THE UNIVERSITY OF CHICAGO

EXTRAGALACTIC POINT SOURCE STATISTICS MEASURED WITH THE SOUTH

POLE TELESCOPE

A DISSERTATION SUBMITTED TO

THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES

IN CANDIDACY FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

DEPARTMENT OF PHYSICS

BY

JOAQUIN D. VIEIRA

CHICAGO, ILLINOIS

DECEMBER 2009

Copyright c© 2009 by Joaquin D. Vieira

All rights reserved

For Thu, who has always supported and encouraged me.

I cannot imagine having done any of this without her.

ABSTRACT

The South Pole Telescope (SPT) has surveyed hundreds of square degrees to milli-Jansky

levels at 1.4 mm and 2.0 mm. We report here on sources of point-like emission detected in the

1.4 and 2.0 mm bands in an 87 deg2 field, centered at R.A. 5h30m, decl. −55, and observed

in 2008. Based on the ratio of flux in these two bands, we are able to separate the detected

sources into two populations, one consistent with synchrotron emission from active galactic

nuclei (AGN) and one consistent with thermal emission from dust. We present source counts

for each population from 11 to 640 mJy at 1.4 mm and from 4.4 to 800 mJy at 2.0 mm.

We detect 119 synchrotron-dominated sources and 49 dust-dominated sources at S/N > 4.5

in at least one band. All of the most significantly detected members of the synchrotron-

dominated population are associated with sources in previously published radio catalogs

and/or in our own long-wavelength follow-up observations. Some of the dust-dominated

sources are associated with nearby (z ≪ 1) galaxies whose dust emission is also detected

by the Infrared Astronomy Satellite (IRAS). However, most of the bright, dust-dominated

sources have no counterparts in any existing catalog. We argue that these sources represent

the rarest, brightest, and possibly strongly-lensed members of the population commonly

referred to as sub-millimeter galaxies (SMGs). Because these sources are selected at longer

wavelengths than in typical SMG surveys, they are expected to have a higher mean redshift

distribution than objects currently in the literature, and may provide a new window on

galaxy formation in the early universe.

iv

ACKNOWLEDGMENTS

I would like to thank the members of the SPT collaboration. I am proud and privileged to

have worked with such an excellent group on such an amazing project.

I would like to thank my advisor, John Carlstrom for giving me all the resources and

guidance I needed to pursue this research. I am grateful to my other advisors who taught

me virtually everything I think I know about science: Stephan Meyer, Steve Padin, Bill

Holzapfel, and especially Tom Crawford.

I would like to acknowledge the love and support of my family, who set me on the path

that I am on today.

v

TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

CHAPTER

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 INSTRUMENT AND OBSERVATIONS . . . . . . . . . . . . . . . . . . . . . . . 92.1 Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 DATA REDUCTION, MAPS, AND CATALOG . . . . . . . . . . . . . . . . . . . 213.1 Flux Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Beam Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 Data Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4 Time Stream Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.5 Map Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.6 Optimal Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.7 Filtered Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.8 Source Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.9 Catalog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.10 Astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.11 Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.12 Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4 SOURCE SPECTRAL CHARACTERIZATION AND CLASSIFICATION . . . . 584.1 Spectral Classification and Source Association . . . . . . . . . . . . . . . . . 584.2 Extended Sources and Other Notes . . . . . . . . . . . . . . . . . . . . . . . 614.3 Correcting for Flux Boosting and Estimating Spectral Behavior . . . . . . . 624.4 Associations with External Catalogs and Follow-up Observations with ATCA 66

5 SOURCE COUNTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.1 Single-band Source Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Individual-Population Source Counts . . . . . . . . . . . . . . . . . . . . . . 72

vi

6 INTERPRETATION AND IMPLICATIONS . . . . . . . . . . . . . . . . . . . . . 756.1 Interpretation of Synchrotron Counts . . . . . . . . . . . . . . . . . . . . . . 756.2 Interpretation of Dust Counts and Arguments for a New Population of Lensed

mm Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

7 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

vii

LIST OF FIGURES

1.1 SED of a dusty star forming galaxy verses redshift . . . . . . . . . . . . . . . 61.2 K-correction of a R-J dusty source . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1 Measured SPT bands and atmospheric transmission . . . . . . . . . . . . . . 112.2 The South Pole Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 1.4 mm transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 2.0 mm transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 1.4 mm signal map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.4 2.0 mm signal map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.5 1.4 mm difference map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.6 2.0 mm difference map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.7 1.4 mm optimal filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.8 2.0 mm optimal filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.9 1.4 mm filtered map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.10 2.0 mm filtered map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.11 Histogram of pixel fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.12 1.4 mm cleaned map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.13 2.0 mm cleaned map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.14 Relative SPT band astrometry offsets . . . . . . . . . . . . . . . . . . . . . . 493.15 Relative SPT band DEC offsets . . . . . . . . . . . . . . . . . . . . . . . . . 503.16 Relative SPT band RA offsets . . . . . . . . . . . . . . . . . . . . . . . . . . 513.17 1.4 mm absolute astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.18 2.0 mm absolute astrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.19 Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.20 Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.1 Expected spectral index verses redshift for a dusty star forming galaxy . . . 594.2 1.4 mm flux verse 2.0 mm flux . . . . . . . . . . . . . . . . . . . . . . . . . . 604.3 Distribution of spectral indices . . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 Distribution of Sources of the Sky . . . . . . . . . . . . . . . . . . . . . . . . 70

5.1 Source Counts by Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.1 Spectral indices of selected AGN . . . . . . . . . . . . . . . . . . . . . . . . . 766.2 Source counts of synchrotron sources . . . . . . . . . . . . . . . . . . . . . . 786.3 Source counts model with lensing . . . . . . . . . . . . . . . . . . . . . . . . 846.4 Source counts of dust sources . . . . . . . . . . . . . . . . . . . . . . . . . . 856.5 IRAS 100 µmflux verses SPT 1.4 mm flux . . . . . . . . . . . . . . . . . . . 86

7.1 IRAC detection of a strongly lensed DSFG . . . . . . . . . . . . . . . . . . . 897.2 ATCA detection of a strongly lensed DSFG . . . . . . . . . . . . . . . . . . 90

viii

CHAPTER 1

INTRODUCTION

The South Pole Telescope (SPT, Carlstrom et al., 2009) is a 10-meter millimeter/sub-

millimeter (mm/sub-mm) off-axis telescope located at the geographic South Pole and opti-

mized for ultra-low-noise observations of Cosmic Microwave Background (CMB) anisotropies.

The first camera installed on the SPT is a 960-element bolometric receiver designed to per-

form a mass-limited survey of galaxy clusters via their thermal Sunyaev-Zel’dovich (SZ)

signature (Sunyaev & Zeldovich, 1970, 1972; Birkinshaw, 1999) over a large area of the

southern sky. The SPT SZ camera images at 1.4, 2.0 and 3.2 mm simultaneously. This sur-

vey is currently underway, and the SPT team recently published the first ever blind detection

of galaxy clusters via their SZ signature (Staniszewski et al., 2009, hereafter S09).

Observations of the cosmic microwave background radiation have enormous power to ad-

dress fundamental questions in cosmology. Primary temperature and polarization anisotropies

in the CMB provide a unique view of the primordial plasma, while secondary anisotropies

yield information about the structures that have formed in the universe (e.g., Hu & Dodelson,

2002).

On small angular scales (l & 3000), CMB temperature anisotropies are expected to

be dominated by the SZ effect. The SZ effect is a powerful tool for finding the largest

gravitationally collapsed objects in the universe, independent of redshift (e.g., Carlstrom

et al., 2002). As CMB photons traverse massive (∼1014.5M⊙) galaxy clusters there is a

roughly 1% chance of being inverse Compton scattered by the hot gas trapped in the deep

dark matter potential well. This results in a net energy gain for the CMB photons, which

leads to a spectral distortion of the CMB along the line of sight of the cluster. At wavelengths

longer than 1.4 mm the SZ effect causes a decrement in the CMB brightness, which is a unique

astrophysical signature. A sufficiently sensitive SZ cluster survey can produce a large, nearly

mass-limited sample of clusters. Follow-up measurements of photometric redshifts will then

1

allow determination of the cluster abundance as a function of redshift. This is a sensitive

probe of structure formation, capable of providing strong constraints on the amplitude of

density fluctuations and on the density and equation of state of dark energy (Holder et al.,

2001). A measurement of the angular power spectrum of this signal will yield constraints

on σ8 and ΩM that are complementary to those from a cluster survey (Komatsu & Seljak,

2002).

The sensitivity and angular resolution of the SPT make it an excellent instrument for

detecting such sources of emission. The goal of this work is to characterize sources of mm

emission in the SPT survey maps, which are also a potential contaminant to the SZ signal.

This thesis reports on point-source detections in a small part of the SPT survey, namely

a single 87 deg2 field centered at right ascension (R.A.) 5h30m, declination (decl.) −55

(J2000). SPT has surveyed this field to roughly mJy depths at 1.4 mm and 2.0 mm (220

and 150 GHz). In a map of this field filtered to optimize point-source detection we find

roughly one source per square degree above 5σ in the 2.0 mm data and roughly half that

number in the 1.4 mm data. Using two-band information for each detected source, we can

separate our detections into two populations: 1) sources with flat or decreasing brightness

with decreasing wavelength, consistent with synchrotron emission (typically S ∝ λ∼1); and

2) sources with increasing brightness with decreasing wavelength, consistent with thermal

emission from dust (typically S ∝ λ∼−3).

The majority of sources detected by the SPT at S/N> 5 are synchrotron-dominated

sources of a population of active galactic nuclei (AGN) well-known from radio surveys. All

but one of our > 5σ sources in this class have a clear counterpart in existing AGN catalogs,

consistent with our expectations for false detection rates (∼ 1 false detection above 5σ in

the 2.0 mm catalog).

Some of our dust-dominated sources have counterparts in the IRAS Faint-Source Catalog

(IRAS-FSC, Moshir et al., 1992) and are typically associated with low-redshift (z < 1) ultra-

2

luminous infrared galaxies (ULIRGs). The majority of our dust-dominated sources have no

counterpart in existing catalogs and are likely members of a population of massive, high-

redshift, dusty star forming galaxies (DSFGs) that has been the subject of considerable

recent interest in the mm/sub-mm community.

Astrophysical thermal emission from dust arises from short-wavelength photons which

are absorbed by dust grains and re-radiated at longer wavelengths (Draine, 2003). The most

striking signature of this process is the cosmic infrared background (CIB) (Hauser & Dwek,

2001; Kashlinsky, 2005; Dole et al., 2006), first detected by the COBE satellite (Puget et al.,

1996), but predicted much earlier (Low & Tucker, 1968; Stecker et al., 1977). Measurements

of the CIB show that over half the energy emitted since the big bang has been absorbed and

re-radiated by dust (Dwek et al., 1998). Intense star formation, specifically the UV radiation

from young, massive stars, is the dominant source of heat for the dust grains (Blain et al.,

2002; Kashlinsky, 2005; Lagache et al., 2005).

Galaxies which emit a significant portion of their luminosity in the infrared have been

known about for over thirty years (see Rieke & Lebofsky (1979) for a pre-IRAS review), but

the IRAS satellite was the first instrument to systematically discover such objects (Sanders &

Mirabel, 1996). These heavily dust-obscured sources typically show disturbed morphologies

and high star formation rates, indicative of recent or ongoing mergers (Lagache et al., 2005).

Because the infrared (IR) emission from local galaxies is only ∼30% of their optical luminosity

(Soifer et al., 1991), while the CIB is roughly equal to the cosmic optical background in terms

of power (e.g. Lagache et al. (2005)), it was understood that there was more star formation

occurring at earlier epochs than the present day, and that the star forming regions would

be dust-obscured. IRAS, however, detected mostly low-redshift (z < 1) objects and these

relatively rare and nearby sources contributed only a small fraction of the CIB (Le Floc’h

et al., 2005; Caputi et al., 2007).

The first systematic survey of high redshift sources which contribute significantly to the

3

CIB was carried out a decade ago at 850 µm by the Submillimetre Common-User Bolometer

Array (SCUBA) on the 15-m James Clerk Maxwell Telescope (JCMT) (Holland et al., 1999;

Smail et al., 1997; Hughes et al., 1998; Barger et al., 1998; Eales et al., 1999). Owing to the

spectrum of these DSFGs—a modified ∼30 K blackbody that rises steeply with decreasing

wavelength, counteracting the expected flux diminution with redshift—at ∼1 mm they can

be detected nearly independent of redshift (Blain et al., 2002). This implies that the source

luminosity is roughly proportional to the brightness from 1 < z < 10 (See Figures 1.1 and

1.2).

SCUBA was soon followed by other instruments such as the Max-Planck Millimeter

Bolometer array (MAMBO) on the IRAM 30-m telescope (Kreysa et al., 1998), Bolocam

on the Caltech Submillimeter Observatory (CSO) 10-m telescope (Glenn et al., 1998), and

AzTEC on the JCMT and the 10-m Atacama Submillimeter Telescope Experiment (ASTE)

(Wilson et al., 2008). The sources discovered in these surveys — often referred to as sub-

millimeter galaxies (SMGs) after the wavelength at which they were discovered— were dis-

tant and heavily dust enshrouded, making them optically faint and thus extremely difficult

to identify in the optical wavebands, especially given the poor resolution of single-dish exper-

iments. Taking advantage of the FIR-radio correlation (Condon, 1992), positions accurate

to the arcsec level were obtained from deep (∼10 µJy) images with the VLA (Ivison et al.,

2002), which enabled spectroscopic redshifts with 10m-class optical telescopes (Chapman

et al., 2005). This method, while successful, introduces a bias against objects at z > 3

because the radio flux becomes undetectable at high redshifts. Interferometric observations

in the mm and sub-mm provided accurate positions, probed the same dust emission with

which the objects were discovered, and were unbiased with redshift (Dannerbauer et al.,

2002; Younger et al., 2007, 2008). The detection of CO lines confirmed the optical redshifts

and facilitated studies of the morphology, dynamical masses, and gas fractions of these ob-

jects (Neri et al., 2003; Greve et al., 2005; Tacconi et al., 2006). With the launch of the

4

Spitzer Space Telescope (Werner et al., 2004; Soifer et al., 2008), the observational connec-

tion between different populations of dust-obscured galaxy populations was made; local and

distant, as well as normal and massive galaxies could be compared in the same samples

(Ivison et al., 2004; Lutz et al., 2005; Ivison et al., 2007; Valiante et al., 2007). Hundreds

of SMGs have now been detected by ground-based telescopes in surveys of blank fields over

a total area on the order of a square degree (Scott et al., 2002; Borys et al., 2003; Greve

et al., 2004; Laurent et al., 2005; Coppin et al., 2006; Bertoldi et al., 2007; Perera et al.,

2008; Scott et al., 2008; Austermann et al., 2009). Recently, results were published from the

Balloon-borne Large-Aperture Submillimeter Telescope (BLAST) which surveyed nearly ten

square degrees at 250, 350, and 550 µm and measured important properties such as dust

temperatures and clustering amplitude for DSFGs (Devlin et al., 2009; Patanchon et al.,

2009; Dye et al., 2009; Viero et al., 2009).

The discovery and study of SMGs has revolutionized our understanding of galaxy for-

mation. Observations of these objects (see Blain et al. (2002) for a review) indicate that:

1) they have dynamical masses of ∼1011M⊙ and total far-infrared luminosities of ∼1013 L⊙

(Swinbank et al., 2004; Greve et al., 2005; Chapman et al., 2005; Kovacs et al., 2006; Pope

et al., 2006); 2) they are forming stars prodigiously at 100–1000 M⊙/year (Chapman et al.,

2005; Tacconi et al., 2006); 3) they are highly biased tracers of large-scale structure (Blain

et al., 2004); and 4) their abundance appears to peak at z ∼ 2.5 (Pope et al., 2005; Chap-

man et al., 2005; Aretxaga et al., 2007). Massive galaxies are of course present in the local

universe, but they differ from the population of distant massive star-forming galaxies in that

they appear to be evolving quiescently (Caputi et al., 2005). The space density of SMGs is

1000 times greater at z = 2.5 than in the local universe (Chapman et al., 2005). From obser-

vations (Sanders et al., 1988; Sanders & Mirabel, 1996) and simulation (Barnes & Hernquist,

1991; Narayanan et al., 2009), the prodigious star formation rates seen in SMGs is believed

to be intrinsically linked to mergers. SMGs are an early phase in the formation of the most

5

Figure 1.1: The SED verses redshift for Arp 220. The 1.4 mm (2.0 mm) SPT band is shown indark (light) gray. A remarkable feature is that for a source between 1 < z < 10 the brightnessis constant because the steep Rayleigh-Jeans spectrum cancels the expected distance-squared fluxdiminution. Arp 220 is a local well-studied ULIRG and its SED is a common benchmark for highredshift dusty star forming galaxies.

massive galaxies and are among the largest gravitationally collapsed objects in this early

epoch of galaxy formation (Blain et al., 2004; Swinbank et al., 2008).

Source selection in this work is significantly different from that of the surveys mentioned

above. First, the DSFGs detected with the SPT are expected to be at higher redshift and/or

colder dust temperatures due to their selection at longer wavelengths (See Figures 1.1 and

1.2). Second, the survey area described here is significantly larger than previous sub-mm

wave studies. This means that the survey probes large volumes at high redshift, permitting

the identification of rare sources with very high star formation rates, and is more likely to

contain strongly lensed systems. These sources are thus strong candidates for multi-band

6

Figure 1.2: The K-correction for Arp 220. This plot demonstrates the flux density at ∼1 mmof a dusty star forming galaxy is constant from roughly 1 < z < 10. Because of this remarkableproperty, these objects can be detected independent of redshift.

studies and could provide valuable information about the evolution and nature of massive

galaxy evolution at high redshift.

The discussion of the detection and characterization of point sources in the SPT 87 deg2

survey is broken into several chapters. Chapter 2 describes the SPT instrument and the

observations which went into this work (see also Ruhl et al. (2004); Padin et al. (2008);

Staniszewski et al. (2009); Carlstrom et al. (2009)). Chapter 3 discusses the calibration, map-

making, properties of the filtered maps, presents the source catalog, describes our procedures

for checking astrometry, and estimating the completeness and purity. Chapter 4 discusses

basic source properties, describes our procedure for estimating each source’s intrinsic flux and

spectral index, which we use to separate our sources into two spectrally distinct (synchrotron-

7

dominated and dust-dominated) populations, and describes associations with existing source

catalogs. Chapter 5 presents source counts for each band and population. Chapter 6 discusses

the implications of the SPT source counts, including the potential of a newly discovered

population of sources. Finally, Chapter 7 concludes.

8

CHAPTER 2

INSTRUMENT AND OBSERVATIONS

The SPT is a 10 meter diameter, wide-field, offset Gregorian telescope with a 960-pixel,

multi-color, millimeter-wave, bolometer camera. It is located at the Amundsen-Scott South

Pole station in Antarctica. The design of the SPT emphasizes a simple and low-noise optics

and was optimized for fine-scale measurements of primary and secondary CMB anisotropies.

The key initial project is a large-area survey at wavelengths of 1.4, 2.0, and 3.2 mm, to detect

clusters of galaxies via the Sunyaev-Zeldovich (SZ) effect and to measure the high-l angular

power spectrum of the CMB. The data will be used to produce a mass-limited sample of

galaxy clusters, characterize the primordial matter power spectrum, and to place constraints

on the equation of state of dark energy.

The measurements of the CMB necessary to achieve these science goals involve imaging

large areas of sky with high sensitivity at millimeter wavelengths. The best bolometer

detectors in this band are already close to sky-noise limited (Holland et al., 2002), so the

SPT must improve sensitivity by increasing the number of background-limited detectors,

observing at the best available site for mm astronomy, and minimizing systematic errors.

The key performance features of the SPT are:

• ∼1 arcmin FWHM beamwidth, to resolve the SZ effect from galaxy clusters. This

requires an 8 m diameter or larger telescope at λ = 2 mm. The SPT has a 10 m

primary with 20µm rms surface error. In the current configuration only the inner 8m

of the primary are illuminated to minimize side-lobe response. The surface rms of the

primary mirror is more than adequate for mm observations and should be acceptable

for observations down to 450 µm.

• Low scattering, to reduce detector loading and reduce potential systematic errors such

as scan-synchronous offsets due to ground pick-up. This leads to an offset optical design

9

with smooth mirrors to reduce scattering and an under-illuminated primary mirror and

co-moving ground shield to control spillover. The secondary mirror is cooled to ∼10 K

and surrounded by cooled absorbing baffles to limit scattered light and loading on the

detectors as well as to simplify and minimize the number of optical elements in the

light path.

• Many detectors with a wide field of view to quickly map large areas of sky. An SZ sur-

vey must cover a large area of the sky to yield enough clusters to set useful constraints

on dark energy. Simultaneously mapping in multiple bands provides spectral discrim-

ination against galactic foregrounds and radio and infrared extragalactic sources, and

allows us to separate CMB and SZ signals.

• High sensitivity, because CMB signals are weak. The amplitude of the SZ effect from

massive galaxy clusters is typically tens to hundreds of µK; the amplitudes of the CMB

polarization and fine-scale temperature anisotropies are much weaker. The SPT uses

transition edge sensor (TES) bolometer detectors with a noise equivalent temperature

(NET) of ∼350 µK√

s (in CMB temperature units) at λ = 2.0 mm. It is located at the

Amundsen-Scott South Pole station, which is one of the best mm and submm sites on

Earth.

2.1 Site

The South Pole is a high, dry site with exceptional atmospheric transparency and stability at

mm and sub-mm wavelengths. In winter, the median precipitable water vapor is ∼ 0.25 mm

(Chamberlin, 2001) and the zenith opacity at λ = 2 mm is ∼ 0.03. The median brightness

fluctuation power at λ = 2 mm is ∼ 31 mK2 rad−5/3 in CMB temperature units (Bussmann

et al., 2005). This is at least an order of magnitude better than other established terrestrial

sites (Peterson et al., 2003; Sayers et al., 2009). Temperatures can fall to −80 C in winter,

10

which places severe constraints on the design of exposed components, but weather conditions

are otherwise fairly benign. Although the physical altitude is 2800 m, the average pressure

altitude in winter is 3300 m. Light (∼ 5 m s−1) katabatic winds blow from the East Antarctic

Plateau most of the time (Schwerdtfeger, 1984), and high winds are rare. The peak recorded

wind speed is only 24 m s−1. Snow accumulation is ∼ 150 mm yr−1, but local drifting

around surface structures is a problem, so most buildings are elevated. The ice pack is over

2 km thick and it moves ∼ 10 m yr−1.

Figure 2.1 shows the atmospheric transmission for the median precipitable water vapor

measured at the South Pole in Chamberlin (2001), as well as the measured SPT band-passes

at 1.4, 2.0, and 3.2 mm (220, 150, and 95 GHz, respectively) for the 2008 season.

Figure 2.1: The measured SPT bands and the atmospheric transmission at the South Pole. Theatmospheric transmission comes from the CSO website. The SPT bands were measured with aFourier transform spectrometer (FTS) at the South Pole in 2008.

11

2.2 Telescope

The SPT (see Figure 2.2) is an offset classical Gregorian design. This was chosen because:

(1) the clear aperture minimizes noise and ground pickup, which is a serious problem for

observations of faint, low-contrast emission such as the CMB; (2) a Gregorian configuration

provides an image of the primary for a chopper or Lyot stop for future receivers; (3) the

secondary in a Gregorian design is concave, which makes testing of the mirror easier; and

(4) the paraboloidal primary of the classical form allows us to change the focal length of the

secondary for future receivers. An aplanatic design offers a wider field of view (Hanany &

Marrone, 2002) but the focal length of the secondary cannot be changed much and the focal

surface is more curved. The optical configuration of the SPT is unusually simple because the

detectors are at the Gregory focus (see Padin et al. (2008)). There are just 2 mirrors (primary

and secondary) and a lens (to make the final focus telecentric and improve the illumination

of the secondary). This scheme gives low loss, scattering and instrumental polarization, and

makes alignment easy. The field of view is roughly λ (mm) × 0.7 degrees.

The primary has a 10 m diameter aperture with a focal length of 7 m. Prime focus is

300 mm below the bottom of the primary. This arrangement gives a reasonable compromise

between aberrations, ease of manufacture, and the size of the secondary support structure.

Millimeter-wave telescopes usually have a chopping mirror that quickly scans or switches

the beam to “freeze” atmospheric and gain fluctuations. A chopping secondary is sometimes

used, but telescopes with a wide field of view usually have a flat chopping mirror at an image

of the primary. The image of the primary just after a Gregorian secondary is a common

choice. Wide field designs favor a fast secondary, to keep the size of the focal plane reasonable,

but this gives a poor image of the primary and increases chop-synchronous offsets. For the

SPT, it was decided to abandon a chopper in favor of rapidly scanning the entire telescope.

This works for the low-impedance TES bolometers and frequency domain readout in our

receiver, but could be a problem for semiconductor bolometers, which are typically sensitive

12

to vibration from the telescope drives. Avoiding a chopper was an important choice because

it allowed us to make the Gregory focus fast enough to feed the detectors directly.

Figure 2.2: The South Pole Telescope.

13

2.3 Optics

The SPT receiver has wafers of detectors mounted behind a close-packed array of smooth-

wall, conical feedhorns. The spacing between horns is 4.8 mm, which gives reasonable sep-

aration between the 4 mm diameter pixels on the detector wafers and provides space for

the readout wiring. For optimum coupling to a point source, the horn aperture diameter

should be 2Fλ, where F is the final focal ratio (Griffin et al., 2002). For λ = 2 mm the F1.3

telescope optics are well matched to the horn apertures.

To control the illumination pattern of the primary while keeping loading low, the optical

system must include a cold stop. The SPT optical design does not have a good image of the

primary for a stop, so we moved the exit pupil to the secondary and surrounded the mirror

with cold absorber. The absorber extends from the secondary to prime focus, and also into

the receiver, so it functions both as the stop and as a shield around the beam. In this scheme,

the obvious place for a cryostat window is near prime focus, where the beam is small. The

large cold stop at the secondary does require additional cryogenics, and the primary must be

a little larger because it is no longer the entrance pupil. The key advantage is good control

of spillover because the entire beam from prime focus to the detectors is contained inside a

cold, absorbing box.

The SPT cryostat has two independent sections that share the same vacuum space. The

optics cryostat contains the secondary mirror, most of the cold stop, and the window and

associated heat-blocking filters. The receiver cryostat contains the lens, band-defining filters

and the detectors. Each cryostat has its own refrigerator system. This arrangement allows

us to test the receiver without the optics cryostat and to change receivers without disrupting

the secondary. The secondary and cold stop are supported by a truss that attaches to the

receiver mounting flange on the optics cryostat. The detectors are attached to the other side

of that flange via a cone and truss. The separation between the secondary and the detectors

is fixed, but the cryostat assembly is mounted on an optical bench that can be moved ±25

14

mm in any direction to maintain alignment with the primary . This allows us to compensate

gravitational flexure of the secondary support structure and changes in the focal length of

the primary with elevation (which are both a few mm over the full elevation range). The

optical bench actuators have a maximum speed of 25 mm min−1, so they can only follow

slow changes.

The secondary is a lightweighted (20 kg) aluminum 7075-T6 mirror, 1 m in diameter ×

50 mm thick. It is attached at 3 points to a triangular back plate, which is in turn supported

by a truss made of 20 mm diameter × 1 mm wall stainless steel tubes. The truss rods have

preloaded ball joint ends that allow some movement during cooling. The secondary surface

profile error was initially 11 µm rms at room temperature (measured using holography at 89

GHz), but this increased to 50 µm rms when the mirror was cooled. It is now 23 µm rms at

room temperature. Stress inside the mirror is likely responsible for these changes. We did

stress relieve the blank by cooling it to 77 K and then slowly warming to room temperature,

3 times, before the final cut. However, the first thermal cycles of the finished mirror were

done in a mount that had no compliance between the mirror and its back plate. We will

probably replace the secondary and improve its mount in the future.

The cold stop is microwave absorber (HR-10) cooled to 10 K. With 20% spillover, this

contributes just a few K to detector background loading. The flexible absorber is glued to

the inside of a shroud made of annealed, high thermal conductivity, aluminum 1100. This

is surrounded by a radiation shield made of the same material. Both the shroud and the

shield are covered with 9 layers of superinsulation (NRC-2-Cryolam) to reduce the radiation

load. The secondary end of the 20 kg stop and shield assembly is attached to the mirror

back plate. The other end is attached to the receiver mounting flange with an axial flexure.

The flexure reduces the torque on the mirror support and allows the end of the stop and

shield to move ∼3 mm on cooling.

Metal-mesh, heat-blocking filters (Tucker & Ade, 2006) are attached to the stop shroud

15

and radiation shield just behind the 100 mm thick expanded polypropylene foam (Zotefoam)

cryostat window. The loss through the window has been measured to be less than 0.5% at

2.0 mm The stop assembly is cooled by a pulse tube refrigerator (Cryomech Inc., model

PT410) with a capacity of 10 W at 10 K and 80 W at 70 K. The stop cools to 10 K, with

< 1 K gradient along its length, and the shield cools to 70 K at the heat-blocking filters and

60 K at the refrigerator end. Cooling time for the optics cryostat is 3 days.

The primary has 218 machined aluminum (Al Mg 4.5 Mn) panels mounted on a composite

back up structure (BUS). The BUS is made of 24 identical, wedge-shaped segments that

are essentially deep, stiff boxes with thick facesheets. The segment walls have an aluminum

honeycomb core covered with carbon-fiber-reinforced plastic (CFRP). Invar inserts are glued

into the composite to provide attachment points for fasteners and panel adjusters. A large,

stiff, Invar cone behind the BUS provides an interface to the steel telescope mount, and an

Invar cylinder running from the center of the BUS to the steel mount adds axial stiffness.

2.4 Receiver

The detectors in the SPT receiver are arrays of horn-coupled, spider-web bolometers with

transition edge sensor (TES) thermometers (Gildemeister et al., 1999, 2000). A voltage-

biased TES exhibits strong electrothermal feedback, resulting in good linearity and a re-

sponsivity that is independent of bath temperature and optical loading (Lee et al., 1996,

1998). The TES devices also have low impedance (typically 1Ω), so they should be fairly

insensitive to vibrationally induced currents. In addition, the resonant circuits in series with

each bolometer pass only a narrow band of signals at several hundred kHz where there are

no mechanical excitations.

The SPT detectors have an Al-Ti TES, with a transition temperature of ∼0.5 K, mounted

near the center of a spiderweb absorber. This absorber is a 1 µm thick, suspended silicon

nitride mesh, 3 mm in diameter suspended by six 0.5 mm legs. It is coated with gold to

16

give a sheet resistance of ∼ 65Ω/. High electrothermal loop gain leads to a short electrical

time constant that can cause instability, so our detectors also have a gold pad coupled to the

TES to increase its heat capacity and slow its electrical time constant. We use triangular

arrays of 161 close-packed bolometers fabricated on 100 mm diameter wafers. The wafers

are metalized on the back to provide a backshort at ∼ λ/4.

The bands are defined by the low-frequency cut off in a short length of circular waveguide

between each smooth-wall conical horn and its detector, and by low-pass, metal-mesh filters

(Ade et al., 2006) mounted in front of each feedhorn array. The focal plane has 6 triangular

bolometer arrays, for a total of 966 detectors; however, due to readout limitations at most

840 detectors can be active.

For a typical detector, the optical time constant is ∼15 ms and the optical coupling from

the sky to the TES is ∼ 25%. For the 2008 season observations described in this work, two

1.4 mm arrays, three 2.0 mm arrays, and one 3.2 mm arrays were installed. The 1.4 and 2.0

mm arrays were very close to being background limited, while the 3.2 mm array was very

noisy and not used in this analysis. Typically, ∼ 600 detectors pass our performance cuts

with high sensitivity and noise close to the background limit.

The SPT receiver (Benson et al., in prep) is cooled by a pulse tube refrigerator (model

PT415) with capacity of 1.5 W at 4.2 K and 40 W at 45 K, and a 3-stage 4He3He3He sorption

refrigerator (model CRC10) with a capacity of 80 µW at 380 mK and 4 µW at 250 mK. The

sub-K refrigerator is cycled automatically in ∼ 3 hrs and the hold time is ∼ 36 hrs

The SPT receiver readout is a frequency multiplexed SQUID readout with 8 detectors

per SQUID (Spieler, 2002; Lanting et al., 2004; Lanting et al., 2006). Each TES is biased

with a constant voltage amplitude sine wave, in the 0.3–1 MHz range, and has a series LC

filter, mounted near the focal plane at 250 mK, to select the appropriate bias frequency

from a comb of 8. In this scheme, only 2 superconducting NbTi wires are needed to connect

8 detectors in the focal plane to their SQUID, which is mounted at 4 K. The LC filters

17

all have 16 µH chip inductors, so the filter Q increases with frequency and the bandwidth

(∼ 5 kHz in the SPT) is constant. The filter frequency is set by the capacitor, which is

a standard ceramic chip device. The SQUIDs are 100-element series arrays (Huber et al.,

2001) with a small input coil to reduce pickup of spurious signals. These devices have 120

MHz bandwidth, 500 V/A transimpedance and the noise (referred to the input coil) is 2.5 pA

Hz−1/2 (cf. ∼ 15 pA Hz−1/2 bolometer noise). SQUIDs are extremely sensitive to magnetic

fields, so the SQUID boards (each with 8 SQUID arrays) are enclosed in a Cryoperm shield to

attenuate any external fields. Inside the Cryoperm shield, each SQUID is mounted on a Nb

film (type 2 superconductor) to pin any residual magnetic flux. To maintain constant voltage

bias across the TES, the input impedance of the SQUID must be small compared with the

TES resistance. This requires that the SQUID be operated with shunt feedback from the

output of the room-temperature amplifier that follows. Negative feedback also linearizes the

SQUID response, reducing intermodulation between the bias signals. The feedback amplifier

has a high gain × bandwidth product, so connections between the SQUID and the room

temperature electronics must be short. This is a severe constraint on the mechanical and

thermal design of the receiver.

2.5 Observations

These data are from observations of the first 100-deg2 survey field mapped in 2008, centered

at R.A. 5h30m, decl. −55 (J2000) The timestream data for each observation, constituting

a single pass over the field, are processed and combined to make a map of the field for

each observing band. The maps from several hundred individual observations of the field

are combined and converted to CMB fluctuation temperature units using a calibration from

the CMB anisotropy as measured by the Wilkinson Microwave Anisotropy Probe (WMAP,

Hinshaw et al. (2009)).

Most SPT observations involve scanning the telescope to fully sample the sky with all

18

the detectors (and hence all of the wavelength bands). We generally scan back and forth in

AZ at constant speed, turning around as quickly as possible, with a step in EL at the end of

each AZ scan. The speed in the linear part of the AZ scan involves a trade off between noise

and observing efficiency. Higher scan speeds move the sky signals to higher frequency in the

detector timestreams, so low-frequency noise from the atmosphere and receiver become less

important, but the observing efficiency is reduced because a larger fraction of the time is

spent turning around. This trade off tends to favor a higher scan speed for a larger field.

The EL steps at the end of each scan are profiled to minimize the excitation of elevation

oscillations, which would lead to scan synchronous modulations of the atmosphere.

The 2008 observations employed two different scan speeds, 0.44 and 0.48 degrees of az-

imuth per second and a scan length of 17.5 degrees in azimuth, resulting in total scan lengths

of 75-80 seconds (including turnarounds). The size of the elevation step between pairs of

scans was 0.125 degrees. A map of the entire field is made using this strategy, and we refer

to such a single-pass map as a single observation. One observation takes two hours. The

short time period for a single observation allows for a conservative schedule of interleaved

calibrations and facilitates data selection and reduction. Each individual observation pro-

duces a fully sampled map of the field, but not fully sampled by each individual detector.

A series of different starting elevations are used for successive observations to provide even,

fully sampled, coverage of the field over several days.

A single observation of this field takes about 2 hours. Between individual observations of

the field, we perform a series of short calibration measurements, including measurements of

a chopped thermal source, 2 degree elevation nods, and scans across the galactic HII regions

RCW38 and MAT5a. This series of regular calibration measurements allows us to identify

detectors with good performance, assess relative detector gains, monitor atmospheric opacity

and beam parameters, and constrain pointing variations. The chopped thermal source is a

∼ 1000 K black-body, with a 4–100 Hz chopper wheel, connected to a 9.5 mm diameter light

19

pipe that runs into the optics cryostat and through a hole in the center of the secondary.

We check the pointing by mapping two bright H II regions near the target field, which takes

∼ 20 min total, and then we scan on the target field for a few hours. The cycle is repeated

until the mK refrigerator in the receiver warms up. Detector outputs and telescope positions

are recorded at 100 Hz, but most of the monitoring (e.g., cryostat temperatures, weather,

receiver readout configuration and optical bench position) is at 1 Hz. The data rate is

typically 30 GBytes/day. 607 hours of observing time with 322 good 2.0 mm detectors and

170 good 1.4 mm detectors went into the maps used for this analysis. From the final map,

an 87 deg2 portion of the field that was mapped with near-uniform coverage was selected

for analysis. Every 1 arcmin patch in the included area was required to have uniform depth

coverage to 10%.

The SPT second year (2008) observations concentrated primarily on SZ and fine-scale

CMB surveys in two ∼100 deg2 fields. Targeted SZ observations toward known galaxy

clusters were also pursued. The first clusters detected via a SZ survey are reported in

Staniszewski et al. (2009).

20

CHAPTER 3

DATA REDUCTION, MAPS, AND CATALOG

From time-ordered data to catalogs, this data analysis pipeline consists of:

• Filtering the time-ordered data from each individual detector to reduce low-frequency

atmospheric and instrumental noise.

• Reconstructing the pointing for each detector.

• Combining data from all detectors in a given band per a given 2 hour observation into

a map by simple inverse-variance-weighted binning and averaging. At this stage in the

pieline there are roughly 300 individual observation maps per band.

• Combining all observations from a given band into one single co-added map. This

procedure produces one map for each band.

• Optimally filtering each map to maximize sensitivity to point sources. Because we are

searching for point-sources, this step acts as a high-pass filter to remove atmospheric,

instrumental, and CMB noise.

• The detected peaks in the filtered maps are extracted and their amplitudes converted

from CMB fluctuation temperature units to flux (in units of Jy). A catalog is produced

for each band down to 3σ. These two catalogs are merged using a simple source

association radius.

3.1 Flux Calibration

The relative gains of the detectors and their gain variations over time are estimated using

measurements of their response to a chopped thermal source. These measurements take

place before each observation of the survey field, or every 2 hours. We estimate an absolute

21

calibration using measurements of degree-scale CMB fluctuations at 2.0 mm and comparing

them directly to the WMAP 5-year maps. This is done using short, dedicated observations

of large sky fields. Details of the cross-calibration with WMAP are given in Lueker et al.

(2009). We estimate the uncertainty of this calibration to be 3.6%. We apply this calibration

to our 1.4 mm band by comparing 2.0 mm and 1.4 mm estimates of CMB anisotropy in our

deep survey regions. We estimate the 1.4 mm calibration uncertainty of 7.2%. Because

the 1.4 mm calibration is derived from the 2.0 mm calibration to WMAP, the calibration

uncertainties in the two bands will be correlated; we estimate a correlation coefficient of

roughly 0.5.

3.2 Beam Measurements

Main-lobe beams are measured using the brightest sources in the field and are adequately

fit by 2d Gaussians with full width at half-maximum (FWHM) equal to 1.05′ and 1.15′ at

1.4 mm and 2.0 mm. Large-angle sidelobes are measured using planet observations, but

the angular scales on which these sidelobes are important are heavily downweighted in the

filter, so these measurements are not relevant to this work 1. We estimate that beam-shape

uncertainties contribute roughly 2% and 5% to our absolute flux estimates in our 2.0 mm

and 1.4 mm bands. This uncertainty is added in quadrature to the calibration uncertainty

in our flux estimates.

A subtlety in estimating the spectral index is that the effective band centers (which fold

into the index determination) depend upon spectral index. Using the measured passbands for

1.4 mm and 2.0 mm, we find that if one were to assume an index α = −1 in the determination

of the band centers, a source with α = 3 would produce a 2% bias in the estimation of the

spectral index. In addition, the beam shape (and so flux) will change with the spectral index.

1. As it turns out, this approximation leads to a ∼5% calibration error. This is fixed in Vieira et al.(2009) but left in for this thesis. Nothing qualitative changes about the conclusions.

22

These can both be neglected to the accuracy of the results presented here.

3.3 Data Selection

The first step in the data reduction process is to identify the data that will be included in

each single-observation map. For every observation, a set of well-performing detectors is

identified, primarily by assessing each detector’s response to the chopped thermal source,

its response to atmospheric emission during the ∼ 2 degree elevation nods, and its noise in

the wavelength band appropriate for cluster signals. Performance is also assessed based on

the shape of the individual detector’s noise power spectrum. If the power spectrum has too

many lines or other deviations from the expected functional form, that detector is omitted

from that observation’s analysis. The median number of detectors stated in Section 2.5 is

obtained after the application of these criteria.

In addition to cutting all data from individual detectors with anomalous noise power

spectra, a small amount of bandwidth is cut from all detectors in certain observations.

The receiver exhibits sensitivity to the pulse-tube cooler, resulting in occasional lines in

the detector noise power spectra at frequencies corresponding to the pulse-tube frequency

(approximately 1.6 Hz) and its harmonics. In every observation, all detectors’ noise power

spectra are combined in quadrature, and a search is performed for features in the resulting

spectrum at every harmonic of the pulse-tube frequency. If a high-significance feature is

found at any harmonic, a notch filter around that harmonic is applied to every detector’s

timestream. The width of the notch is determined by the fit, with a maximum of 0.007 Hz

full-width. The maximum amount of bandwidth that could be cut with this filter is 0.4%,

but the actual amount is far smaller.

The data are eventually parsed into individual azimuth scans and are further selected

for inclusion in the analysis on a scan-by-scan basis. Only the constant-azimuthal-velocity

portion of each scan is eligible for inclusion; data taken while the telescope is accelerating

23

are omitted. Scans during which there were data acquisition problems or large (> 20 arcsec)

instantaneous pointing errors—roughly 5% of total scans—are flagged for omission. For each

detector, data from an individual scan are flagged if the detector or its associated readout

channel exhibits high noise, if the demodulated detector output comes close to the limits of

the analog-to-digital converter, if the readout SQUID associated with the detector exhibits

an anomalously large DC offset, or if the detector demonstrates any cosmic ray-like events

in its time-ordered data. Typically about 5% of all otherwise well-performing bolometers

are flagged within a given scan for one of these reasons. Data that remain unflagged after

all of these cuts have been applied are processed and included in the maps.

Finally, individual observations are assessed for quality before inclusion in the final coad-

ded maps. Observations are excluded if the thermal conditions of the receiver were not

sufficiently stable, if the number of well-performing detectors was anomalously low, or if the

observation was not fully completed. Individual observation maps are also excluded from

the final maps if the RMS in the single-observation map exceeds an empirically determined

threshold. Of the complete observations of this field, approximately 83% (314/377) are

included in the final maps.

3.4 Time Stream Filtering

Detector-response deconvolution and low-pass filtering are done in a single step. The detector

temporal-response functions are measured periodically by sweeping the chop frequency of

the thermal calibration source and measuring the amplitude and phase of each detector’s

response. These temporal-response functions are fit adequately by a single-pole low-pass

filter, and the time constants do not vary significantly from observation to observation.

Across the focal plane, the time constants ranged from 10-20 ms. The cutoff for the applied

low-pass filter is set to 25 Hz for the 2008 data, such that in conjunction with a digital filter

already applied by the data acquisition computer, they filter spatial scales at . 0.5′. This

24

combination acts as an anti-aliasing filter for our eventual resampling of the data onto 0.25′

map pixels but does not suppress power on scales of the SPT beams. The time-ordered

detector data were filtered with a 0.18 Hz Fourier-domain high-pass filter. With our scan

speeds, the high pass filter removes spatial scales & 45′.

We project out a common mode which consists of three spatial modes (mean, and tilts

along two axes) constructed from the mean of all working detectors in a single band, weighted

by the x and y position in the focal plane. Removing this common mode should eliminate

the majority of the atmospheric fluctuation power in the detector timestreams, because this

atmospheric signal is highly correlated between detectors. The common-mode subtraction

acts as a spatial high-pass filter with a characteristic scale that roughly corresponds to the

one degree angular size of the array. This filter option was demonstrated to remove more

atmosphere from the timestream than the method described in Staniszewski et al. (2009),

but its choice was not critical. As the common mode is constructed independently for each

band, the response to spatial modes on the sky can be slightly different, but is unimportant

for this work as we do not care about large spatial modes. We did not use any bright point

source masking because we wanted to simplify and linearize the transfer function, and did

not want to introduce a bias by treating bright source differently than faint sources.

The effects of this filtering on the beam in k-space is shown in Figures 3.1 and 3.1. For

these plots we convolved a delta function with the measured beam and inserted that into a

noiseless timestream and performed the filtering described above.

25

Figure 3.1: The 1.4 mm transfer function.

26

Figure 3.2: The 2.0 mm transfer function.

27

3.5 Map Making

For every observation, a map is made for each observing wavelength using the processed data

for all detectors in that band. Pointing information (R.A. and decl.) is calculated for each

detector using focal-plane offsets measured in observations of the galactic HII regions, and

boresight pointing calculated using data from the telescope pointing readout system, with a

set of corrections described below.

Small corrections must be applied to the pointing information in the timestream to ensure

that pointing errors are suitably small compared to the size of the SPT beams. The largest

pointing errors of the SPT are attributed to thermal gradients across the telescope support

structure. These pointing errors are corrected from 20 arcseconds RMS to better than 8

arcseconds RMS by using an offline model which incorporates information from thermal and

linear displacement sensors on the telescope structure and observations of HII regions. The

astrometry of the pointing model is tied to the PMN and SUMSS catalogs (Wright et al.,

1994; Mauch et al., 2003) and is accurate to 6 arcseconds in the final maps (see Section 3.10).

As the beams include the effects of pointing variations and the timestream filtering, they are

larger than expected from the diffraction of the central 8-meter diameter region of primary

mirror illuminated by the SPT-SZ optics (see Padin et al., 2008).

The filtered time-streams are inverse noise weighted according to the calibrated, pre-

filtering detector PSD in the range 1-3 Hz (corresponding to 1400 < ℓ < 4300). The filtered

time-streams binned and co-added to produce an observation map. All observation maps

are then inverse noise weighted and coadded to produce a final map. Each map pixel is

0.25′ × 0.25′.

The coadded signal maps are shown in Figures 3.3 and 3.4. We also produce a difference

map2, shown in Figures 3.5 and 3.6. constructed by multiplying half of the individual-

2. Sometimes referred to as a jackknife map.

28

observation maps of the field by -1, half by +1, and then summing. The difference map has

all astrophysical signal removed, but the atmospheric and detector noise remains.

The maps used in this work are pixelized using a flat-sky projection of the sphere in

which the mapping of right ascension to map rows is a function of position in the map.

We chose this pixelization because it minimizes beam distortions, which are significant in

flat-sky pixelizations in which pixel rows are at constant declination.

29

1.4 mm signal map

0 500 1000 1500 2000 2500 3000X pixel number

0

500

1000

1500

2000

2500

3000Y

pix

el n

um

ber

-34.00mJy -22.67mJy -11.33mJy 0.00mJy 11.33mJy 22.67mJy 34.00mJy

Figure 3.3: The 1.4 mm signal map in a flat sky projection. The field center is right ascensionR.A. 5h30m, decl. −55 (J2000). Each pixel is 0.25′ × 0.25′. Because of time domain filtering, thesource signal produces an arc from the impulse response of the filter as the detectors scan left andright across the field. The RMS in the map is 30 µK and the gray scale is roughly ±10σ.

30

2.0 mm signal map

0 500 1000 1500 2000 2500 3000X pixel number

0

500

1000

1500

2000

2500

3000Y

pix

el n

um

ber

-14.00mJy -9.33mJy -4.67mJy 0.00mJy 4.67mJy 9.33mJy 14.00mJy

Figure 3.4: The 2.0 mm signal map in a flat sky projection. The RMS in the map is 15 µK andthe gray scale is roughly ±10σ. Most of the visible large scale structure is primary CMB. See thecorresponding Figure 3.3 for comments common to all maps.

31

1.4 mm difference map

0 500 1000 1500 2000 2500 3000X pixel number

0

500

1000

1500

2000

2500

3000Y

pix

el n

um

ber

-34.00mJy -22.67mJy -11.33mJy 0.00mJy 11.33mJy 22.67mJy 34.00mJy

Figure 3.5: The 1.4 mm difference map in a flat sky projection. The gray scale is roughly ±10σ.See the corresponding Figure 3.3 for comments common to all maps.

32

2.0 mm difference map

0 500 1000 1500 2000 2500 3000X pixel number

0

500

1000

1500

2000

2500

3000Y

pix

el n

um

ber

-14.00mJy -9.33mJy -4.67mJy 0.00mJy 4.67mJy 9.33mJy 14.00mJy

Figure 3.6: The 2.0 mm difference map in a flat sky projection. The gray scale is roughly ±10σ.See the corresponding Figure 3.3 for comments common to all maps.

33

3.6 Optimal Filter

We enhance the point-source signal-to-noise ratio in the SPT maps by applying a matched

spatial filter (see e.g., Tegmark & de Oliveira-Costa, 1998) to each single-band map. The

matched filter combines knowledge of the instrument beam and any other filtering that has

been performed on the data with an estimate of noise covariance to optimize the signal-to-

noise of a source in the filtered map. This matched filter ψ is applied in the Fourier domain

and is given by:

ψ ≡ τTN−1√τTN−1 τ

(3.1)

whereN is the noise covariance matrix (including astrophysical contaminants such as primary

CMB anisotropy), and τ is the assumed source shape in the map, which in the case of point

sources is a function of beam and filtering only.

The instrumental and atmospheric contributions to the noise covariance in each band

are estimated by computing the average power spectrum of hundreds of signal-free maps,

constructed from the difference map (see Section 3.5). The main astrophysical contribution

to the noise covariance is expected to be primary CMB anisotropy, so an estimate of the

CMB power spectrum (using the best-fit WMAP5 model from Nolta et al. (2008)) is added to

the noise covariance. Adding further astrophysical contributions such as the SZ background

and point sources below our detection threshold has a negligible effect on our results.

The source shape used in the matched filter is the convolution of our measured beam

and the map-domain equivalent of any timestream filtering we have performed. We measure

the effect of timestream filtering on the expected shape of point sources in our maps by

performing signal-only simulations of our data processing (see Section 3.4). The observations

from which the maps used in this work were made were performed in the standard SPT

horizontal raster scanning mode, which at the South Pole means that scans are at constant

declination. As a result of our flat-sky projection (See Section 3.5), the effects of timestream

34

filtering on source shape are map-position-dependent. To account for this, we break both

single-band coadded signal maps into nine tiles3 and perform our signal-only simulations

nine times — once with the model source located at the center of each tile. We also estimate

the noise covariance separately for each tile, since the projection of non-white timestream

noise into the map will also be a function of position. We construct nine matched filters from

these inputs and perform source finding on each map tile individually with the matched filter

constructed from that tile’s inputs. We chose to break the map into nine tiles (as opposed

to four or sixteen) as it solved the problem and with the greatest economy. The locations of

the signal only simulations and the borders defining the nine tiles are shown in Figures 3.12

and 3.13.

The optimal filter is shown in k-space in Figures 3.7 and 3.8.

3. Refereed to internally as “Brady sectors”.

35

Figure 3.7: The 1.4 mm optimal filter.

36

Figure 3.8: The 2.0 mm optimal filter.

37

3.7 Filtered Maps

The filtered 1.4 mm and 2.0 mm maps used for source candidate identification are shown in

Figures 3.9 and 3.10. The total area shown in each map is 86.7 square degrees. The noise

varies at the level of ±6% across the maps, mainly as a function of declination (i.e. the noise

is systematically 6% lower at decl.=-60 than at decl.=-55). This trend with declination is

due to the fact that the coverage is nearly uniform in right ascension, resulting in coverage

per unit solid angle that varies as cos(δ), and also the higher airmass at lower elevations.

The typical RMS of the map is 1.4 mJy at 2.0 mm and 3.4 mJy at 1.4 mm. The noise

distribution closely approximates a Gaussian, as is evident from the central part of the pixel

distributions shown in Figure 3.11. The fact that the maps are so uniform and the noise

is so well-understood makes the analysis much easier and gives us great confidence in the

robustness of our results.

38

1.4 mm filtered map

0 500 1000 1500 2000 2500 3000X pixel number

0

500

1000

1500

2000

2500

3000Y

pix

el n

um

ber

-17.00mJy -11.33mJy -5.67mJy 0.00mJy 5.67mJy 11.33mJy 17.00mJy

Figure 3.9: The filtered 1.4 mm map in a flat sky projection. The total sky area is 87 deg2 andthe field center is right ascension R.A. 5h30m, decl. −55 (J2000). Each pixel is 0.25′ × 0.25′. TheRMS in the map is 3.4 mJy and the gray scale is roughly ±5σ; the brightest source is > 150σ(> 500 mJy), and the scale saturates for most of the sources visible here. Because of time domainfiltering, the source signal produces an arc from the impulse response of the filter as the detectorsscan left and right across the field. The azimuthally symmetric ringing around bright sources isdue to spatial high-pass filtering both in the pre-map processing and in the point-source matchedfilter.

39

2.0 mm filtered map

0 500 1000 1500 2000 2500 3000X pixel number

0

500

1000

1500

2000

2500

3000Y

pix

el n

um

ber

-7.00mJy -4.67mJy -2.33mJy 0.00mJy 2.33mJy 4.67mJy 7.00mJy

Figure 3.10: The filtered 2.0 mm map in a flat sky projection. The RMS in the map is 1.4 mJy andthe gray scale is roughly ±5σ; the brightest source is > 500σ (> 700 mJy), and the scale saturatesfor most of the sources visible here. See the corresponding Figure 3.9 for comments common toboth maps.

40

Figure 3.11: The distribution of fluxes in map pixels. For each band, the lines are as follows: solid :the coadded signal map; dashed : the coadded difference map (see Sec. 3.5); dotted : fit to the signalmap pixel histogram. For each band, the fit is done to the full signal map and gives σ = 1.4 mJyfor 2.0 mm and σ = 3.4 mJy for 1.4 mm. The noise across the map is gaussian. The dotted-line isfit to the noise peak for the signal map but it is also a good fit to the noise in the difference map.The tails are due to ringing from the various effective high-pass filters on the sources in the map.

3.8 Source Extraction

Source candidates are identified in the filtered maps using a variant of the CLEAN algorithm

from radio astronomy (Hogbom, 1974). The CLEAN procedure involves identifying the

highest peak in the filtered map and iteratively subtracting off a model for the source shape

centered on that peak until no peaks are left above the detection threshold. To account

for several non-idealities, including finite-sized map pixels, slightly imperfect source shape

models, and possibly extended sources, the source model subtraction is performed with

a multiplicative factor less than unity, usually called the loop gain (after the analogous

parameter in electronic feedback circuits). We use a loop gain of 0.1 in this work.

In interferometric radio observations, the source shape template in the CLEAN process

41

is the interferometer’s “dirty beam”; in our case, it is the source shape in the filtered maps:

τ ′ = ψ τ. (3.2)

As discussed in Section ??, in each band’s map, the matched filter ψ (see Eq. 3.1) is in-

dependently calculated for nine different regions of the map, in order to account for the

map-position-dependent shape of the noise and filtering. In constructing the source shape

template ψτ , we use the appropriate version of ψ depending on the position of the peak being

CLEANed. We also use a pre-matched-filter source shape τ that is position-dependent; in

fact, we calculate the pre-filter shape τ independently every time we detect a new peak. In

the map pixelization we are using, the effect of the timestream filtering as a function of map

position is a simple rotation of what it would be for a pixelization in which pixel rows had

constant-declination, so this step is not unduly computationally intensive.

We run our version of CLEAN on each band’s filtered map individually until there are no

peaks above 3σ left in the map. All map pixels identified above the 3σ threshold within the

tile are then sorted by significance and gathered into discrete sources using an association

radius between 30 arcsec and 2 arcmin, depending on the brightness of the source. In other

words, the brightest pixel found by CLEAN is declared to be the first source, then we go down

the list of pixels in descending order of brightness, asking if each pixel should be declared

a new source or associated with a source already identified. Source fluxes are assigned by

converting the value in the filtered map of the brightest pixel associated with a source from

CMB fluctuation temperature units to flux (in units of Jy) using the following relation:

S[Jy] = Tpeak × ∆Ωf × 1026 × 2kB

c2

(

kBTCMB

h

)2 x4ex

(ex − 1)2, (3.3)

42

where x = hν/(kBTCMB) and ∆Ωf is defined by:

∆Ωf =

[∫

dudv ψ(u, v) τ(u, v)

]−1

, (3.4)

which can be thought of as the effective solid angle under the filtered source template, in

that a point source of flux S will have peak surface brightness S/∆Ωf in the filtered map.

Source positions are obtained by calculating the center of brightness of all pixels (each pixel

being 0.25′ × 0.25′) associated with a given source.

The CLEANed maps are shown in Figures 3.12 and 3.13. Overplotted onto the clean

maps are the locations of the

43

Figure 3.12: The 1.4 mm cleaned filtered signal map. The map has been cleaned down to 3σ andthe gray scale is roughly ±3σ. The blue crosses mark the location of the simulations for measuringthe transfer function (see Sec. 3.4). The white lines mark the borders between the nine tiles (seeSec. ??). The red circles mark the positions of sources detected at S/N> 4.5 in this band.

44

Figure 3.13: The 2.0 mm cleaned filtered signal map. The map has been cleaned down to 3σ andthe gray scale is roughly ±3σ. See the corresponding Figure 3.12 for comments common to bothmaps.

45

3.9 Catalog

We run our version of the CLEAN algorithm (described in Sec. ??) on each (for a total of

9 tiles × 2 bands = 18) map individually, and every source candidate above 3σ is extracted

from each map. Detections in both bands are listed in the final catalog as a single source if

they are offset < 30 arcsec between bands. For sources detected in both bands we adopt the

position of the more significant detection. If there does not exist a cross-matched counterpart

above 3σ within 30′′ of a source then the cross-matched flux is given as the pixel-value in

the other map. It would be possible to do something more sophisticated for cross matching

sources between bands, but found this simple and intuitive method to be adequate (see

Fig. 3.14).

The catalog described here can be found in Vieira et al. (2009) and from the public SPT

website. Descriptions of the catalog fields are as follows:

1. Source ID: the IAU designation for the SPT-detected source.

2. RA: right ascension (J2000) in degrees.

3. DEC: declination (J2000) in degrees.

4. S/N (2.0 mm): detection significance (signal-to-noise ratio) in the 2.0 mm band.

5. Sraw (2.0 mm): raw flux (uncorrected for flux boosting) in the 2.0 mm band.

6. Sdist (2.0 mm): de-boosted flux values encompassing 16%, 50%, and 84% (68% proba-

bility enclosed, or 1σ for the equivalent normal distribution) of the cumulative posterior

probability distribution for 2.0 mm flux, as estimated using the procedure described in

Sec. 4.3.

7. S/N (1.4 mm): same as (4), but for 1.4 mm.

8. Sraw (1.4 mm): same as (5), but for 1.4 mm.

46

9. Sdist (1.4 mm): same as (6), but for 1.4 mm.

10. αraw: estimate (from the raw flux in each band) of the 2.0 mm−1.4 mm spectral index

α, where α is defined by the relation:

S(λ) = S0

(

λ

λ0

)−α

. (3.5)

11. αdist: 16%, 50%, and 84% estimates of the spectral index, based on the probability

distributions for spectral index estimated using the procedure described in Sec. 4.3.

12. P (α > 1): fraction of the spectral index posterior probability distribution above the

threshold value of 1.0. P = 0 is a synchrotron source and P = 1 is a dust source.

13. Type: source classification (synchrotron- or dust-dominated), based on P (α > 1).

14. ∆θsumss: angular distance (in arseconds) from the nearest source in the 36 cm (843 MHz)

Sydney University Molongolo Sky Survey (SUMSS) (Mauch et al., 2003). There are

2731 SUMSS sources in the SPT survey area. For a 1′ association radius there is a

2.7% chance of random association for each SPT source.

15. ∆θrass: angular distance (in arseconds) from the nearest source in the The ROSAT

All-Sky Survey (RASS) Bright Source Catalog (Voges et al., 1999) or Faint Source

Catalog (Voges et al., 2000). There are 1441 RASS sources in the SPT survey area.

For a 1′ association radius there is a 1.4% chance of random association for each SPT

source.

16. ∆θiras: angular distance (in arseconds) from the nearest source in the IRAS Faint

Source Catalog (Moshir et al., 1992). There are 493 IRAS sources in the SPT survey

area. For a 1′ association radius there is a 0.8% chance of random association for each

SPT source.

47

3.10 Astrometry

SPT pointing is reconstructed through a combination of an online pointing model (tied to

regular observations with optical star cameras), corrections based on observations of galactic

HII regions (performed many times each observing day), and information from thermal

and linear displacement sensors on the telescope. The pointing reconstruction process is

described is Section 3.5. We check the absolute pointing accuracy in the maps used in this

work by comparing our best-fit positions for bright sources in our catalog with three external

determinations of those positions: 1) the publicly available 36 cm SUMSS catalog; 2) the

recently published Australian Telescope 20 GHz Survey (AT20G, Murphy et al. (2009));

and 3) from follow-up observations of SPT-selected sources at 6 cm with the Australian

Telescope Compact Array (ATCA). Figures 3.17 and 3.18 shows the distribution of offsets

between SPT-determined positions and all sets of external positions. It indicates that the

absolute SPT pointing is good to ∼ 7 arcsec RMS. There is a 2′′ absolute pointing offset in

cross-declination (RA× cos(DEC)) 2′′ offset in declination in the 1.4 mm maps. There is a

5′′ absolute pointing offset in cross-declination 2′′ offset in declination in the 2.0 mm maps.

There is also a 3′′ relative offset in RA between the two bands, which is consistent with the

absolute offsets, as shown in Fig. 3.16. As these offsets are small compared to our beamsize

we have opted to neglect this small offset, but we plan of fixing this in the future.

48

Figure 3.14: Relative angular offsets between the SPT bands. This plot shows the relative angularoffset between SPT bands as a function of S/N. Blue points are for 1.4 mm detected sources andRed points are for 2.0 mm sources. The black dashed horizontal line shows the value of the cutplaced on the association radius of SPT sources between bands.

49

Figure 3.15: Relative DEC offsets between the SPT bands. This plot shows the relative DECoffset between SPT bands as a function of S/N. Blue points are for 1.4 mm detected sources andRed points are for 2.0 mm sources. There is evidence for a small (< 1 arcsec) DEC offset betweenthe two bands.

50

Figure 3.16: Relative cross-declination offsets between the SPT bands. This plot shows the relativeangular offset between SPT bands as a function of S/N. Blue points are for 1.4 mm detected sourcesand Red points are for 2.0 mm sources. There is evidence for a 3 arcsec cross-declination offsetbetween the two bands.

51

Figure 3.17: A comparison of absolute pointing between the SPT 1.4 mm band, SUMSS catalogsources, ATCA 20GHz survey, and ATCA 5 GHz followup observations. Only sources at S/N> 10for SPT and S/N> 5 for the radio catalogs have been used. Only sources which have a robustcounterpart within 20′′ have been plotted. There is evidence for a 2.0′′ cross-declination and 2.5′′

declination absolute offset. For near-by extended sources the cm emission does not necessarilycoincide perfectly with the mm emission, so some extra scatter to these offsets is expected, but thisscatter should be random.

52

Figure 3.18: A comparison of absolute pointing between the SPT 2.0 mm band, SUMSS catalogsources, ATCA 20GHz survey, and ATCA followup observations. Only sources at S/N> 10 for SPTand S/N> 5 for the radio catalogs have been used. Only sources which have a robust counterpartwithin 20′′ have been plotted. There is evidence for a 5.0′′ cross-declination and 2.5′′ declinationabsolute offset. For near-by extended sources the cm emission does not necessarily coincide perfectlywith the mm emission, so some extra scatter to these offsets is expected, but this scatter should berandom.

53

3.11 Completeness

We follow Scott et al. (2008) and estimate our completeness by placing simulated sources

in the real maps and performing the source extraction as with the real data. We place the

simulated sources into the filtered map. For the simulated source profile, we use the measured

beam convolved with the map-domain estimate of our timestream filtering and the matched

filter. As with the matched filter and the CLEAN process, we use a different simulated

source profile in each of the nine map tiles (see Sec. 3.6 for details). The simulated source is

considered detected if it would have made it into our catalog — i.e., if it is detected by the

source extraction algorithm at ≥ 3σ. As expected for maps whose variance is nearly uniform

and is dominated by random, Gaussian-distributed noise, our cumulative completeness curves

(fraction of simulated sources detected above a given flux) are fit well by error functions, as

shown in Figure 3.19. The exact functional form used here is

fcompl(S) =1

σ√

2π

∫ ∞

Se− (S′−Sthresh)2

2σ2 dS′ (3.6)

Our source detection threshold is set to 3σ and so there is only one free parameter (σ) with

a best fit of σ = 1.3 mJy for 2.0 mm and σ = 3.1 mJy for 1.4 mm. On the basis of this

test and the error-function fits, we expect the full ≥ 3σ catalog to be 50% complete at 3.8

and 8.9 mJy in the in the 2.0 and 1.4 mm bands and to be 95% complete at 5.9 mJy and

14.6 mJy in the 2.0 and 1.4 mm bands.

3.12 Purity

There is some ambiguity in the definition of “purity” or “false detection” when one is dealing

with a very steep source population, especially if the detected fluxes are anywhere near the

confusion limit. In such a situation, there will be at least one source at some fraction of

54

Figure 3.19: The left panel shows the results of the completeness simulation at 2.0 mm; the rightpanel shows the results of the completeness simulation at 1.4 mm. In each plot, the symbols witherror bars show the fraction of recovered sources with error bars estimated from binomial statistics.The dashed line shows the best-fit model of the form shown in Eq. 3.6.

the detection limit in every beam. In this work, we have chosen to define a false detection

as a fluctuation above the detection threshold in the absence of any mean point source

contribution to the maps. We treat the problem of low-flux sources scattering above the

detection threshold in the context of flux boosting, Sec. 4.3.

We estimate our purity using two different methods, both of which are fairly common in

the SMG literature (e.g., Perera et al., 2008). First, we invert our maps and run the matched

filter and source-finding algorithm on the negative maps. This method is complicated by

the fact that, at 2.0 mm, we expect to have real negative signal near the beam scale due to

thermal SZ signal from galaxy clusters. To deal with this, we mask the inverted 2.0 mm map

around SZ cluster candidates detected at ≥ 4.5σ. These candidates are identified using a

filter optimized for extended sources with a particular spatial profile, in this case a spherical β

model (see S09). This procedure should not mask point-like noise fluctuations. 61 SZ sources

are masked with a radius of 2′, resulting in a total of 0.213 deg2 or < 0.25% of the total

map being masked. Our second estimate of purity comes from running the matched filter

55

and source-finding algorithm on simulated maps. These simulated maps contain atmospheric

and instrumental noise (taken from our difference map – see Sec. 3.5), a realization of the

CMB, and a white, Gaussian noise term meant to approximate the contribution from the

background of sources (SMGs) below the detection threshold. Because of pointing offsets

and an imperfect estimate of our time constants the difference maps show residual signal

from the brightest point sources. This manifests itself in the difference map as a dipole with

∼ 1% of the peak amplitude of the source in the signal map. So as not to bias our estimate

of the purity we mask the locations of the 24 brightest sources (S/N > 20 at 2.0 mm) with

a 1′ radius mask in both the 1.4 and 2.0 mm difference maps. The results from both tests

are shown in Figure 3.20. In all cases, the quantity plotted is

fpure = 1 − Nfalse

Ntotal, (3.7)

where Nfalse is the number of false detections (as estimated, alternately, by one of the two

methods described above), and Ntotal is the total number of detections in the real map. Both

methods agree that at S/N > 4.5 our sample is & 90% pure. Perera et al. (2008) argue that

both of these methods will overestimate the true false detection rate, and this hypothesis is

supported by the fraction of our synchrotron-dominated sources that have clear counterparts

in other catalogs and/or our ATCA follow-up observations (see Sec. 4.4 for details).

56

Figure 3.20: Purity in the 2.0 mm-selected sample (left) and the 1.4 mm-selected sample (right).In each plot, the black line indicates the purity (see Eq. 3.7) calculated using the inverted mapto estimate the number of false detections, the red line indicates the purity calculated using thedifference maps, the blue line indicates the difference map plus a realization of the CMB, and thegreen line uses the difference map, a realization of the CMB, and a gaussian white noise termto match the white noise seen in the signal map (referred to as the simulated map). The purityestimation for 2.0 mm is more complicated than 1.4 mm due to the presence of SZ (see Sec. 3.12for details). The inverted and simulated purity curves are used to estimate the number of falsedetections in each single-band catalog.

57

CHAPTER 4

SOURCE SPECTRAL CHARACTERIZATION AND

CLASSIFICATION

4.1 Spectral Classification and Source Association

Based on previous surveys of sources at other wavelengths we expect the SPT sources to

be dominated by two populations: one dominated by synchrotron emission, the members of

which should have an emission spectrum that is flat or falling with decreasing wavelength,

and one dominated by thermal emission of reprocessed starlight by cold dust, the members

of which should have an emission spectrum that increases with decreasing wavelength. The

spectral index of the synchrotron sources is not expected to be well-behaved as the sources

are known to be highly variable and different regions of the objects (e.g. the lobes verses

the core) can show different spectral indices. The spectral index for dust sources should be

relatively well-behaved between 1.4 and 2.0 mm as those frequencies lie on the Rayleigh-

Jeans side of the greybody, independent of redshift. Figure 4.1 shows the expected change

in spectral index verses redshift for a standard SED template (Arp 220) as well as the mean

of 30 SED templates for nearby ULIRGs from Silva et al. (1998).

Our results confirm this simplified picture. Of course, any individual source may have

components of each in its emission, and the local slope of the spectral energy distribution

(SED) will be further modulated by the redshift of the source (see Figures 1.1 and 1.2).

Though our actual source characterization is based on the integrated posterior probability

density function (PDF) of the spectral index, estimated using the method described in

Sec. 4.3, a plot of raw 1.4 mm flux vs. raw 2.0 mm flux, as in Figure 4.2, gives the basic

picture. Of the sources detected above 4.5σ in both bands, the synchrotron-dominated

sources occupy a locus of points close to the line α = −1, where the spectral index α is

defined in Eqn. 3.5. The dust-dominated sources detected in both bands occupy a clearly

58

Figure 4.1: Expected 1.4mm/2.0mm spectral index verses redshift for a dusty star forming galaxy.SED templates come from Silva et al. (1998). The dashed line is for Arp 220. The black line andthe grey contours are the mean of fits to 30 local ULIRGs with the standard deviation betweenSEDs given as the error.

separated locus of points close to the α = 3 line. Also worth noting in this plot is that

effectively all of the high-S/N synchrotron-dominated sources have counterparts in external

catalogs, while many of the high-S/N dust-dominated sources do not. This point is explored

in greater detail in Sec. 4.4 and Sec. 6.2.

59

Figure 4.2: Raw 1.4 mm flux versus raw 2.0 mm flux for sources detected above 4.5σ in bothbands. long-dashed line: A spectral index α = 3 typical for sources dominated by dust emission.short-dashed line: A spectral index α = −1 typical for sources dominated by synchrotron emission.dotted : The approximate 4.5σ raw-flux threshold of the catalog (see text). A source is identi-fied as synchrotron-dominated (red +) or dust-dominated (blue ×) if P (α > 1) in the posteriorspectral index distribution (see Sec. 4.3) is < 50% or > 50%, respectively. By finding associa-tions with IRAS (a source within 1 arcmin) and SUMMS (a source within 1 arcmin), we see thatmost synchrotron-dominated sources are previously known. The bright dust-dominated populationwithout counterparts in IRAS is discussed in Sec. 6.2.

60

4.2 Extended Sources and Other Notes

As is evident from Eq. 3.3 and Eq. 3.4, our flux estimates rest on the assumption that all

sources have the same shape in our filtered maps. Since the assumed source shape is just

that of our beam and filtering, this assumption will only be valid for point-like objects.

This method will not provide accurate flux estimates for resolved sources. For example, our

method will underestimate the flux of a source with a FWHM = 0.25′ Gaussian profile by

3% at 2.0 mm and 4% at 1.4 mm; a 0.5′ source will be underestimated by 10% and 11%; a

1′ source by 31% and 36%.

Given the 1′ beams of the SPT, we expect that comparatively few extended sources will

appear in our catalog. A normal galaxy will appear point-like to the 1-arcmin beam of the

SPT at redshifts z & 0.05 (distances greater than ∼ 200 Mpc), so only very nearby objects

or objects with very extended structure (such as AGN with 100-kpc-scale jets) would appear

extended in our maps. Furthermore, the matched filter applied to the maps is optimized for

unresolved sources and will degrade the signal-to-noise on any extended source. We search

for extended sources by fitting a cut-out of the (unfiltered) map around each detected source

to a model of our measured beam convolved with a Gaussian of variable width. We then

flag sources for which the best-fit profile width is at least 0.25′ and is inconsistent with zero

at the 3σ level. We also visually inspect the filtered map at each ≥ 4.5σ source location for

possible extended sources and any other anomalies.

Of the 168 sources detected at S/N ≥ 4.5σ or above in one or both bands, 13 have

a best-fit width of at least 0.25′ and are inconsistent with zero width at 3σ or more. Of

these 13, three are also listed in the SUMSS catalog as having detectable extent beyond the

∼ 30 arcsec SUMSS beam. Our visual inspection of all sources above 4.5σ in either band

revealed the following cases of note (some of which are also flagged by the quantitative test

for extended structure):

SPT-S J051614-5429.7 : This detection may be spurious, caused by sidelobes from the

61

deep SZ decrement at 2.0 mm from the galaxy cluster SPT-CL J0516-5430 (also RXCJ0516.6-

5430 and Abell S0520). There is no counterpart at 1.4 mm or in external catalogs, the source

is classified as extended by the method described above, and visual inspection shows it to

have an irregular shape. The other bright source very near a galaxy cluster with a deep

SZ decrement, SPT-S J050908-5339.2 (near SPT-CL J0509-5342) is almost certainly not

spurious, since it is detected more strongly at 1.4 mm (which is near the SZ null) than at

2.0 mm.

SPT-S J051217-5723.9 and SPT-S J051214-5724.2 : These are classified as two separate

sources — one dust-dominated and one synchrotron-dominated — because the source centers

at 2.0 mm and 1.4 mm are more than 30 arcsec apart. However, both sources are almost

certainly associated with the low-redshift (z = 0.0047) galaxy NGC 1853. Visual inspection

does confirm that the 2.0 mm and 1.4 mm emission centers are clearly offset, indicating that

we may be resolving different components of emission within the galaxy.

SPT-S J050511-5346.0 and SPT-S J050507-5346.4 : This pair of sources sources strongly

resemble the pairing discussed above, except that there is no counterpart for either in existing

catalogs.

SPT-S J050653-5943.2 : Visual inspection reveals a clear offset between the 2.0 mm and

1.4 mm emission here as well, but the separation is not quite large enough for our algorithm

to classify the two emission centers as separate objects. This source is almost certainly the

low-redshift galaxy NGC 1824.

4.3 Correcting for Flux Boosting and Estimating Spectral

Behavior

The differential counts of mm point sources as a function of source flux are expected to be

very steep, so the measured flux of a point source in the SPT survey will almost certainly

62

suffer flux boosting. In this work, we define flux boosting as the increased probability that a

source we measure to have flux S is really a dimmer source plus a positive noise fluctuation

relative to the probability that it is a brighter source plus a negative noise fluctuation.

Because of this asymmetric probability distribution, naive measurements of source flux will

be biased high. The standard method in the SMG literature for dealing with this problem

(e.g., Coppin et al., 2005) is to construct a posterior probability distribution for the intrinsic

flux of each detection. The situation with SPT data is more complicated for two reasons:

1) as discussed in Crawford et al. (2009), the current implementation of this method in the

SMG literature is not appropriate for estimating properties of individual sources, which is

a key aim of this work; 2) we have data in more than one observing band, and the prior

information that is applied to create the posterior flux likelihood will be highly correlated in

the two bands.

In Crawford et al. (2009), we develop a method of correcting for flux boosting (based

on the Bayesian posterior method used in Coppin et al. (2005) and others) which preserves

information on individual source properties, and we extend that method to estimate the

intrinsic multi-band flux of a source based on the measured flux in each band and the prior

knowledge of the source populations in the various bands. In the two-band SPT case, the final

product for each source is a two-dimensional posterior likelihood, where the two variables are

either the flux in each band or the flux in one band and the spectral index between bands.

The two likelihood distributions are trivially related by:

P (Smax,1, Smax,2|Sp,m,1, Sp,m,2) = (4.1)

P (Smax,1, α|Sp,m,1, Sp,m,2)dα

dSmax,2,

where Sp,m,i is the measured flux in a resolution element or pixel in band i, Smax,i is the

true flux of the brightest source in that resolution element and band, and dα/dSmax,2 is

63

derived from Eqn. 3.5. If we cast our prior information on source behavior in terms of source

counts in one band and spectral behavior between bands, and we make the assumption that

spectral index does not depend on flux, then we can write:

P (Smax,1, α|Sp,m,1, Sp,m,2) ∝ (4.2)

P (Sp,m,1, Sp,m,2|Smax,1, α)P (Smax,1)P (α),

(see Crawford et al. (2009) for details).

These posterior probability distributions are used to calculate most of the quantities

reported in subsequent sections.The source counts shown in Figure 5.1, Figure 6.2 and Fig-

ure 6.4.

For the source-count prior P (Smax,1) in Eqn. 4.2, we use an extrapolation of the Negrello

et al. (2007) counts from 850 µm to our wavelengths using a spectral index of 3.0 for the

SMGs and 2.0 for the IRAS-type galaxies (assuming zero scatter in the index in both cases).

The choice of these spectral indices was taken from an Arp 220 SED template and the

outcome is not very sensitive to the input.1

De Zotti et al. (2005) make direct predictions for the synchrotron-dominated population

counts at 2.0 mm; we extrapolate these to 1.4 mm using a Gaussian distribution of spectral

indices, centered on −0.5 with RMS of 0.5. We have found that the choice of source-count

prior makes only a small difference in the resulting posterior probability distributions (in the

S/N range presented here), consistent with the result in Scott et al. (2008).

For the spectral index prior, we have chosen a flat prior between α = −2 and α = 4.

Given what is known about the two populations expected to contribute to sources at our

wavelengths (e.g., Knox et al., 2004; Mason et al., 2009), this estimate conservatively brackets

1. While we compare to the integral counts predictions of Lagache et al. (2004) in Sec. 6.2, we found thata kink in those differential counts produced a bias toward drawing ∼ 10 mJy sources from the posterior.Negrello et al. (2007) was then used by virtue of its smoothness.

64

the expected spectral behavior of SPT sources.

There is a slight asymmetry in how we account for the spectral index of the source

populations. On the one hand, the counts models used here (Negrello et al. (2007); De Zotti

et al. (2005)) assume a specific spectral energy distribution to produce counts at 1.4 mm

and 2.0 mm. On the other, we find the joint posterior flux distribution using a flat prior

on the spectral index between α = −2 and α = 4 – taking a definite spectral index prior

(as the counts models do) would make the measurement of the index much less agnostic by

dictating the indices to expect. Yet, if bands 1 and 2 are swapped in Eqn. 4.2, the two-

dimensional posterior will only be unchanged if the two source-count priors are perfectly

consistent with each other given the flat prior on α. The outcome of this is that the joint

posterior distribution is slightly asymmetric in whether one takes band 1 to be 1.4 mm or

2.0 mm (likewise for band 2). In short, a flat prior on the spectral index from −2 to 4 can not

explain the difference between the counts models at 1.4 mm and 2.0 mm which, in reality,

is due to the spectral energy distributions of the contributing populations.

In this work, we take the 1.4 mm counts model prior for the derived 1.4 mm counts and

the 2.0 mm counts model prior for the derived 2.0 mm counts. Thus, for 1.4 mm, the flux

posterior is determined by the model counts at 1.4 mm plus the information that is available

in the 2.0 mm band, translated to the 1.4 mm band using the flat prior on the spectral index

from −2 to 4 that we employ here (and the converse for the counts at 2.0 mm). To test the

sensitivity to this choice, we have also considered the case where one uses the counts model

in the band with the highest signal-to-noise. (That is, there are sources that contribute to

the 1.4 mm counts where there is higher signal-to-noise available in 2.0 mm.) The counts

are insensitive (at < 1σ) to this distinction.

By marginalizing the two-dimensional posterior in Eqn. 4.2 over the flux in the detection

band P (Smax,1), we obtain a posterior likelihood for the spectral index of each detected

source. The 16%, 50%, and 84% values of α shown in Fig. 5.1 are taken from the cumulative

65

version of this likelihood distribution for each source. These individual distributions can be

summed to produce the measured α distribution of all sources detected in our two bands

(which will be the convolution of the intrinsic distribution with a complicated function of the

noise from instrumental, atmospheric, and source background contributions in both bands).

Figure 4.3 shows that the posterior spectral index distribution for sources detected at greater

than 4.5 σ in both bands has a clear population split. We use this split to identify the sources

as either dust or synchrotron-dominated through the posterior.

In Fig. 5.1, sources with P (α > 1) > 0.5 (having > 50% of its posterior index distribution

in excess of 1) are classified as dust-dominated and sources with P (α > 1) < 0.5 (having <

50% of its posterior index distribution in excess of 1) are classified as synchrotron-dominated.

The source counts by population use a probabilistic method based on P (α) that is described

in Sec. 5.1, but there, too, we take α = 1 to be the threshold. The classification is robust

to the spectral index threshold, and one finds similar results taking α = 0 or α = 2 as

classification thresholds (see Figure 4.3).

4.4 Associations with External Catalogs and Follow-up

Observations with ATCA

Where possible, we identify candidate counterparts to the SPT-detected sources in several

external catalogs and databases. We have queried the NED2 and SIMBAD3 databases for

counterparts within 0.5, 1.0, and 2.0 arcmin of all 3241 of our ≥ 3σ sources, and we have

searched catalogs from four individual observatories for counterparts: 1) the SUMSS catalog

(Mauch et al., 2003); 2) the IRAS Faint Source Catalog (Moshir et al., 1992); 3) the ROSAT

All-Sky Survey (RASS) Bright Source Catalog (Voges et al., 1999) and Faint Source Catalog

2. http://nedwww.ipac.caltech.edu/

3. http://simbad.u-strasbg.fr/simbad

66

Figure 4.3: The distribution of the posterior spectral indices measured between 1.4 mm and 2.0 mmfor sources with signal-to-noise > 4.5 in both bands (thick black line). Because we take a flat prioron the spectral index between −2 and 4 (and zero outside), the distribution outside the plottedrange here goes to zero. We sum the P (α) for each source (described in Sec. 4.3 and normalized tointegrate to 1 over α for each source) to give an effective dN/dα for this selection. We then classifythe source by the probability that its posterior spectral index distribution exceeds a classificationcut, taken here to be α = 1. Those with > 50% probability of posterior α > 1 are classified asdust dominated and those with < 50% probability of posterior α > 1 are synchrotron-dominated.There are 9 dust sources (light gray) and 37 synchrotron sources (dark gray) that contribute to thisdistribution. The population split shown here is robust to changes in the signal-to-noise cut. Atlower signal-to-noise cuts, the population features broaden slightly and many sources have poorly-localized P (α) distributions which contribute a floor in dN/dα.

(Voges et al., 2000); and the Parkes-MIT-NRAO (PMN) catalog (Wright et al., 1994). We

search these catalogs because these observatories are particularly relevant for extragalactic

sources in the Southern Hemisphere. (For our purposes, PMN is redundant with the SUMSS

catalog. Given that the SUMSS survey depth is deeper than that of PMN we shall only

refer to SUMSS from here on out.) Additionally, as mentioned in Sections 3.10 and 3.12,

67

we have performed follow-up observations on many of our brightest sources with ATCA.

Observations were performed at 6 cm, 12 mm, and 7 mm. We use only the 6 cm data in this

work.

The majority of our brightest sources have a clear counterpart either in an external cat-

alog, in our 6 cm ATCA observations, or both, with the notable exception of the population

of bright, dust-dominated sources discussed in Sec. 6.2. In fact, of the 110 sources above

5σ that we classify as synchrotron-dominated, only six of them do not have SUMSS coun-

terparts within 30 arcsec (we would expect < 1 due to false associations). Of these six, the

two brightest sources have SUMSS counterparts within 1 arcmin and are robustly detected

(> 20σ) in the 6 cm ATCA observations. The SUMSS survey depth is 6 mJy and the SPT

5σ depth at 2.0 mm is 7 mJy. AGN are known to be highly variable, and it is not surpris-

ing for a source to be below 6 mJy at the time of the SUMSS observations, and then be

above 7 mJy at the time of the SPT observations. We assume that the offset between the

SUMSS and SPT/ATCA positions for these sources arises because the synchrotron emission

from these sources (presumably AGN) are dominated by the radio-lobe contribution in the

36 cm SUMSS observations but dominated by emission from the core at shorter wavelengths.

This frequency-dependent core-to-lobe flux ratio is commonly seen in radio-loud AGN (e.g.,

Kharb et al., 2008; De Zotti et al., 2009) and is predicted by certain unified AGN models

(e.g., Jackson & Wall, 1999). Indeed, we see that for the brighter of these two sources,

(SPT-S J053346-5818.0), visual inspection reveals two SUMSS sources ∼ 45 arcsec on either

side of the SPT location and a RASS-BSC object (also presumably dominated by emission

from the AGN core) directly on top of the SPT location. Of the remaining four sources, two

are nearby galaxies (NGC 1853 and NGC 1824, discussed in Sec. 4.2), and one has a coun-

terpart ∼ 11 arcsec away in the Veron-Cetty & Veron (2006) and Hamburg-ESO (Wisotzki

et al., 1991) catalogs as well as a possibly associated SUMSS source 1.3 arcmin away. That

leaves only one > 5σ synchrotron-dominated source with no counterpart. If we assume this

68

source is a false detection, we estimate a ∼ 1% false rate above 5σ. Similarly, if we assume

all synchrotron-dominated sources above 4.5σ with no counterparts are false, we estimate

a false rate above 4.5σ of ∼ 7% (9 out of 128 sources). These are, of course, the most

pessimistic assumptions about false detection rate, and they are just barely compatible with

the most pessimistic estimates of purity in Figure 3.20. A more likely explanation is that

we happened to observe the source while it was flaring. The sources without counterparts

were too far down the S/N list to be targeted by ATCA. Such data would enable a stronger

statement about false rate.

The situation with our dust-dominated sources is very different. Of the 18 (49) sources

above 5σ (4.5σ) that we classify as dust-dominated, only 6 (7) have counterparts (in any of

the above mentioned catalogs) within 30 arcsec, and only 9 (12) have counterparts within

2 arcmin. Given the studies summarized in Sec. 3.12 and the counterparts found for the

synchrotron-dominated sources, the chances that all (or even a majority of) these detections

are false are vanishingly small. Of the dust-dominated sources that do have counterparts,

most are nearby galaxies detected by IRAS, with one notable exception: SPT-S J054716-

5104.1 appears to be associated with the debris disk around the star β Pictoris. There are

no other SPT sources within 30 arcsec of a SIMBAD database star.

Figure 4.4 shows the spatial distribution of sources on the sky flagged with their associa-

tions from the SUMSS, RASS, and IRAS catalogs, in addition to the positions of SZ detected

clusters.

69

Figure 4.4: The spatial distributions of source on the sky. SPT sources detected at S/N> 4.5in either the 1.4 mm or 2.0 mm bands are plotted with the size of the cross proportional to thelogarithm of the flux. Synchrotron-dominated sources are shown in red and dust-dominated sourcesare shown in blue. If the source has a counterpart in either the SUMSS, RASS, or IRAS catalog itis marked with a purple circle, light blue square, or green diamond, respectively. The dusty sourceswithout a counterpart have yellow orange circles around them. Black circles denote the locationsof SPT SZ clusters at S/N > 4.5.

70

CHAPTER 5

SOURCE COUNTS

5.1 Single-band Source Counts

For each source we estimate the distribution of intrinsic fluxes by constructing the two-band

posterior likelihood from the flux measurements in each band

P (Smax,1, Smax,2|Sp,m,1, Sp,m,2) as described in Sec. 4.3.

To derive the counts as a function of flux from these distributions of intrinsic fluxes, we

apply the bootstrap method similar to the one described in Austermann et al. (2009). Here,

for each source, we randomly draw 5 × 104 intrinsic fluxes from the two-band posterior,

forming effectively 5× 104 mock catalogs of intrinsic fluxes in both bands. For each catalog,

we draw a subset of these sources with replacement, where the number of sources drawn

is a Poisson deviate of the catalog size. This resampling accounts for sample variance but

not cosmological variance (which would require an additional variance term to describe how

counts are expected to vary from sky patch to sky patch because of large scale structure). For

each of these 5×104 catalogs we estimate dN/dS and N(> S). In each flux bin, we then find

the 16%, 50%, and 84% percentile points (that is, 68% of the enclosed probability around the

median) of the distributions of dN/dS and N(> S) in that bin. This yields the equivalent of

1σ normally-distributed errors in each flux bin. The N(> S) and dN/dS bootstraps account

for sample variance and posterior distribution variance (which includes noise, calibration

error and deboosting). Because the posterior flux distributions per source span several flux

bins in the counts, even the errors on differential counts will be correlated. The counts are

corrected for completeness using the simulations described in Sec. 3.11. Figure 5.1 shows

differential counts in both bands as well as the differential counts of population that we

identify as either dust or synchrotron-dominated.

To find the counts statistics for sub-populations, we first find the spectral index of

71

the drawn two-band posterior fluxes for each source. Sources in a given bootstrap resam-

pling with α ≥ 1 are counted as dust-dominated, while those with α < 1 are counted as

synchrotron-dominated. Thus, the counts of the sub-populations are determined probabilis-

tically. In this way, a source with P (α > 1) = 0.3, is added to dust-dominated counts 30%

of the time. If, on the other hand, we were to determine that source once and for all based

on whether P (α > 1) > 0.5, it would always be counted as a synchrotron dominated source.

We also estimate purity in each flux bin of the counts statistics using the resampled

catalogs. The purity is not evaluated for the flux at the bin center (which represents an

intrinsic flux), but is instead related to the signal-to-noise of the raw flux of the sources that

contribute to that bin. In each resampling, if a source lies in a flux bin, we find the associated

purity from its raw signal-to-noise. The purity in the bin is then the weighted average of the

purity of each source detection that contributes to the bin. In the counts presented here,

the purity of the low flux end is 0.65 at 2.0 mm and 0.7 at 1.4 mm.

The Bayesian method accounts for a particular sense of the purity which is slightly

different than purity presented in Sec. 3.12. In Sec. 3.12, we take purity to be the fraction

of noise fluctuations that are counted as sources. In principle, one would then suppress this

fraction of the counts. The outlook of the Bayesian method is that there is always some

source at a given pixel so rather than throw out some fraction of sources that are likely

to be noise fluctuations, one should instead draw from the background point source flux

(small fluxes below threshold). Such sources then scatter out of the flux range presented,

so are effectively thrown out. While completeness needs to be corrected explicitly, purity is

accounted for in the Bayesian method.

5.2 Individual-Population Source Counts

To briefly summarize the results of the last several sections, three broad classes of point

sources are detected with high significance in the SPT 1.4 mm and 2.0 mm maps:

72

1. Sources with 1.4 mm-to-2.0 mm flux ratios consistent with synchrotron emission, the

vast majority of which appear in radio catalogs or in our centimeter-wave follow-up

observations with ATCA and which we generically refer to as AGN;

2. Sources with 1.4 mm-to-2.0 mm flux ratios consistent with dust emission which have

low-redshift (z ≪ 1) counterparts in the IRAS-FSC, and which we will generically call

IRAS sources;

3. Previously undetected sources with 1.4 mm-to-2.0 mm flux ratios consistent with dust

emission.

This third population warrants special treatment in this discussion, as 1) and 2) have been

previously studied and are relatively well-characterized. The AGN are the brightest objects

in the mm sky and dominate the number density of source counts down to the mJy level

at 2.0 mm and longer wavelengths. At 1.4 mm, the dusty sources begin to become more

numerous on the sky than the AGN at flux levels below 10 mJy.

In Figure 5.1 we present the measured differential source counts as a function of flux for

each of these populations.

73

Figure 5.1: Source counts by population for the 2.0 mm (upper plot) and 1.4 mm (lower plot)bands. Gray boxes and black crosshairs indicate the total counts in that band (when only anupper bound is available, this is shown as a black arrow with a hat). Red crosshairs indicate thesynchrotron-dominated population counts and blue crosshairs indicate the dust-dominated counts.All upper bounds extend from the 84% percentile of that bin’s CDF to the median. Crosshairswith full error enclose 68% of the probability about the median and are estimated in the bootstrapover flux described in Sec. 5.1. Here we have offset the two populations slightly in flux so that theydo not lie on top of one another and the total counts are at zero offset. A source is identified assynchrotron-dominated (dust-dominated) if α < 1 (α ≥ 1) in the bootstrap resampling from thejoint posterior flux distributions, see Sec. 5.1. This splits the populations so that their differentialcounts sum to the total counts. A correction for survey completeness from simulations describedin Sec. 3.11 is also applied, and impacts primarily the 1.4 mm counts in the lowest two flux bins.

74

CHAPTER 6

INTERPRETATION AND IMPLICATIONS

6.1 Interpretation of Synchrotron Counts

From associations with radio catalogs and from our 6 cm followup observations with ATCA,

we conclude that the SPT sources that have 1.4 mm-to-2.0 mm spectral indices less than

1 are consistent with being members of the classical radio-source population (see De Zotti

et al. (2009) for a recent review). The mean 2.0 mm–6 cm spectral index we measure for

the sources followed up with ATCA is −0.09 ± 0.25, confirming this assumption (See

Figure 6.1). Although contributions to this population can come from synchrotron and free-

free emission in normal and starburst galaxies (Condon, 1992; De Zotti et al., 2009), the

population is dominated at short radio wavelengths (30 cm and below) and moderate to

high fluxes (10 mJy to 1 Jy) by synchrotron emission from AGN (De Zotti et al., 2009). At

even shorter wavelengths (1 cm and below), the moderate-to-high-flux counts are expected

to be dominated by the sub-class of AGN known as flat-spectrum radio quasars (FSRQs)

(De Zotti et al., 2009).

The behavior of this source population at mm wavelengths is interesting for several rea-

sons. Cosmologically, it is important to observe the build up of super massive black holes

over time (Alexander et al., 2008). Astrophysically, mm measurements of AGN have the po-

tential to inform models of AGN emission mechanisms and evolution, particularly whether

FSRQs undergo spectral steepening at shorter wavelengths. This short-wavelength behavior

of FSRQs is also of interest to the CMB and SZ communities, as predictions of contami-

nation of mm CMB power spectrum measurements and SZ galaxy cluster surveys by AGN

emission depend heavily on extrapolations of well-measured long-wavelength counts to mm

wavelengths (Lin & Mohr, 2007; Reichardt et al., 2008). Finally, the compact angular size

of FSRQs (along with their short-wavelength brightness) make them attractive candidates

75

Figure 6.1: The long-wavelength spectral index verses the short-wavelength spectral index forsynchrotron sources with ATCA followup. The long-wavelength(6 cm—2.0 mm) spectral indexmeasured with ATCA and SPT over roughly concurrent time intervals shows the sources to beFSRQs. The short-wavelength (6 cm—2.0 mm) spectral index has much larger error bars due tothe proximity of the two bands but shows evidence for a steepening in the spectral index comparedto the long-wavelength data.

for phase calibration sources for the Atacama Large Millimeter Array (ALMA).

De Zotti et al. (2005) make predictions for radio source counts at wavelengths down to

1 cm, and they have since produced versions of the model at 3 mm (shown in Sadler et al.

76

(2008)) and 2 mm. The De Zotti et al. (2005) model includes contributions from many

populations of radio sources, including normal and star-forming galaxies and many types

of AGN, but at 1 cm and below, the > 10 mJy model counts are dominated by FSRQs.

Figure 6.2 compares our synchrotron-dominated 2.0 mm counts to the De Zotti et al. (2005)

2 mm model. The model is completely consistent with our measured counts, indicating that

the spectral behavior used to extrapolate the long-wavelength FSRQ counts in the model

— in this case, simply assuming α = −0.1 for all FSRQs — is reasonably accurate down to

2.0 mm. (We note that our result is in contrast to that of Sadler et al. (2008), who found

that the De Zotti et al. (2005) model overpredicted FSRQ counts at 3 mm by nearly a factor

of two.)

However, our simultaneous 1.4 mm and 2.0 mm observations of these sources indicate

that this simple spectral behavior of FSRQs does not continue all the way to 1.4 mm.

The distribution of spectral indices in Figure 4.3 shows that the our synchrotron-dominated

sources have 1.4 mm-to-2.0 mm spectral indices peaked around α = −0.8. The individual

α distributions for the brightest sources in our catalog demonstrate even more clearly the

incompatibility of our measurements with an assumption of nearly flat spectral behavior.

Each of the ten brightest sources has a posterior alpha probability density that peaks some-

where between α = −1.1 and α = −0.7 and is at least 2.5σ inconsistent with α = 0. This

result indicates that either SPT synchrotron-dominated counts are not actually dominated

by FSRQs, and that the agreement with the De Zotti et al. (2005) model is pure coincidence

or that the spectra of FSRQs do appear to steepen significantly in the SPT wavelength range.

77

Figure 6.2: Differential counts for the population of sources identified as synchrotron-dominatedcompared to the De Zotti et al. (2005) model. Here the counts are scaled by S2.5 relative toby-band differential counts shown in Figure 5.1 to match the (geometrical) convention in AGNliterature. The error regions enclose 68% of the probability centered about the median counts, andare calculated using the bootstrap over the two-band posterior intrinsic flux (at 2.0 mm) that isdescribed in Sec. 5.1. A source is identified (probabilistically) as synchrotron-dominated if α < 1in the resampling.

6.2 Interpretation of Dust Counts and Arguments for a New

Population of Lensed mm Sources

We have referred throughout this work to the population of sources with 1.4 mm-to-2.0 mm

spectral indices greater than 1 as “dust-dominated.” While thermal dust emission is the most

natural candidate for explaining these sources, we cannot a priori rule out self-absorbed

synchrotron emission from AGN. This emission mechanism is the leading model for the

population of gigahertz-peaked-spectrum (GPS) radio sources (see O’Dea (1998) for a re-

78

view). As the name suggests, GPS sources typically peak around wavelengths of 30 cm

(e.g., Stanghellini et al., 1998), but GPS sources have been observed with peaks at wave-

lengths as short as 1 cm (Edge et al., 1998), and there is no fundamental physics that

rules out self-absorbed synchrotron peaking at much shorter wavelengths. However, several

lines of reasoning suggest that the α > 1 sources observed by SPT are not dominated by

self-absorbed synchrotron.

The first argument against GPS radio sources as the explanation for our “dust-dominated”

counts is that the spectral behavior is too steep even for self-absorbed synchrotron, while it

is perfectly consistent with thermal dust emission. Stanghellini et al. (1998) show that, even

well longward of the peak wavelength, the mean spectral index of GPS sources is α ∼ 0.8,

and rarely do they find spectral indices as high as 2.0; meanwhile, our brightest N dust-

dominated sources have mean spectral index α = 2.7. Another argument against the GPS

explanation for these sources is the lack of radio and x-ray counterparts. Siemiginowska et al.

(2008) found that GPS sources have 2-10 keV fluxes of up to 1046 erg s−1, easily detectable

in the ROSAT All-Sky Survey, and our brightest “dust-dominated” sources would have to

be almost an order of magnitude dimmer at 36 cm than at 1.4 mm to evade detection in

SUMSS. Finally, Kellermann & Pauliny-Toth (1981) argue that the peak wavelength of a

GPS source should be proportional to flux density to the −0.4 power, meaning that sources

that peak at mm wavelengths should be 2.5 orders of magnitude brighter than sources that

peak at cm wavelengths, so they should be much rarer as well. Based on this set of argu-

ments, we conclude that our sources with 1.4 mm-to-2.0 mm spectral indices greater than 1

are indeed dominated by thermal dust emission.

SMG source counts at 850 µm are found to drop precipitously above fluxes 5-10 mJy

(e.g., Coppin et al., 2006). Assuming an average spectral index of α = 2.8, this drop in the

counts would occur at ∼ 2 mJy at 1.4 mm, leading one to expect a 1.4 mm survey to see very

few SMGs above the ∼ 10 mJy level needed for a robust detection in the SPT 1.4 mm band.

79

Indeed, extrapolating two of the models used to fit SCUBA counts in Coppin et al. (2006)

to 1.4 mm and 10 mJy indicates that there should be ≪ 1 SMG in the SPT 87 deg2 field.

Quite contrary to this expectation, SPT detects 15 dust-dominated sources above 10 mJy

at 1.4 mm, including 7 above 20 mJy. What are these sources if not SMGs?

One possibility is that they are nearby ULIRGs, the low-redshift analogues of SMGs. As

noted in Sec. 4.4, some of the bright (S1.4 mm > 15 mJy) dust-dominated sources detected

by the SPT have counterparts in the IRAS-FSC. These sources exhibit extreme evolution

(their density locally is much less than at z ∼ 1), and while their density on the sky is not

high, SPT surveys enough area to detect ∼ .1/deg2. The majority of SPT dust-dominated

sources, however, do not have IRAS-FSC counterparts, or counterparts in any existing cat-

alog. Likewise, in deep (∼ 24.4 AB mag) griz optical data taken by the Blanco Cosmology

Survey (BCS)1 (which encompass roughly half of the 87 deg2 described here) there are no

obvious counterparts.

It is unlikely that these sources are just below the threshold for inclusion in IRAS-FSC,

given that the brightest three SPT dust-dominated sources (and 13 of the brightest 18) do not

have IRAS-FSC counterparts within 1 arcmin. Figure 6.5 makes an even stronger argument

that these sources are a very different population than the SPT sources with IRAS-FSC

counterparts. This figure shows a scatter plot of IRAS 100 µm flux — estimated from an

IRAS Sky Survey Atlas (ISSA, Wheelock et al., 1994) 100 µm map filtered to enhance point-

source S/N — vs. SPT 1.4 mm flux.2 The sources with and without IRAS-FSC counterparts

occupy clearly distinct loci of points. The sources with IRAS-FSC counterparts are consistent

with nearby sources that have typical dust temperatures of 25 − 35 K, while the sources

without IRAS-FSC counterparts have ISSA 100 µm flux consistent with zero and thus must

either be at moderate to high redshift or have anomalously cold dust (. 15 K). Despite

1. http://cosmology.illinois.edu/BCS/

2. We chose to plot the IRAS 100 µm channel (as opposed to 60 µm) because it is the closest band tothe SED peak and to the SPT 1.4 mm band.

80

the fact that the mean SMG dust temperature measured from previous work appears to be

∼ 35 K (Dunne & Eales, 2001; Chapman et al., 2005; Kovacs et al., 2006), there have been

detections of nearby (z < 1) galaxies with dust temperatures in this range (e.g. Kovacs

et al. (2006)). There is also expected to be both a hot (∼ 40K) dust component from the

ISM surrounding actively star forming regions with many young stars, as well as a cold

(∼ 20K) dust component surrounding the diffuse quiescently evolving population of old red

stars (Dunne & Eales, 2001; Vlahakis et al., 2005; Coppin et al., 2008). IRAS would be

largely insensitive to the cold dust component. If these sources were at z ≪ 1 then we would

expect to see them in DSS or 2MASS images, and we do not.

Another explanation for the existence of the bright, dust-dominated SPT sources could

be that the SMG population does not follow a simple extrapolation of the mJy-level counts

at 850 µm to the tens-of-mJy level at 1.4 mm. There are a number of reasons why this could

be true. One is that the longer-wavelength SPT observations will be sensitive to a higher-

redshift population than the sub-mm surveys (due to the stronger negative K-correction),

and there is considerable evidence that the very brightest SMGs are at the highest redshifts

(Ivison et al., 2002; Pope et al., 2005; Greve et al., 2008). This empirically observed trend of

SMG brightness with redshift is plausible both because more distant systems have a higher

probability of being gravitationally lensed (Blain, 1996; Blain et al., 1999b) and because

evolution in star formation as a function of environment, called “cosmic downsizing”, is

consistent with a higher star-formation rate in massive systems at high redshift (Cowie

et al., 1996; Juneau et al., 2005). A second, related reason why SMG counts in a survey like

SPT might not follow an extrapolation of the SCUBA counts is simply that SPT surveys so

much more area (87 square degrees for this small subset of the SPT survey to ∼ 1 square

degree for the total area surveyed by SCUBA) and is hence much more likely to find rare,

bright systems (due to strong lensing or intrinsic luminosity) that a smaller survey might

miss.

81

Comparisons of SPT dust-dominated source counts with model predictions provide some

evidence that the high-redshift/lensing hypothesis could be correct. Figure 6.3 shows one

model of lensed SMG counts from Negrello et al. (2007) which have been scaled to 1.4 mm

from 850 µmusing a spectral index of 2.5, which comes from assuming an Arp 220 SED at

z = 3. Figure 6.4 shows the cumulative SPT dust-dominated counts vs. flux and predictions

from three models. Lagache et al. (2004), and Pearson & Khan (2009) make predictions

for counts at or very near our 1.4 mm band. Both models have two basic components:

moderate-to-high-redshift starburst galaxies (which account for basically all the counts seen

by SCUBA at 850 µm) and nearby galaxies (including the LIRGs and ULIRGs seen in IRAS).

At first glance, both models agree fairly well with the SPT counts at 1.4 mm. However, the

counts at fluxes above 10-20 mJy are dominated in both models by sources that should

be detectable in the IRAS-FSC above the 60 µm flux cut of 200 mJy, while our measured

counts are dominated by sources without IRAS-FSC counterparts. We have modified the

publicly available Lagache et al. (2004) code to exclude such sources from their model,3 and

Pearson & Khan (2009) have supplied us with model counts excluding sources that should

have 60 µm flux greater than 200 mJy. We then re-calculate our 1.4 mm dust-dominated

counts excluding sources with IRAS-FSC counterparts and compare these modified counts

to the modified predictions in the bottom panel of Figure 6.4. As expected, there are

significant discrepancies between our measured counts without IRAS counterparts and the

model predictions, indicating the potential presence of another dust-dominated population,

possibly due to strong lensing of high-redshift SMGs. The models from Negrello et al.

(2007) have been scaled and as we do not know the exact spectral index to use it is difficult

to directly compare these counts to the other models.

If a subset of the SPT-identified dusty sources are indeed high-redshift, strongly lensed

3. Using the template SED models supplied by Lagache et al. (2004), we find that any source detectedat > 10 mJy at 1.4 mm below redshift z = 0.2 should have 60 µm flux above 200 mJy, so our modificationto their model is effectively just a redshift cut at z = 0.2.

82

systems, they would represent an exciting new class of mm sources.4 Strongly lensed sys-

tems allow observers to detect fainter background sources at higher redshift than would

otherwise be obtainable. Because lensing is achromatic, these sources will be brighter at all

wavelengths, facilitating detailed studies which have otherwise been difficult to achieve.

There are currently 3 spectroscopically confirmed SMGs at z > 4 (Capak et al., 2008;

Daddi et al., 2009; Coppin et al., 2009). Because of the unique features of this survey (a

very wide area, a favorable K-correction in the mm band, an internal veto mechanism to

reject the more numerous AGN, and an external catalog to reject low-z ULIRGs), SPT is

in a unique position to detect more of these very high redshift SMGs. The identification of

massive galaxies at very high redshifts will be a critical test of models of galaxy formation

and evolution. Because SMGs are detected by the dust emission from reprocessed UV light,

they are necessary to determine the total star formation rate of the universe that is otherwise

impossible to detect by the Lyman break technique alone. A sample of high-redshift, strongly

lensed SMGs therefore has the potential to be a useful tool for the study of very early epochs

of star and galaxy formation.

4. Using intervening structure as a gravitational lens to boost the flux of fainter background SMGs hasbeen exploited for over a decade (Blain, 1996; Blain et al., 1999a,b; Cowie et al., 2002; Borys et al., 2004;Kneib et al., 2004; Dunlop et al., 2004; Capak et al., 2008). Also, the two highest-redshift objects detected byIRAS were strongly lensed by foreground galaxies with magnification factors of ∼ 10: IRAS F10214+4724, az=2.3 ULIRG (Rowan-Robinson et al., 1991) and APM 08279+5255 (Irwin et al., 1998), an AGN at z=3.9.

83

Figure 6.3: Cumulative SPT dust-dominated source counts vs. 1.4 mm flux, with the Negrelloet al. (2007) model overplotted. The counts have been scaled to 1.4 mm from 850 µmusing aspectral index of 2.5, which comes from assuming an Arp 220 SED at z = 3. The actual scaling usunknown, but this plot is useful for illustrating the effect of lensing on the source counts. The dark

gray contour shows the SCUBA SMG sources counts from Coppin et al. (2006) scaled to 1.4mm.The light grey boxes and black crosses show the SPT cumulative counts. The orange line shows themodel counts for nearby (z < 1) ULIRGs which would typically be found in the IRAS FSC. Thered line shows the high redshift (z > 1) underlaying SMG population, which has been scaled to fitthe Coppin et al. (2006) points. The green line shows the expected source counts due to the stronglensing of the underlaying SMG population. The blue line shows the sum of the three populations.

84

Figure 6.4: Cumulative SPT dust-dominated source counts vs. 1.4 mm flux, with models overplot-ted. Model curves are as follows: red line: Lagache et al. (2004) 1.38 mm prediction (no lensing);blue line: Pearson & Khan (2009) 1.38 mm prediction (no lensing); blue line: Negrello et al. (2007)850 µmprediction (with lensing), scaled to 1.38 mm as described in the text. The error regionsenclose 68% of the probability centered about the median counts, and are calculated using thebootstrap over the two-band posterior intrinsic flux (at 1.4 mm) that is described in Sec. 5.1. Asource is identified (probabilistically) as dust-dominated if α ≥ 1 in the resampling (see Sec. 4.3).Top Panel : This plot shows counts and models with all dust-dominated sources included. Bot-

tom Panel : This plot shows counts calculated excluding sources that have IRAS-FSC counterparts(within 1 arcmin) and models calculated excluding populations that should be detectable in theIRAS 60 µm band above the typical FSC limit of 0.2 Jy. The SPT detects sources in excess ofwhat is predicted by the two models without lensing once the IRAS sources have been removed.

85

Figure 6.5: IRAS 100 µm flux vs. SPT 1.4 mm flux for all SPT dust-dominated sources at S/N > 5.IRAS flux is taken from a version of the ISSA (Wheelock et al., 1994) 100 µm map which has beenfiltered to enhance point-source signal-to-noise. Horizontal error bars are the 68% enclosed intervalin the posterior 1.4 mm flux distribution. Vertical error bars are the width of the noise distributionin the filtered IRAS map. SPT sources with counterparts within 1 arcmin in the IRAS FSC areshown with diamond symbols. Lines of constant 100 µm–1.4 mm flux ratio are shown for fiveemission models, all modified blackbody laws with a dust emissivity index of β = 1.5 (consistentwith the value of β used in Dunne & Eales (2001), Chapman et al. (2005), and Kovacs et al. (2006))and with dust temperatures of 10,15, 20, 25, 30, 35, and 40 K (if the emitter is nearby) or thosetemperatures times 1 + z (if the emitter lies at redshift z). There is a clear distinction betweenthe locus of sources with IRAS-FSC counterparts — which have flux ratios consistent with warm,low-redshift dust emission — and the points which lie along the x axis and have no counterparts,which must be either at moderate to high redshift or have anomalously cold dust.

86

CHAPTER 7

CONCLUSIONS

The South Pole Telescope (SPT) has detected 168 sources above 4.5σ (over 3000 above

3σ) in two-band data over a small (87 deg2) subset of the full survey region. Using the

two bands (1.4 mm and 2.0 mm ) to estimate spectral behavior, we can separate these

sources cleanly into two populations, one of which (the dust-dominated sources) has many

bright members with no counterparts in known catalogs, while the other consists of dust-

emission dominated sources. The dust-dominated sources have some counterparts in the

IRAS FSC, but a majority of sources have no known counterparts in any existing catalog

and are thus represent a new population of sources. Evidence indicates that these sources

are high-redshift, dusty star forming galaxies (DSFGs) and may be strongly lensed. These

sources have the potential to provide a new window on the early stages of galaxy formation.

As with previous SMG detections by mm and sub-mm experiments, it is not possible to

unambiguously identify the SPT sources directly in optical data due to the many-arcsecond

positional uncertainty and also because the sources are highly obscured in the observed opti-

cal bands (rest-frame ultra-violet). In previous campaigns to characterize SMGs, bolometric

receivers were used to survey and detect SMG candidates, pointed follow-up observations

with interferometric arrays provided accurate positional information, and space- and ground-

based infrared (IR) observations provided characterization of the sources (Chapman et al.,

2005; Pope et al., 2005; Younger et al., 2007).

Our short-term goal is to obtain accurate positions for these objects through a com-

bination of mm interferometry with ATCA and SMA and mid-IR imaging with Spitzer

IRAC. Both efforts are now well underway. With arcsec positions it will be possible to make

crude photometric redshift estimates, as well as select targets for followup spectroscopy.

Key observables to understand the nature of this population include measuring the redshift

distribution N(z) to study their evolution, the mean spectral energy distribution (SED) to

87

measure their dust temperatures, and high resolution imaging to test for strong-lensing. Fig-

ures 7.1 and 7.2 show one SPT DSFG candidate for which we have already obtained deep

IRAC imaging. The DSFG is detected at S/N> 10 at 1.4mm (blue contours) and sits on

top of an SZ detected cluster (red contours). We have detected this source with both IRAC

and ATCA and the study is ongoing.

The survey described here, with unprecedented mapping speed in multiple bands at mm

wavelengths, is the first of its kind and has detected a new population of extragalctic sources.

A new era of mm and sub-mm astronomy will begin in the next few years as instruments such

as Herschel, ALMA, SOPHIA, JWST, WISE, Planck, CCAT, and the LMT begin taking

data.

88

Figure 7.1: A strongly lensed DSFG. All contours are in units of S/N, starting at 3σ. Red contours

are the 2.0 mm SZ decrement. Blue contours are the 1.4 mm dust emission. The optical imageis from BCS r- and i- band images, and IRAC 3.6 µmimaging. Notice the red source which ismultiply imaged and observed only at 3.6 µm.

89

Figure 7.2: A strongly lensed DSFG. Contours are the same as for Fig. 7.1, with the addition ofthe green contours, which show the ATCA 3 mm detection.

90

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