial fit. Note that, we have set to zero all instances when asm < 0. At negative af54° the D C E relation gives unphysical values. Chapter 3. Results & Analysis 41 0 0.5 1 1.5 z Figure 3.6: The sub-mm/radio spectral index as a redshift indicator. The thick solid line is the relation based on the SLUGS sample (104 galaxies - IRAS selected), with the dashed lines being its ±Ao envelope. The thin solid line is the stan-dard C Y relation [8] (17 galaxies - IRAS and N R A O selection) with dotted ±lcr envelope. The circles are 5 galaxies from our sample with spectroscopic redshifts. Chapter 3. Results & Analysis 42 increasing redshift into the observer-frame near-IR. Thus the K magnitude for a given sub-mm flux is dependent on both redshift and dust obscuration. Fig. 3.5 plots the flux at 850 yum against K magnitude, where the higher-z sources clearly populate a different locus from the nearby galaxies. They are roughly 3 a removed from the best-fit line for the other sources, with a distinct gap between the two groups (apart perhaps from two sources which we discuss later). The gap is more pronounced than in Fig. 3.3 as here the (1 + z ) /T d degeneracy is somewhat broken. Using the 6 spectroscopic redshifts available (see beginning of chapter), we fit a model for ln( l + z) = aK + blog(585o) + c, arriving at the lines overlaid in the figure. Explicitly, ln( l + z) = (0.07 ± 0.03)tf + (0.09 ± 0.30) log(S 8 5 0) - (0.86 ± 0.39). (3.5) This should be interpretted as only a very rough indicator of redshift, since only 6 sources were used in the fit. Due to the parameter space not being equally sampled, there is little sensitivity for varying sub-mm flux for a given K magnitude. In particular, information is lacking at the faint sub-mm/faint near-IR end. The fact that the if-magnitude of distant faint galaxies can be used as a redshift indicator was also discussed in a recent paper by Willot et al. [66] who derive the following relation from their sample of radio galaxies: K = 17.37 + 4.531og10 z - 0.31(log10 z ) 2 . (3.6) We compare this (dashed line) with our relation (solid line) in the bottom panel of Fig. 5.6. Since ours is more heavily biased towards local, starforming galaxies, whereas Willot et al.'s relation is based on radio galaxies, these lines can be regarded as a rough envelope encompasing a wide variety of galaxy types. A redshift relation based solely on the K magnitude is bound to be degenerate in some other galaxy properties (amount of dust, luminosity etc), and can only work for a very homogeneous sample of galaxies. The addition of sub-mm flux would make this relation more general as the if-band is dust absorption attenuated (specifically for distant, luminous galaxies), whereas the sub-mm flux is due to dust emission, and thus the combination of the two will somewhat break Chapter 3. Results & Analysis 43 K magnitude Figure 3.7: Sgso vs K magnitude for our sample (crosses and circles). The filled squares and if-band upper limits are from the lens survey of Smail et al. [61], while the pentagons are from the U K 8mJy survey [40]. The circles are our high-z candidates which populate a similar region to these S C U B A survey sources. The lines are the results from fitting a model to the 6 sources where zspec is available (see text) and are labelled with redshift. The bottom panel shows the K-z relationship obtained above (solid, for 5 8 5 0 = 5 m j y ) , compared with the Willot et al. [66] relation for radio galaxies (dashed). The error bar in the lower right-hand corner is a representative one for our measurements. Chapter 3. Results & Analysis 44 the dust degeneracy. This diagnostic of both the absorption and emission spectrum, would allow for a more robust redshift indicator over different galaxy types, although our particular relation is not well constrained due to the limited spectroscopic sample. However, it is clear that in general, object which are detected at 850 /zm, and are faint at if-band, are at higher redshift. The two possible exceptions to this are the sources Nl-032, and Nl-034 which have K magnitudes of ~ 19 and sub-mm fluxes of ~ 1 mJy. Without redshifts and other detailed follow-up, it is not clear what their nature is and why they occupy this part of the diagram. One possibility is multiple sources within the beam and related confusion issues. We can use the predictions of the galaxy evolution model of Devriendt et al. [20] for the K magnitudes and sub-mm fluxes for a variety of galaxy types to estimate the most likely type of source to occupy this location. It appears that a L I R G galaxy (such as M82) at z ~ 0.3 would be similarly faint at both sub-mm and near-IR bands. Although this is not a robust conclusion, it appears to be in reasonable agreement with both the sub-mm/radio redshift estimates (Table 3.3) and the unexceptional location of these galaxies in our scatter plots. Note however that Nl-034 has the highest 450/xm detection of our sample which (coupled with the low 850 /mi signal) we cannot easily explain with a single source. 3.5 SED fits We now fit single grey-body SEDs to the 170 /mi, 450 /mi, and 850 /mi fluxes of each source (see Fig. 3.8). As discussed previously, we assume optically-thin sources. The effect of including a non-negligible r in the fits is (as described by Blain et al. [4]) to suppress the peak with respect to the Rayleigh-Jeans tail such that the best-fit dust temperature inferred will be 10-20% higher than otherwise. This is therefore not an important effect for sub-mm spectra dominated by single temperature dust emission (to the precision of our fits of three points). In order to avoid stretching that assumption too much, we only use the 170 /mi, 450 /zm, and 850 /xm points in the fits, where the SED Chapter 3. Results & Analysis 45 1.3 15 6 10 1.5 20 5 6 1.7 22 4 5 1.9 18 2 1 1 is dominated by the coldest significant dust component. We fit for two parameters (ft is held constant) - the overall normalization, which gives the luminosity (if the redshift is known), and the wavelength shift, which is proportional to (1 + z)/TA. The best fit x2 a n d fit parameters were obtained with the PIKAIA genetic algorithm [12]. With only 3 points for each galaxy, we could not also fit for ft. However, we are able to investigate how different values of ft would affect the quality of fits for the sample as a whole. Table 3.4 shows the distribution of x2 values derived from fitting the SEDs with various ft values. We can see that for the sample as a whole values of ft = 1.5 — 1.7 are far better than either smaller, or larger values. The sources, with a poor fit in all cases are: Nl-001, Nl-002, Nl-015, Nl-034, and Nl-056. For the lowest B tested, 5 additional sources show a poor fit: Nl-008, Nl-009, Nl-012, Nl-013, Nl-016 (note that these are all among the brighter ISO sources from our sample). On the other hand, the high ft = 1.9 value, provides a poor fit for all the sources we singled out in the previous section as potentially being at higher redshifts. For local ULIGs, previous studies [23, 44] already show this trend, with lower ft providing a better fit when single temperature grey-bodies are used, whereas generally a ft ~ 2 is inferred for multi-temperature fits. Our sample is generally faint enough that apart from those significantly redshifted, none of our sources compare with local ULIGs. Thus they may be more comparable to the thermal spectrum characteristics of normal starforming galaxies. In a previous section we showed that the best-fit ft for our sample was around 1.5 (although with large uncertainties). We show the results for this ft in Table 3.5, and show Chapter 3. Results & Analysis 46 the SEDs in Fig. 3.8. Notice in particular that indeed the sub-mm slopes are generally well fit, and the fits fail (when they do) at the 170 /im point which tends to be above the curve. Conversely, when a /3 of 1.9 is used, the failed fits generally have their sub-mm points above the curve, which is suggested by the best fit (/5,T) from the 170 /xm/850 pm slope. This suggests that, even if more than one is present, a single dust component dominates the far-IR/sub-mm emission for these sources. Among the Sgso < 3a sources, the one which is not well fit by our simple model is Nl-034, which has an anomalously high 450 pm flux. Besides this one, which does not appear to be easily fit even with a 2-component SED, there are a few sources with a somewhat higher x2(2-3), suggesting that a combination SED (i.e. one with a warm and a cold component) might provide a better fit, although this could not be reliably investigated with these data alone. Notice that, in Fig. 3.8, we overlay the IRAS 100 pm points are not in the fits. For about half the sources, the 100 pm fluxes are clearly lower than the fit. However they are all on or above the fit for those sources suspected to be at somewhat higher-redshift (i.e. above z ~ 0.2 from Table. 3.5 using a generous temperature of 40 K ) . 3.6 Luminosity and SFR In this section, we wish to examine some of the physical characteristics of our sample. Since, fundamentally, the dust properties/distance degeneracy is still present, all such derivations are highly uncertain. However, we will provide such physical parameters for what we consider to be reasonable ranges of redshifts (for the likely higher redshift sources only) in order to allow for some comparison with other studies, and some handle on the physical nature of our sources. We also calculate these for all sources with available spectroscopic redshifts. We somewhat arbitrarily decide on the (/3,Td) combinations which both agree with the fit results presented in Fig. 3.5, with the redshift estimated from the sub-mm/radio, and sub-mm/near-IR relations, and are in general agreement with expectations from other studies (see Chapter 5). These are (1.7,30K), and (1.5, 40K). Table 3.6 shows the considered Chapter 3. Results & Analysis 47 i 1 N 1 D o o z> o i O xn X [1-1000/xm] Figure 3.8: The SED fits for our sample with /3 = 1.5. The £,y-ranges in all panels are the same (shown in the labels), and the sources are arranged with decreasing 170/im flux. The IRAS 100 /zm point is not used in the fit. For the sake of clarity, we rescale the flux via (A/170/im) 2. er 3. Results & Analysis Table Source Td/(l + z) x2 Nl-001 47.96 8.84 Nl-002 47.96 2.45 Nl-004 38.47 0.20 Nl-007 35.97 0.44 Nl-008 47.96 0.63 Nl-009 47.96 1.83 Nl-010 47.96 0.38 Nl-012 47.96 1.16 Nl-013 47.96 2.35 Nl-015 47.96 7.25 Nl-016 47.96 1.50 Nl-024 30.82 0.99 Nl-029 47.96 0.75 Nl-031 46.54 0.17 Nl-032 47.96 0.14 Nl-034 39.30 8.72 Nl-039 47.96 0.57 Nl-040 22.74 0.05 Nl-041 47.96 0.47 Nl-045 32.69 0.25 Nl-048 25.72 0.80 Nl-056 47.96 5.80 Nl-059 20.40 0.74 Nl-064 21.16 0.08 i: Fit results for f3 = 1.5. z(Td = 30 K) z(Td = 35K) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ,0.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.32 0.54 0.00 0.00 0.00 0.07 0.17 0.36 0.00 0.00 0.47 0.72 0.42 0.65 z(Td = AOK) 0.00 0.00 0.04 0.11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.30 0.00 0.00 0.00 0.02 0.00 0.76 0.00 0.22 0.56 0.00 0.96 0.89 Chapter 3. Results & Analysis 49 Table 3.5: continued... Source T d / ( l + z) x2 z(Td = SOK) z(Td = 35^) z(TA = AOK) Nl-068 32.70 0.00 0.00 0.07 0.22 Nl-077 47.96 0.31 0.00 0.00 0.00 Nl-078 20.03 0.03 0.50 0.75 1.00 Nl-083 47.96 0.34 0.00 0.00 0.00 Nl-101 29.69 1.11 0.01 0.18 0.35 N2-013 30.69 0.01 0.00 0.14 0.30 redshift ranges, luminosities2, and distances for the sources in our sample which are likely at non-zero redshift (at the resolution of our fits). The ranges illustrate how the values vary with input parameters, and also the qualitative agreement over a range of parameters. The sources in the upper half of the table are our S 8 5 0 > 3cr detections (excluding Nl-001, and Nl-002). They are consistent with z ~ 0.4 - 0.9 ULIGs - based on the average luminosity of the sample in the given range being above 1 O 1 2 L 0 . The likely lowest luminosity, and redshift source of this set is N1-048 which may even be only a Luminous Infrared Galaxy (LIG) depending on the exact dust parameters. The bottom half of Table 3.6 contains five LIG candidates (Nl-101, N2-013, Nl-024, Nl-068, and Nl-045) based on the considered range in dust parameters. The only surprise here is Nl-008 since, with its zspec — 0.26, it should have been grouped with the above. Possible explanations for its omission are: 1) its dust properties are too far outside the considered range, and 2) it is affected by confusion. The second one is more likely as there are two radio sources within the ISO beam (see Fig.3.2). In an upcoming observing run, we plan to observe the second radio source with S C U B A which should allow us to disentable the contribution of each radio source to the total far-IR flux, and thus, potentially, bring our photometric estimate in better agreement with the 2We solve for the luminosity simply by integrating our fitted SEDs. This is not entirely accurate, however, is sufficient given the far larger systematic uncertainties (such as the unknown T d ) . The key mathematical step is the integral xs~1(ex — l)_1cfa; = T(s)((s). Chapter 3. Results & Analysis 50 Table 3.6: Fit results for the higher-z sources" Source z log(L) [LQ] DL [Mpc] Nl-078 0.66-1.00 12.14-12.63 3662-6121 Nl-059 0.64-0.96 12.16-12.64 3526-5854 Nl-064 0.58-0.89(0.91) 12.07-12.56 3180-5326 Nl-040 0.49-0.76(0.45) 12.01-12.53 2580-4372 Nl-048 0.33-0.56 11.65-12.26 1632-2989 Nl-101 0.18-0.35 11.02-11.79 807-1711 N2-013 0.15-0.30 11.14-11.93 684-1462 Nl-024 0.14-0.30 11.11-11.97 621-1434 Nl-068 0.08-0.22 10.41-11.53 329-1031 Nl-045 0.08-0.22 10.46-11.61 320-1031 a The ranges correspond to different (/?, T d ) combinations the first being (1.7,30 K) the second (1.5,40 K ) . The redshifts in brackets are spectroscopic. The top half of the table has the > 3a detections while the bottom half has the other sources from the sample with non-zero redshifts from our fits. The sources are arranged by decreasing redshift. Chapter 3. Results & Analysis 51 spectroscopic redshift. Based on our available data we have two routes to estimating the SFR. The first SFR estimator we consider is the based on the FIR luminosities. The idea behind this is that, the thermal dust emission is reprocessed stellar light which was absorbed primarily in the U V (i.e. where young stars are the primary contributors). For a review discussion of the uncertainties associated with this and other SFR estimators see Schaerer 1999 [56]. Essentially, the problem is to find a universal calibration given the vastly varying conditions (e.g. different dust properties, and contribution of cirrus, old stars, or A G N to the thermal spectrum) from galaxy to galaxy. One parametrization is SFR = a x l O ~ l o L F i R / L 0 [ M 0 y r _ 1 ] , where a = / ( IMF) if we neglect all the above uncertainties and calibrate the SFR based on stellar evolution models alone. Here we adopt the form of Chariot et al.[13], which is based on a Salpeter IMF and is as follows: SFR = 1.7 x l O - ^ ^ f M o y r - 1 ] . (3.7) L 0 The second is based on the radio continuum, where the idea is essentially the same as above and use is made of the well known far-IR/radio correlation (see discussion in Chapter 1). Here we largely follow Yun et al. [68] who derive the empirical relations based on IRAS galaxies with radio observations. S F R / M o y r - 1 ) = (5.9 ± 1 .8)10- 2 2 L 1 . 4 G Hz (WHz- 1 ) (3.8) The radio luminosity is obtained via l o g - L i ^ G H z t W H z - 1 ) = 20.08 + 21ogD + l o g S M G H z (3.9) where D is in Mpc and SIAGHZ is in Jy. We use both these methods to estimate the SFRs for the non-zero redshift sources. The results are presented in Table 3.7. The two estimators agree with each other reasonably well (as can be expected). The strongest deviation is observed for Nl-059, however that source has a greater radio flux by a factor of roughly ~ 2 from its peers. In general estimates for lower luminosity sources are more affected by the various systematic uncertainties discussed above. Chapter 3. Results & Analysis 52 Table 3.7: Estimating the Star Formation Rates a. Source z SFRx^cHztMoyr" 1] S P R ^ M ^ 1 ] Nl-078 0.66-1.00 228-638 235-725 Nl-059 0.64-0.96 529-1459 246-742 Nl-064 0.58-0.89(0.91) 165-463 200-617 Nl-040 0.49-0.76(0.45) 156-447 174-576 Nl-048 0.33-0.56 70-235 76-309 Nl-101 0.18-0.35 18-81 18-105 N2-013 0.15-0.30 10-45 23-145 Nl-024 0.14-0.30 21-109 22-159 Nl-068 0.08-0.22 3-33 4-58 Nl-045 0.08-0.22 3-32 5-69 a This table is arranged in an analogous way to Table 3.6. CHAPTER 4 53 A M O D E L In this chapter we present a simple phenomenological model that reproduces the main characteristics of the observed distribution of fluxes for our F I R B A C K targets. Our goal is a model for N(z) expected from our selection criteria. This involves determin-ing the luminosity function (LF) as a function of z, and the limiting flux per (L,z) pair as determined from evolving reasonable SED templates. A specific cosmological model needs to be used to determine the distance and volume element (ie dV/dz) variation with redshift. The cosmological relations leading to these are presented in Appendix B. First, we start with the z-dependent L F . The main premise of the model involves the separation of the galaxy population into a quiescent component and a U L I G component, and then to evolve the two separately. This rather approximate treatment is inspired by the IRAS local L F where the previously unknown luminous dusty galaxies modify the shape to be more like a double power law rather than the exponentially declining (at high luminosities) Schecter function of normal galaxies [55]. On the other hand, at high-z, no-evolution models completely fail to fit the observed number counts (e.g. [21]). Since less luminous, quiescent galaxies will likely not contribute much to higher-z counts (due to selection), evolving the higher luminosity population is a reasonable approximation. A similar phenomenological model has been carried out by Lagache et al. [45]. We thus use a luminosity function of the combined form: <j> — ^Schecter + </>ULIG (4.1) where the Schecter luminosity function has the form: For the quiescent galaxies we use as=-0A, (jfs = 7x 1 0 _ 4 M p c _ 3 M b o r 1 , and L* = 1 0 n L Q . The U L I G L F we use behaves in the opposite way - it cuts off exponentially at smaller Chapter 4- A Model 54 luminosities and is a power law at higher luminosities, where the Schecter function is exponentially cut off. Explicitly, the ULIG L F we use is: 0ULIG = K (J^J 'e-VWW with g = (1 + z)\ (4.3) where a u=-2.5, (j)*u = 1 x l O ^ M p c ^ M b o l - 1 , L*u = 2x 1 O U L 0 , and / is a fudge factor to smooth over the gap of the two components due to the strong evolution. It has the form 1/(1 + z)0-3. Thus the combination of the two essentially results in two power laws in the local Universe to match observations: typically, the knee is estimated at 1 — 5 x l O n L 0 [14], and the U L I G slope at -2.2 [55]. Clearly, there are degeneracies between the various parameters in such phenomenological modelling. We chose the ensemble of values to be such as to make our particular parametrization fit the local L F . The luminosity evolution of (1 + z ) 4 is assumed based on models in the literature [67]. We must break this evolution at some point (to avoid running into inifinities). We do so by freezing the evolution at z—1 (which is also our range of interest). This is similar to the step taken by X u [67] who freeze the evolution at z = 1.5. We do not explicitly consider number evolution (as from merging); however, note that the fudge factor above acts slightly as a luminosity-dependent density evolution (although with an awkward parameterization). In general, the observations can be fit also either by pure number evolution or a combination of number and luminosity evolution within a variety of parameterizations of the L F (e.g. [45], [14], [33], [67]). A more decisive test of the validity of a particular model is how well does it reproduce the observed intensity of the CIB for example. We have not performed such a test, thus the model at present lacks true robustness, but is sufficient to our purposes. To obtain the flux at some wavelength for a given luminosity and redshift, we use a cold and a starburst galaxy templates (for each of the two components) [45] and evolve them with redshift. These are compared in Fig. 4.2 which also highlights the effect of cold dust on the SED shape. Fig. 4.3 shows an example of a L w 1 O 1 2 L 0 spectral template being evolved from z = 0.1 — 5. The templates are evolved with redshift using S " o d j / o = -rradve (4.4) Chapter 4- A Model 55 1 0 11 12 ' o g ( L ) [ L j 13 o O Q. O - 2 =0.5 : -\ >v \ N. -\ \ 1 0 11 12 log(L)[Lj 13 • i i i i < i i r , i i 2 =1.0 : .**\ . > > ' - \ \ \ 1 0 11 1 2 "og(L)[g 13 o 2 o a 2 •e- _ cn o 1 0 11 12 " o g ( L ) [ L j 13 Figure 4.1: This is the luminosity function used for our models and its evolution with redshift. The dashed line is a non-evolving cold, dusty galaxy population, while the dotted line is an evolving ULIG population - the solid line is the sum of the two. See text for details. Chapter 4- A Model 56 where L \ is the conventional luminosity distance, and the subscripts "o" and "e" refer to "observed" and "emitted", respectively (see Appendix B). This can be rewritten using the /c-correction k = LVe/LVo and using due/du0 = (1 + z) so that kL = ( 4 5 ) L A n instructive exercise is to plot the 850 //m flux as a function of redshift as an illustration of the effect of the negative ^-correction at that wavelength. This is shown in Fig. 4.4 (for a typical galaxy out of our subsample of 5 higher-z sources) - the 850 /im flux hardly changes beyond z ~ 1. The number of galaxies in the range L to L + dL and z to z + dz is simply the product of the L F and volume element. Thus N(z) is the above integrated over all luminosities above a minimum L which, at the given redshift, corresponds to some observational flux limit (e.g. the F I R B A C K 3 a flux limit). Explicitly, this is as follows: dV 0([OgL,Z] llogL(S>Slim,z) Of particular interest to us are the number counts at 170 /im, from which population our sample is selected, and at 850 /mi where we are making a connection with the "blank-sky" S C U B A sources. The results of these are presented in Fig. 4.5 and 4.6 respectively. Fig. 4.5 suggests that a bimodal redshift distribution might be expected, which is dis-cussed in greater detail in Chapter 5. Since redshifts are difficult to obtain for distant dusty galaxies (e.g. see Results section of this thesis), a more observationally testable distribution is which is: N(z,S > Slim) = j ( l o g L , z ) ^ l o g L . (4.6) JloRL(S>SKm,z) dz dN / - * m a x x n ^ t ^dlogLdV Is We therefore plan to test this model (with better characterization of the high-z evolution) against the observed A^(> S) distribution 1. At this stage, this model aims at illustrating 1The zeroth, first and second moments of the ^ distribution are, respectively, the counts JV(> S) = J jjgdS, the background intensity h = J ^-SvdS, and the background fluctuations (6(IV)2) = J ^SldS, which are all observationally testable. Chapter 4- A Model 57 1 10 100 1000 10000 wavelength[/^m] Figure 4.2: This shows the cold galaxy template (solid) compared with the starburst galaxy template (dashed) at the same luminosity (~ 1 O 1 X L 0 ) . These were used in our model, but are shown here also as an illustration of the effect of cold dust on the SED shape. These templates are the work of Guilaine Lagache and are used in her model [45]. Chapter 4- A Model 58 10000.01 1 .10 100 1000 10000 wavelength[/^m] Figure 4.3: This shows the starburst galaxy template for a L ~ 1 O 1 2 L 0 galaxy. The template is evolved with redshift - from top to bottom z=0.1, 0.5, 1.0, 3.0, and 5.0. Notice that this figure also illustrates the negative /c-correction at 850 /im (see next figure). Chapter 4- A Model 59 E X 0 4 redshift 8 Figure 4.4: Here we plot the 850pm flux vs. redshift for a 4x 1 O 1 2 L 0 starburst (template) galaxy. This serves the double purpose of illustrating the effect of the negative ^-correction at 850 pm, and predicting what our 5 higher-z sources would look like at different redshifts. We cut the curve at z = 0.5 for scaling purposes. Chapter 4- A Model 60 4.0x10 3.0x1 (TE-JjL 2.0x10 f-N 1.0x10 0 n 1 r-0.0 ~ i i i I i i i i I r~ 0.5 _j i i i i _ 1.0 redshift 1.5 2.0 Figure 4.5: The result of our model for the predicted number counts at 170 pm with limiting flux of 135 mJy (=3 a for F I R B A C K ) Chapter 4- A Model 61 4.0x10 3.0x10 F-jjL 2.0x10 E" N 1.0x104 0E ~T 1 1 1 1 1 1 — ~l 1 1 1 1 r-0.0 0.5 _i i i i_ 1.0 redshift 1.5 2.0 Figure 4.6: -The result of our model for the predicted number counts at 850 /im with limiting flux of 3.5 mJy (=3cr for our sample) Chapter 4- A Model 62 some of the essential intredients in phenomenological galaxy evolution modelling, as well as illustrating how a reasonable set of assumptions results in a redshift distribution which is reminiscent of what we observe for our sample. Similar models from the literature, and their results, are discussed in Chapter 5. 63 CHAPTER 5 SUMMARY & DISCUSSION The multiwavelength photometric analysis of the sample of galaxies presented in the previous sections provides us with an insight into the brightest contributors to the CIB. This sample holds information on galaxy evolution roughly in the range z ~ 0 — 1. Here we discuss the results of this work, and place them in the context of similar or comple-mentary observations as well as model predictions. The first thing we looked at was the series of scatter plots in Fig. 3.3. We noticed that a group of 5 sources (Nl-040, Nl-048, Nl-059, Nl-064, Nl-078) stand out from the rest in several of the plotted relations (particularly far-IR/sub-mm, and sub-mm/radio). Their position in the far-IR/sub-mm plot can be explained either by their being much colder, or at somewhat higher redshift than the rest of the sample (the T<j/(1 + z) degeneracy). However, when the sub-mm slope (S^so/S'sso) alone is examined, these sources do not stand out as might be expected if their instrinsic SED shapes were substantially different from the rest of the sample. Thus, we assume an essentially constant SED shape across the sample, and arrive at a combined best-fit single grey-body (from the Sno/S^o and S450/S850 slopes) with /3 ~ 1.5 and Td/(1 + z) ~ 3 0 K . See Fig. 3.5 for confidence levels. When the sub-mm/radio relation is examined, the group of 5 stands out again, with a number of redshift estimators agreeing as to their being at higher (~0.4-1.0) redshifts. These indicators have large intrinsic uncertainties (Az ~ 0.5), which, added to the large uncertainties in the spectral indices themselves, means that they do not give very reliable redshifts, although they do provide a useful qualitative way of distinguishing the higher redshift candidates. The D C E (Dunne, Clements & Eales [24]) relation seemed to provide the best-fit to the spectroscopic data, and thus is considered more reliable. The above five sources are the only ones for which this relation gives a redshift > 0.4. A n exception is N2-013, but on the basis of the SED fits, we suspect this source of being a luminous Chapter 5. Summary & Discussion 64 infrared galaxy at non-negligible redshift, perhaps ~0.3, which is consistent with the redshifts provided by the sub-mm/radio relations. On the whole, these redshift relations are based on samples of extremely luminous infrared and radio galaxies. This may not apply well to our local sample, since it is consistent with lower luminosity starforming galaxies (in particular Nl-001, and Nl-002 both have spectroscopic redshifts which are poorly fit by all considered relations). A different way to look at the data is the sub-mm/near-IR relation (Fig. 3.7). Here, the segregation of the higher redshift candidates is most pronounced - more than 2cr separate each of the above 5 sources from any of the rest of the sample (although the location of Nl-032, and Nl-034 is poorly understood at this point). This projection has the advantage of sampling two spectral regions with completely different emission mechanisms: thermal dust emission vs. stellar light plus dust attenuation (luminosity dependent). This means that the Td/(l + z) degeneracy is largely broken. However, since no robust relation is known, at present, we can do little beyond obtaining a qualitative confirmation of the approximate redshift range of the sources. From our sample, and the K-z relation for radio galaxies, from Willot et al. [66], we construct a rough envelope in the K-z diagram (see bottom of Fig. 3.7). It is possible that the 850/xm point could be used (as a luminosity gauge) in conjunction with the ^-magnitude, leading to a redshift indicator encompassing the entire range of dusty, lu-minous, high-SFR galaxies. Although we attempt this here, with only 6 galaxies for which spectroscopic redshifts are available we cannot provide a robust relation. The situation will improve once our sample has more complete spectroscopic coverage. Since such a relation would suffer from a completely different set of systematic uncertainties than the radio/sub-mm photometric redshifts, the combination of both would be a good way to constrain the redshifts at the same time as distinguishing between the colder and warmer sources. This is difficult for the traditional sub-mm/radio relations alone for sources be-low 60 K . The potential of such an approach was already shown by Dannerbauer et al.[18] in the context of their mm-selected galaxies compared with the IRAS-selected galaxies of the SLUGS sample [23]. Chapter 5. Summary & Discussion 65 Finally, we used the knowledge of the general trends in our sample, inferred from the above steps, to attempt to constrain some of their individual properties. We thus fit single, optically-thin, grey-bodies to the 170/im, 450 /mi, and 850/im points. Since /3 was poorly constrained from fitting the slopes alone (see section 3.2), we investigated a number of representative values (1.3, 1.5, 1.7, and 1.9). We discovered that for the sam-ple as a whole only (3 ~1.5-1.7 provides a good fit, while 1.3 is a poor fit to many of the probably local sources, and 1.9 is a poor fit to our higher-z candidates. Since the fits only provide T/(l + z), a dust temperature needs to be assumed in order to obtain a redshift. We esimate that an acceptable range is the [/3, T] combinations [1.7,30 K]->[1.5,40 K] . These give redshifts which are in reasonable agreement with all relations examined so far (including the D C E , and C Y (Carilli & Yun [8]) redshift indicators). In Section 3.6, we uses this range to estimate the luminosities, and SFRs of the 5 high-z candidates, along with some sources which are possible LIGs at z ~ 0.3. Our results, from near-IR to radio, are consistent with having a sample of mostly local galaxies, some slightly higher redshift LIGs and a handful of probable ULIGs at redshifts about 0.4 < z < 1.0. Merger Morphology: We have selected a representative sample of ULIGs (possibly merger systems) at red-shifts z ~ 0.5 — 1.0, which are likely to be the counterparts of faint (585o=2-3mJy) high-z S C U B A sources (Fig. 4.4), which are usually modelled with local ULIGs as tem-plates. By providing a longer baseline compared to local studies[64], our sample will allow for evolutionary effects in merger morphology to be investigated. This would per-haps also allow for more realistic local counterparts to the high-z systems to be selected. A better understanding of mergers at various epochs has obvious implications for our understanding of galaxy formation, since mergers are crucial within the popular hierar-chical structure formation picture. We discuss some of these issues below, in the context of the two spectroscopically confirmed ULIGs. The physical size of an object is related to its angular size by d = 7J M A0/(1 + z), where DM is the comoving radial distance defined in Appendix B, and A9 is the angular size. Chapter 5. Summary & Discussion 66 Thus from our if-band images we infer for Nl-064 a fairly compact size of ~3 kpc (based on a half-light radius of ~ 0.4") for each of the interacting components, and a projected separation between them of ~18kpc. The J l component of Nl-040 (at z=0.45) is also very compact (~1.5kpc), and its separation from J2 is ~15kpc - assuming that J2 is interacting with it (which is not confirmed at this stage). Typical separations in local ULIGs are 1-2 kpc although some extend to > lOkpc [64], [55]. Higher redshift merger morphologies are hard to obtain as they are rarely resolved and often have no confirmed redshift. A n example is a set of lens-amplified z ~ 2 ULIGs which, in high-resolution near-IR imaging, show compact components at projected separations of 5 —10 kpc (based on H0=5Q, q=0.5 cosmology) [41]. This is quite similar to Nl-064. This issue, in gen-eral, has not been addressed thoroughly enough to be able to claim that the average U L I G merger at higher-z involves.wider separations than locally. If true however, this has important implications as an indication of the inadequacy of using local systems as templates for high-z systems of equal luminosity, since the SED shapes would differ. Pursuing such morphological studies of high-z mergers has implications for our under-standing of galaxy formation, especially the formation of spheroids which are believed to result directly from mergers at various epochs. For example, one possible mechanism for achieving ULIG-like luminosities at such early stages of the merger is to funnel more gas into the centre of the galaxies via bar instabilities which would be impeded by the presence of large bulges (such as are usually present in local ULIGs) [6] [41]. It is clear that, as an alternative to mechanical dumping of more gas into the starforming region, the same effect can be achieved by allowing for easier propagation of photons through the ISM. This can be achieved either by different ISM (smaller dust grains, lower metal-licity, ionization, etc.), or different ISRF (InterStellar Radiation Field) properties (e.g. an IMF leaning towards more massive stars). Exactly how our sample relates to merger sequences and local ULIGs will await more detailed observational follow-up. Chapter 5. Summary & Discussion 5.1 Comparison with related studies 67 A survey similar to F I R B A C K in depth (with 3 o limit of Si 7 0=150 mjy) was carried out in the Lockman Hole region [43]. Optical/NIR and radio follow-up, including imaging and spectroscopy of 35 out of 45 detected sources, revealed 1 hyperluminous galaxy at z=1.6, 11 ULIGs at 0.3 < z < 1.2, 12 LIRGs at z < 0.3, and the rest a mixture (in spectroscopic classification) of local starforming galaxies. This is in qualitative agreement with our results. However, we do seem to find fewer ULIGs relative to this study. It is not clear how the 35 were selected out of the 45 detections. Assuming that all their remaining detections are local sources, we still have ~ 10% fewer higher-z ULIGs candidates than they find. Our U L I G candidates were selected on the basis of their photometric proper-ties with respect to the rest of the sample, but there are enough intermediate sources in our sample (e.g. Nl-045, Nl-068, N2-013) that could be at redshifts of ~ 0.3 to bring the two surveys in even closer agreement. Until we have full spectroscopic coverage of our sample, we cannot confidently differentiate between redshift binning finer than ~ 0.5. However, our additional radio selection would exclude a hyperluminous galaxy such as found in this Lockman Hole survey. A much shallower (detection limit ~600mJy) ISO 170 /xm survey was the Serendipity Survey [63]. Their sample was found to be primarily composed of local, L ~ 1 O 1 O L 0 spirals which were well fit by cold (~20 K) dust temperatures. Some fraction of our local sample are likely to overlap with this sample. A much better overlap can be achieved by deeper mid-IR surveys such as the 12 /xm selected sources of Clements et al. [16]. Optical follow-up of this sample was found to be composed of mostly z ~ 0 sources of low L ~ 10 1 0 I / Q with a higher-z tail extending to z ~ 0.5. Notice that a 12 /xm survey is insensitive to higher redshift objects due to the unfavourable ^-correction. We are clearly observing the similar type of population with our low-z sources. Our higher-luminosity sources (LIRGs, and ULIGs) on the other hand are likely to be more similar to IRAS-bright galaxies. The S C U B A Local Universe Galaxy Sur-vey (SLUGS) consists of 104 galaxies selected form the IRAS Bright Galaxy Catalogue Chapter 5. Summary & Discussion 68 (BGC), and followed-up with S C U B A [23]. The single grey-body fits yield 8 = 1.3 ± 0.2 and Td = 38±3K. However, including some 450 /im data they fit two grey-bodies and find that although some galaxies continue to be well described by ~ 40 K dust temperatures, some require an additional much lower T ~ 20 K temperature component (and 8 = 2) much more consistent with regular local starforming galaxies (e.g. the Milky Way). Klaas et al. [44] present a set of far-IR to mm SEDs for 41 local ULIG galaxies from which they infer a 3-component dust model. The warm one (T > 50 K) is only important at mid-IR wavelengths, the far-IR/sub-mm being represented by a combination of a cool (30 < T < 50 K) component, and a cold (T < 30 K) component. In addition they infer 8 = 2, and low opacity. From their SEDs, it is clear that although the cold component is the best description for the sub-mm points, it is a negligible contribution around the peak. On the other hand, their cool component fits the peak well while somewhat under-estimating the sub-mm fluxes (however a lower 8 than their value of 2 would account for that). Thus, since we can only fit single grey-bodies to the SEDs, over 170/im->-850/im, and a poor fit is provided for our higher-luminosity sources by /3=1.9, it seems as though the best fit equivalent single grey-body corresponds most closely to the cool temperature component of Klaas et al.[44]. Whether this is simply a phenomenological fit parameter, or represents a true physical temperature for the dust will require further study. 5.2 Bimodality Some of the scatter plots discussed above suggest a bimodality in our sample. Whether our particular observational selection effects result in bimodality in redshift, or just a higher-z tail is an important point for distinguishing various galaxy evolution models (discussed in Section 5.3). Due to the small size of our high-z candidates sample, it is difficult to test their distribution properties. A test which we can perform involves comparing the x2 resulting from fitting a single line (y = mx), against that for fitting two lines, both with zero y-intercept, to the 5 i 7 0 vs. 5 8 5 0 projection. We chose this Chapter 5. Summary & Discussion 69 particular projection as here the bimodality is implied, but is not as clean as in the sub-mm/near-IR relation. We show the result in Fig. 5.1. We performed this test with the ID x2 simply assuming constant error for each source (since they are fairly uniformly distributed). The single line fit results in x2 of 108, while the two-line fit results in x2 °f 37. By comparing the x2s we conclude that the two line fit provides a much better fit to our data (where N=31) than the single line fit. This supports the idea that a handful of our sources lie at z ~ 0.5, while most of the sample are at z ~ 0. 5.3 Comparison with evolutionary models The sources studied here are a represenetative sample of the brightest ~10% of the CIB. They thus provide a test of the various evolutionary models abounding in the literature. Models which are consistent with both the CIB intensities observed, and the number counts obtained by various surveys, imply that the majority (~80%) of the CIB near its peak (~200 / i m ) will be resolved by sources 0 < z < 1.5. The same redshift range sources contribute only ~ 30% of the 850/im background [28, 14]. The same models result in a peak of the SFR density at z ~ 1.0, which is essentially flat from there until z ~ 4. In general, > 70% of the star formation takes place in galaxies with L-pm. > 10 1 1L© [14]. From the redshifts we infer for our sample, it seems to span a crucial epoch over which the strongest evolution of the SFR density takes place. In general there is no way to fit the F I R B A C K counts without strong far-IR evolution over at least this redshift range. With the starburst template we use in Chapter 4, we see that sources less luminous than about 1 0 1 2 L Q fall below the F I R B A C K detectability beyond redshift ~0.4. Fig. 5.2 shows the relative contributions to the CIB of normal galaxies, LIRGs, and ULIGs as a function of redshift from the models of Chary k, Elbaz [14]. It makes it clear why the F I R B A C K survey resolved only a small fraction of the CIB. Since the F I R B A C K selection excludes normal galaxies beyond z ~ 0.1 and LIRGs beyond z ~ 0.3, but allows for higher-luminosity sources up to z ~ 1.0, our mix of normal, starforming galaxies, a Chapter 5. Summary & Discussion 70 I i i I i i i I i i • i I / i i i i i i i i i | I 200 400 600 200 400 600 S 1 7 0 M m [m Jy] Figure 5.1: Here we test the hypothesis of our sample being bimodal by comparing the X2 of a single-line fit for the entire sample (right panel) to a two-line fit to each sub-sample (left panel). The dashed lines are ±la where a is the rms scatter in the y-direction. Notice that, apart from Nl-048, even with the single-line fit to the entire sample, our high-z candidates are > 2a away from the best-fit line. Chapter 5. Summary & Discussion 71 15 - i — i — i — i — r - i — i — i — i — i — I — i — i — i — r n — i — i — i i — r c 3 o u o CD E o c o 3 XI c o o 10 / / • 0 —J I I I I I I I L . _L . -L! '. 'i."-*.r ' "i °~* T " r ""i -»> — 1 - - T -2 Redshi f t Figure 5.2: One example of redshift contributions to the CIB. Here the dot-dashed line represents normal, starforming galaxies, the dotted line is the ULIGs, and the dashed line is the LIGs (reproduced from Chary & Elbaz 2001 [14]). few possible LIRGs, and a handful of most likely higher-z ULIGs is in good qualitative agreement with this model. The bimodality, which this hints at for our selection (and which we appear to observe), is more directly shown by other models [45, 10, 22, 65, 33]. The easiest way to achieve it is to build-in the discontinuity phenomenologically by decomposing the luminosity function into a component of normal, quiescent galaxies, and a much more luminous component of ULIGs (or AGN) , and have the luminous component evolve more strongly than the quiescent one so that it dominates the luminosity funciton by z ~ 1 [22, 65, 33]. This approach was exploited in the context of the F I R B A C K Chapter 5. Summary & Discussion 72 sources by Lagache et al. [45], confirming our results in that a double-peaked redshift distribution is predicted. Other models with the same feature amount to the same basic physics (rapid evolution of the far-IR bright population), although some may be more directly related to galaxy evolution models. One example is that of Chapman et al. [10]. It combines the colour (i.e. temperature) distribution of local galaxies with a strong luminosity evolution (such as in [67]), to produce a bi-variate distribution for the F I R B A C K population (including cold luminous sources), as observed in our sample. Discriminating in detail between such models, including issues such as separating density evolution from luminosity evolution, will require the full redshift distribution. The F I R B A C K selection allows us to investigate the range 0 < z < 1. On the other hand z ~ 1 is the lower limit of sub-mm/mm selected surveys (e.g. [61, 18]). Thus samples such as ours should act as a bridge between the local Universe and the higher redshifts population detected in long-wavelength surveys. We show this explicitly in Fig. 3.7 where we overlay a number of SCUBA-selected sources, and show that they occupy essentially the same sub-mm/near-IR space as our high-z candidates. Hence it should be possible, by investigating our higher-z candidates in detail, to determine the properties of a subset of SCUBA-type galaxies, in a way which is next to impossible for the typical z ~ 3 sources. 5.4 Future Direction In conclusion, even though the majority of the sources are not individually detected: 1) the sample as a whole is strongly detected (~ 10a for both bands); and 2) there is a wealth of statistical information to be extracted about the nature of the sources comprising the sample. This highlights the importance of carefully obtaining a uniform sample, rather than an inhomogeneous collection of data. Such targetted photometry observations reveal some of the same fundamental trends as a more costly (observationally) full-imaging survey. We have learned that the brightest 10% of the CIB is composed of two different types of Chapter 5. Summary & Discussion 7 3 galaxy: about 1/6 is the low redshift tail of a rapidly evolving ULIG population; and the other 5/6 are mainly nearby quiescently star-forming galaxies like the Milky Way. Further progress on constraining models in detail will come from spectroscopic and morphological studies of the entire sample. Understanding what makes up the other ~ 90% of the CIB will await future far-IR missions with smaller beamsizes, such as B L A S T and Herschel, as well as high sensitivity mid-IR facilities such as SIRTF. 74 BIBLIOGRAPHY [1] Archibald E. , Wagg J.W., Jenness T., 2000, J A C , J C M T , http://www.jach.hawaii .edU /JACdocs/JCMT/SCD/SN/002.2/ [2] Barger A . J . , Cowie L .L . , Mushotzky R., et al. 2001, A J , 121, 662 [3] Barger A . J . , Cowie L . L . , Sanders D.B. , 1999, A J , 518, L5 [4] Blain A .W. , Smail I., Ivison R.J . , Kneib J.-R, Prayer D.T., 2002, astro-ph/0202228 [5] Blain A . W . , Kneib J.-R, Ivison R.J . , Smail I., 1999, ApJ , 512, L87 [6] Binney J., Merrifield M . , 1998,"Galactic Astronomy",Princeton University Press [7: Bridger A. , Wright G.S., Economou F., Tan M . , Currie M . , Pickup D., Adamson A. , Rees N . , Purves M . , Kackley R., 2000,SPIE, 2009, 227 Carilli C.L. , Yun M.S., 1999, ApJ , 530, 618 [9] Carroll S.M., Press W.H. , Turner E.L. , 1992, A R A A , 30, 499 [10] Chapman S . C , Helou G., Lewis G., Dale D., 2002, ApJ , to be submitted [11] Chapman S.C.,Smail I., et a l , 2001, submitted to A p J [12] Charbonneau P., 1999, ApJ , 101, 309 [13] Chariot et al., 2002, astro-ph/0111289 [14] Chary R., Elbaz D., 2001, ApJ , 556, 562 [15] Ciliegi P., et al., 1999, M N R A S , 302, 222 Bibliography 7 5 [16] Clements D.L. , Desert F - X , Fracescini A . , 2001, accepted by M N R A S , astro-ph/0103242 [17; [18 [19 [20 [21 [22 Dole H. , et al., 1999,"ISO surveys a dusty Universe", Eds. D. Lemke, M . Stickel, K . Wilke, p.54 [23; [24; [25; [26; [27 [28; [29 [31 [32 Cowie L . L . , Barger A . J . , Kneib J.-P., 2002, A J , in press Dannerbauer H. , Lehnert M.D. , Lutz D. et al., 2002, astro-ph/0201104 Davis R., Burston A. , Ward M . , 2000, astro-ph/0012221 Devriendt J .E.G. , Guiderdoni B. , Sadat R., 1999, A & A , 350, 381 Dole H.,Gispert R.,Lagache G., et a l , 2001, A & A , 372,364 Dunne L. , Eales S.A., 2001, M N R A S , 327, 697D Dunne L. , Clements D.L. , Eales S.A., 2000, M N R A S , 319, 813D Dunne L. , 2000, PhD thesis, University of Wales Dwek E., Arendt R., Hauser M . , et al., 1998, ApJ , 508, 106 Elbaz D.,Cesarsky C.J . , Fadda D., et a l , 1999, A & A Letters, 351, L37 Elbaz D.,Cesarsky C.J. , Chanial P., et al., 2002, astro-ph/0201328 Fabian A.C.,Smail I., Iwasawa K. , Allen S.W.,Blain A .W. , Crawford C.S.,Ettori S., Ivison R.J . , et al., 2000,MNRAS, 315L, 8F [30] Fadda D., Flores H. , Hasinger G., Franceschini A . , Altieri B. , Cesarsky C.J. , Elbaz D., Ferrando Ph., 2002,A&A, 383, 838F Fixsen D.L. , Dwek E., Mather J.C., Bennett C.L.,Shafer R.A. , 1998, ApJ , 508, 123 Finkbeiner D.P., Davis M . , Schlegel D.J. , 2000, ApJ , 524, 867 Bibliography 76 [33] Pranceschini A.,Aussel H.-.Cesarsky C.J. , et al., 2001, astro-ph/0108292 [34] Gispert R., Lagache G., Puget J-L., 2000, A & A , 360, 1 [35] Hauser M . G . , Arendt R.G. , Kelsall T., et a l , 1998, ApJ , 508, 25 [36] Holland W., et al.,1999, M N R A S , 303, 659 [37] Hornscheimer A.E.,Brandt W.N.,Garmire G.P.,Schneider D.P.,Barger A . J . , Broos P.S.,Cowie L.L.,Townsley L.K.,et al., 2000,HEAD, 32, 2613H [38] Hughes, Dunlop, & Rowlings, 1997, M N R A S , 289, 766H [39] Imanishi M . , Dudley C.C., Maloney P R . , 2001, ApJ , 558, L93-L96 [40] Ivison R.J . , Greve T.R., Smail I., Dunlop J.S., Roche N.D. , et al., 2002, M N R A S , astro-ph/0206432 [41] Ivison R.J . , Smail I., Barger A . J . , Kneib J . -P , Blain A .W. , Owen F .N . , Kerr T .H. , and Cowie L . L . , 2000,MNRAS, 315, 209 [42] Jenness T., Lightfoot J.F., 1998, in ASP Conf. Ser. 145, 216 [43] Kakazu Y . , Sanders D.B. , Joseph R.D., Cowie L . L . , Murayama T., et a l , 2002, astro-ph/0201326 [44] Klaas U . , Haas M . , Muller S.A.H., et al., 2001, A & A , submitted [45] Lagache G., Dole H. , Puget J.-L., 2002, M N R A S , in press, astro-ph/0209115 [46] Lagache G., Abergel A . , Boulanger F., et al., 1999, A & A , 344, 322 [47] Lagache G. , Haffner L . M . , Reynolds R.J . , Tufte S.L., 2000, A & A , 354, L247 [48] Li l ly S., Eales S.A., Gear W.K. , Webb T., et al., 1999,"The formation of galactic bulges", Eds. C M . Carollo, H . C Ferguson, R .F .G . Wyse, p.26 [49] Longair M.S., 1984, "Theoretical concepts in physics", Cambridge University Press Bibliography 77 [50] Magliocchetti M . , Maddox S.J., Wall J.V., Ben C.R., Cotter G., 2000, M N R A S , 318, 1047M [51 [52 [53; [54 [55; [56; Schaerer D., 1999, "Building galaxies", Eds. F. Hammer, T . X . Thuan, V . Cayette, B. Guiderdoni, J .T.T. Van., p.389 [57 [ss; [59 [60; [61 [62 [63 [64 [65 Meusinger H. , Stecklum B, Theis C., Brunzendorf J., 2001,A&A, astro-ph/0111521 Particle Physics Booklet, 2002, Particle Data Group, Springer Puget J-L., Abergel A . , Bernard J.P., et al., 1996, A & A , 308, L5 Puget J-L., Lagache G., Clements D., et a l , 1999, A & A , 345, 29 Saunders D.B. , Mirabel I.F., 1996, A R A & A , 34, 749 Scott D.,Lagache G.,Borys C.,et al., 2000, A & A , 357, L5 Scott D., and the B L A S T team, 2001, 'The Promise of FIRST' , ESA SP-460, eds. G.L. Pilbratt et al Scott S.E., Fox M.J . , Dunlop J.S., et al., 2002, M N R A S , in press, astro-ph/017446 Slinglend K. , Batuski D., Miller C , Haase S., Micaud K . , 1998, ApJS, 115, IS Smail I., Ivison R.J . , et al., 2001, astro-ph/0112100 Soifer B.T. , Sanders D.B. , Madore B.F. , Neugebauer G., et al., 1987, ApJ , 320, 238 Stickel M . , Lemke D., Klaas U . , et al., 2000, A & A , 359:865 Veilleux S., K i m D . - C , Sanders D.B. , 2002, astro-ph/0207401 Wang Y . , Biermann P.L., 2000, A & A , 356, 808W [66] Willott C.J . , Rowlings S., Jarvis M.J . , Blundell K . M . , 2002, M N R A S , astro-ph/0209439 Bibliography [67] X u C , 2000, ApJ , 541, 134X [68] Yun M.S., Reddy N.A. , Condon J.J., 2001, ApJ , 554, 803 79 APPENDIX A PHOTOMETRY WITH SCUBA Here we expand the discussion on reducing S C U B A photometry data, and give some of the details of the process. In the following we demonstrate the process using the example of a single observation (taken on March 17, 2001 of Nl-078, which is a detection). Fig. A . l shows an example of the first stage of our code where the mean and variance of each bolometer are calculated by the following: JVj = no. of jiggles (A.l) The noisier bolometers found using this procedure are excluded from the next stage in which the sky signature is removed. We also remove all jiggles which are > 5 a a r r a y , where Carray is the average a for the array. This removes the very largest spikes (caused by cosmic rays or other artefacts). After these two cuts, we calculate a weighted mean for the sky (shown in Fig. A.2). Then we perform a further despiking step by removing all jiggles 3a (a now is for each sky-subtracted bolometer) away from the mean of the bolometer. Notice that with this cut-off, only the 405th jiggle in the plot at the bottom of Fig. A.2 was cut so this step removes only a very small fraction of the data. The overall mean and variance can be estimated using the weighted values of the quan-tities estimates in bins containing some number of jiggles. We notice that there appears to be little advantage in using smaller bins in order to obtain the mean and error. We therefore estimate them using the entire observation rather than estimating the mean and error per integration (9 points) and coadding (SURF bins each integration, however does not use the obtained variances to weight each integration when coadding). We use Appendix A. Photometry with SCUBA 80 10 20 b o l o m e t e r Figure A . l : This is an example of the raw bolometer variances which are used to select the bad bolometers. Here, any bolometer above the dashed line (=1.25<7array)is excluded form the sky calculation. Note that since, the sky level is later estimated as a weighted mean, the effect of the outliers is reduced. Appendix A. Photometry with SCUBA 81 the following: J . 1 / 1 o t \ "=^|>" ff=7Rsfjw^S(*'-")>) (A-2) The above is the final answer when the entire observation is used, and in the case of binning the above for each bin are coadded in quadrature. Note that this has the further advantage of smoothing over some residual sky (such as smaller time scale gradients). In general, we did not proceed further with the refinement of the sky removal procedure since for the purposes of this project it is sufficient to remove features in the timestream that are larger than the scatter so the residual signal in Fig. A.2 is sufficiently clean. Folding-In the Off-bolos: A non-standard aspect of the way our photometry data is taken and analyzed is that the chopping is done in array coordinates so that it lands on a specific off-centre bolometer. This allows for the negative beams to be folded-in increasing the signal-to-noise per observation compared to standard photometry where essentially the signal from half the observing time is lost. The folding is done as follows: £ i= i ^ 1 Ptot - — : — a n d cr t o t = - = (A.3) V 1 We define w=l for the central bolometer and scale the other two accordingly. Since the source spends only half as much time in any of the off-centre positions as in the central one, wOff=-0.5 (can also see this in that both quantities scale as N~* from eq-n A.2). Note that this differs from the standard weighted mean since we are not coadding independent measurements of the same quantity - the negative beam is x0g = — 0.5x o n- Due to the array assymetry, forcing one negative beam to align with an off-centre bolometer means the other one will be slightly misaligned. Assuming a Gaussian beam shape we thus have w0ff — — 0 .5exp(— | ( 2 34XFWHM ) 2 ) w h e r e &x means the distance between the beam and the bolometer centre in arcseconds. We can see that folding-in the off-beams improves the rms by roughly a factor of (setting cr's as equal for simplicity) ^ Q 5 z ^ 1 + 0 5^ = ^/2/3, or ~ 20% taking into account the Gaussian attenuation of the second off-beam. Appendix A. Photometry with SCUBA 82 0.001 0 -0.001 -0.002 0.001 > 0 h -0.001 -0.002 0.001 -0.001 -0.002 H 1 1 1 1 1 h sky weighted mean \ — I — I 1—I— I—I—1 1—I 1— residual signal i i i _i i i i_ _i i i_ 100 200 300 400 j i g g l e Figure A.2: The upper panel shows the extinction-corrected timestream of the central bolometer. The middle panel is the weighted mean of all the bolometers (excluding those containing signal or excessive variance). The lower panel is the residual after subtracting the middle from the top. Notice that the vertical scales are the same in each case. APPENDIX B 83 COSMOLOGY Here are presented some basic cosmological relations which serve as a basis for the models presented in Chapter 4. This appendix draws from several sources (where the material is covered in more depth) [49, 9]. The expansion of the Universe is Hubble's law: f = H(t) x x (B.l) where H(t) is the Hubble constant (H0 today). However due to the effects of components such as matter, cosmological constant, and possibly curvature, the dynamics and geom-etry of the Universe can be complicated. Hence the scale factor R is introduced which relates the proper distance x, to a comoving radial distance r, such that x(t) = R(t)r, and R(t0) = 1). In curved space the radius of curvature is just Rc(t) = TZR(t), with TZ constant. The Friedmann-Robertson Walker (FRW) metric (general metric for isotropic curved spacetime) can be written 1 as: ds2 = dt2 - ^^(dr2 + TI2sin2 (r/ll)(dd2 + sin29d(j>2)). (B.2) r is given by r = J / 2 jjjr^. By the definition of r as comoving distance we have itk) ~ ^ ' e " ^ m e dilation). The scale factor is a function of the specific model adopted, determined through the Friedmann equation (describing the dynamics of the Universe in the hot big bang model) which is as follows: * - ( i ) , - 5 ? < ^ - £ where A is the cosmological constant, and k is the curvature parameter. 1For the closed case we have sin in the radial line element, while for the open case sin—»sinh, and for the flat case it is linear (i.e. sin(a;) —> x) Appendix B. Cosmology 8 4 At the present epoch, we can rewrite the above as: 1 = fiM + + fik, (B.4) where fiA = A / 3 # 2 , QM = !$PM, and f2k = The currently favoured model has P.M=0.3, r>A=0.7 and Q k=0 [52]. To extract from the above some observables we step back a bit to recall that redshift is defined as _ A 0 — A e ve . z=— = 1. (B.5) From the time dilation expression above, the fact that R(t0) = 1 by definition, and A t = v~l we have 1+z=m (a6) The basic parameter we need to estimate is the distance within the particular cosmolog-ical model. The definition of luminosity distance is / r \ l / 2 ^ = (s?) • (B'7) where L and F refer to bolometric quantities. On the other hand: F = L x (surface area) - 1 x (frequency shif t) - 1 x (time di lat ion) - 1 = 47r#2(i)r2(l + z ) 2 ' ^ This leads to the definition D\ = R(t)r(l + z) - which is very crudely ~ c(l + z)/HQ. To do this more precisely must go back to the integral for r and re-express it in terms of z as ^ = where ^ = —c(l + z) and | | is the Friedmann equation rearranged (since R = — ( 1 + \ ) 2 %) so have H = J jf^y- For a flat Universe with no curvature we have H{z) = / / 0 [ ^ M ( 1 + zf + f2 A ] 1 / 2 which leads to Dh = [Z\(l + z)*Qu + S1A]-V*dz. (B.9) Ho JO Fig. A . l shows the variation of the distance estimate for a matter-dominated, and a A-dominated flat Universe. For increasing redshift the later is larger than the former as expected due to A's repulsive effect. Appendix B. Cosmology 85 Figure B . l : The effects of different cosmological models on the luminosity distance es-timation. In terms of [ f i t o t , ^ A , ^ M ] , the solid line is [1,0.7,0.3], while the dashed line is [1,0,1]. Here # 0 = 7 5 k m s - 1 M p c - 1 . Appendix B. Cosmology 86 3x10* ~i—|—i—i—i—i—i—i—i—i—i—|—i—i—i—i—i—i—i—i—r 0 1 2 3 r e d s h i f t Figure B.2: The volume element. The other quantity of interest here is the differential volume element ^ per unit solid angle2 dQ, which represents the volume sampled in the shell z to z + dz. Since we only consider the simpler case of a flat Universe, it is essentially (over the whole sphere) %=^jrz-{Du)dz where DM is the proper radial distance. It is related to the luminosity distance as DL = £>M(1 + z). In terms of the later (and per unit solid angle), the volume element turns out to be: dV Dl dzdQ, Hi 0 (1 + Z)2y/(1 + Z ) 3 £ ) M + (B.10) 2The total number of square degrees in a sphere is given by 4ir(^)2 = 41,253. 

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