THE ATACAMA COSMOLOGY TELESCOPE: COSMOLOGICAL PARAMETERS FROM THE 2008 POWER SPECTRA

Transcription

1 Draft version September 7, 2010 Preprint typeset using L A TEX stye emuateapj v. 08/13/06 SLAC-PUB THE ATACAMA COSMOLOGY TELESCOPE: COSMOLOGICAL PARAMETERS FROM THE 2008 POWER SPECTRA J. Dunkey 1,2,3, R. Hozek 1, J. Sievers 4, V. Acquaviva 5,3, P. A. R. Ade 6, P. Aguirre 7, M. Amiri 8, J. W. Appe 2, L. F. Barrientos 7, E. S. Battistei 9,8, J. R. Bond 4, B. Brown 10, B. Burger 8, J. Chervenak 11, S. Das 12,2,3, M. J. Devin 13, S. R. Dicker 13, W. Bertrand Doriese 14, R. Dünner 7, T. Essinger-Hieman 2, R. P. Fisher 2, J. W. Fower 14,2, A. Hajian 4,3,2, M. Hapern 8, M. Hassefied 8, C. Hernández-Monteagudo 15, G. C. Hiton 14, M. Hiton 16,17, A. D. Hincks 2, K. M. Huffenberger 18, D. H. Hughes 19, J. P. Hughes 5, L. Infante 7, K. D. Irwin 14, J. B. Juin 7, M. Kau 13, J. Kein 13, A. Kosowsky 10, J. M Lau 20,21,2, M. Limon 22,13,2, Y-T. Lin 23,3,7, R. H. Lupton 3, T. A. Marriage 24,3, D. Marsden 13, P. Mauskopf 6, F. Menanteau 5, K. Moodey 16,17, H. Moseey 11, C. B Netterfied 25, M. D. Niemack 14,2, M. R. Nota 4, L. A. Page 2, L. Parker 2, B. Partridge 26, B. Reid 27,2, N. Sehga 20, B. Sherwin 2, D. N. Sperge 3, S. T. Staggs 2, D. S. Swetz 13,14, E. R. Switzer 28,2, R. Thornton 13,29, H. Trac 30,31, C. Tucker 6, R. Warne 16, E. Woack 11, Y. Zhao 2 Draft version September 7, 2010 ABSTRACT We present cosmoogica parameters derived from the anguar power spectrum of the cosmic microwave background (CMB) radiation observed at 148GHz and 218GHz over 296deg 2 with the Atacama Cosmoogy Teescope (ACT) during its 2008 season. ACT measures fuctuations at scaes 500 < < We fit a mode for the ensed CMB, Sunyaev-Ze dovich (SZ), and foreground contribution to the 148 GHz and 218 GHz power spectra, incuding therma and kinetic SZ, Poisson power from radio and infrared point sources, and custered power from infrared point sources. At = 3000, about haf the power at 148GHz comes from primary CMB after masking bright radio sources. The power from therma and kinetic SZ is estimated to be B 3000 = 6.8 ± 2.9 µk 2, where B (+1)C /2π. The IR Poisson power at 148GHz is B 3000 = 7.8±0.7 µk 2 (C = 5.5±0.5 nk 2 ), and a custered IR component is required with B 3000 = 4.6±0.9 µk 2, assuming an anaytic mode for its power spectrum shape. At 218GHz ony about 15% of the power, approximatey 27 µk 2, is CMB anisotropy at = The remaining 85% is attributed to IR sources (approximatey 50% Poisson and 35% custered), with spectra index α = 3.69±0.14 for fux scaing as S(ν) ν α. We estimate primary cosmoogica parameters from the ess contaminated 148 GHz spectrum, marginaizing over SZ and source power. The ΛCDM cosmoogica mode is a good fit to the data (χ 2 /dof = 29/46), and ΛCDM parameters estimated from ACT+WMAP are consistent with the 7-year WMAP imits, with scae invariant n s = 1 excuded at 99.7% CL (3σ). A mode with no CMB ensing is disfavored at 2.8σ. By measuring the third to seventh acoustic peaks, and probing the Sik damping regime, the ACT data improve imits on cosmoogica parameters that affect the sma-scae CMB power. The ACT data combined with WMAP give a 6σ detection of primordia heium, with Y P = 0.313±0.044, and a 4σ detection of reativistic species, assumed to be neutrinos, with N eff = 5.3 ±1.3 (4.6 ± 0.8 with BAO+H 0 data). From the CMB aone the running of the spectra index is constrained to be dn s /dnk = 0.034±0.018, the imit on the tensor-to-scaar ratio is r < 0.25 (95% CL), and the possibe contribution of Nambu cosmic strings to the power spectrum is constrained to string tension Gµ < (95% CL). Subject headings: cosmoogy: cosmic microwave background, cosmoogy: observations 1 Sub-department of Astrophysics, University of Oxford, Denys Wikinson Buiding, Kebe Road, Oxford OX1 3RH, UK 2 Joseph Henry Laboratories of Physics, Jadwin Ha, Princeton University, Princeton, NJ, USA Department of Astrophysica Sciences, Peyton Ha, Princeton University, Princeton, NJ USA Canadian Institute for Theoretica Astrophysics, University of Toronto, Toronto, ON, Canada M5S 3H8 5 Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, NJ USA Schoo of Physics and Astronomy, Cardiff University, The Parade, Cardiff, Waes, UK CF24 3AA 7 Departamento de Astronomía y Astrofísica, Facutad de Física, Pontificía Universidad Catóica, Casia 306, Santiago 22, Chie 8 Department of Physics and Astronomy, University of British Coumbia, Vancouver, BC, Canada V6T 1Z4 9 Department of Physics, University of Rome La Sapienza, Piazzae Ado Moro 5, I Rome, Itay 10 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA Code 553/665, NASA/Goddard Space Fight Center, Greenbet, MD, USA Berkeey Center for Cosmoogica Physics, LBL and Department of Physics, University of Caifornia, Berkeey, CA, USA Department of Physics and Astronomy, University of Pennsyvania, 209 South 33rd Street, Phiadephia, PA, USA NIST Quantum Devices Group, 325 Broadway Maicode , Bouder, CO, USA Max Panck Institut für Astrophysik, Postfach 1317, D Garching bei München, Germany 16 Astrophysics and Cosmoogy Research Unit, Schoo of Mathematica Sciences, University of KwaZuu-Nata, Durban, 4041, South Africa 17 Centre for High Performance Computing, CSIR Campus, 15 Lower Hope St., Rosebank, Cape Town, South Africa 18 Department of Physics, University of Miami, Cora Gabes, FL, USA Instituto Naciona de Astrofísica, Óptica y Eectrónica (INAOE), Tonantzinta, Pueba, Mexico 20 KaviInstitute forparticeastrophysicsandcosmoogy, Stanford University, Stanford, CA, USA Pubished in Astrophys.J.739:52,2011 and arxiv: Work supported in part by US Department of Energy under contract DE-AC02-76SF00515.

2 2 J. Dunkey et a. 1. INTRODUCTION Measurements of anisotropies in the cosmic microwave background (CMB) have payed a centra roe in the deveopment of the current concordance cosmoogica mode (e.g., Smoot et a. 1992; Mier et a. 1999; de Bernardis et a. 2000; Hanany et a. 2000; Sperge et a. 2003). The ΛCDM mode describes a fat universe with 5% norma matter, 23% dark matter, 72% dark energy, and power-aw Gaussian primordia fuctuations consistent with simpe infationary modes (see e.g., Komatsu et a. 2010). Its parameters have been measured to a few percent eve accuracy, using CMB data from the WMAP sateite and higher resoution experiments, combined with observations of arge scae structure and the oca expansion rate (Brown et a. 2009;Riess et a. 2009; Reid et a. 2010; Perciva et a. 2010; Larson et a. 2010; Komatsu et a. 2010). The mode fits a range of recent astronomica data incuding Type Ia supernova (Hicken et a. 2009; Kesser et a. 2009), gaaxy custer measurements (Vikhinin et a. 2009; Mantz et a. 2010b; Rozo et a. 2010) and gravitationa ensing observations (Massey et a. 2007; Fu et a. 2008; Schrabback et a. 2010; Suyu et a. 2010). The WMAP sateite has measured the CMB over the fu sky down to 0.2 resoution. Measurements at higher resoution have been made by a set of compementary baoon and ground-based experiments (e.g., Jones et a. 2006; Brown et a. 2009; Reichardt et a. 2009; Sievers et a. 2009). The Atacama Cosmoogy Teescope (ACT) now measures fuctuations on scaes from 0.4 to an arcminute. The signa observed in this anguar range is composed of the damped acoustic peaks of the primordia CMB signa (Sik 1968), subsequenty ensed by arge-scae structure, as we as point source emission and fuctuations due to the Sunyaev-Ze dovich (SZ) effect(sunyaev& Ze dovich 1970), in which CMB photons scatter off eectrons in the hot intra-custer and fiamentary inter-gaactic media. Limits on the SZ power spectrum have been reported from the ACBAR, CBI and SZA experiments (Reichardt et a. 2009; Sievers et a. 2009; Sharp et a. 2010), with a recent detection reported by the South Poe Teescope (SPT) (Lueker et a. 2009). The first power spectrum measurement from ACT (Fower et a. 2010) provided a imit on the SZ power 21 Department of Physics, Stanford University, Stanford, CA, USA Coumbia Astrophysics Laboratory, 550 W. 120th St. Mai Code 5247, New York, NY USA Institute for the Physics and Mathematics of the Universe, The University of Tokyo, Kashiwa, Chiba , Japan 24 Dept. of Physics and Astronomy, The Johns Hopkins University, 3400 N. Chares St., Batimore, MD Department of Physics, University of Toronto, 60 St. George Street, Toronto, ON, Canada M5S 1A7 26 Department of Physics and Astronomy, Haverford Coege, Haverford, PA, USA Institut de Ciencies de Cosmos (ICC), University of Barceona, Barceona 08028, Spain 28 Kavi Institute for Cosmoogica Physics, 5620 South Eis Ave., Chicago, IL, USA Department of Physics, West Chester University of Pennsyvania, West Chester, PA, USA Department of Physics, Carnegie Meon University, Pittsburgh, PA Harvard-Smithsonian Center for Astrophysics, Harvard University, Cambridge, MA, USA spectrum, as we as on the point source contribution. In this paper we present cosmoogica parameter constraints from power spectra estimated from the ACT 2008 observing season. We use the power spectrum to constrain a mode for the SZ and point source contribution in the ACT 148GHz and 218GHz data. We then combine the ACT 148GHz data with WMAP observations, and additiona cosmoogica distance measures, to constrain the ΛCDM mode and a set of extensions that have particuar effects at sma scaes. This is one of a set of papers on the ACT 2008 data in the southern sky: Swetz et a. (2010) describes the ACT experiment; Dunner et a. (2010) describes the observing strategy and the data; Hajian et a. (2010) describes the caibration to WMAP; Das et a. (2010) presents the power spectra measured at 148GHz and 218 GHz, and this paper estimates parameters from the power spectrum resuts. A high-significance SZ gaaxy custer cataog is presented in Marriage et a. (2010a), with muti-waveength observations described in Menanteau et a. (2010) and their cosmoogica interpretation in Sehga et a. (2010b). Marriage et a. (2010b) presents the 148GHz point source cataog. Hincks et a. (2009) and Fower et a. (2010) presented the first maps of custers and power spectra respectivey, from a preiminary version of these maps. Improved map-making and power spectrum estimates, with use of a arger area of sky, now aow us to pace new constraints on cosmoogica modes. The paper is structured as foows. In 2 we describe the ACT ikeihood and parameter estimation methodoogy. In 3 we present resuts on SZ and point source parameters from the sma-scae power spectra. In 4 we present constraints on a set of cosmoogica modes in combination with other cosmoogica data, and concude in METHODOLOGY This section describes the methods used to estimate parameters from the ACT power spectra. The power spectra, estimated from 296deg 2 of skyobservedin 2008, are described in Das et a. (2010), and detais of the experiment, data reduction and map-making are described in Swetz et a. (2010) and Dunner et a. (2010). We wi estimate two sets of parameters: primary and secondary. Primary parameters describe the cosmoogica mode from which a theoretica primary CMB power spectrum can be computed. Secondary parameters describe the additiona power from SZ fuctuations and foregrounds. We construct an ACT ikeihood function that returns the probabiity of the ACT data given some theoretica CMB power spectrum and a set of secondary parameters. Primary and secondary parameters are then estimated from ACT and additiona datasets using Markov Chain Monte Caro (MCMC) methods. The ACT ikeihood function is described in Section 2.1, and the MCMC methods in ACT Likeihood For maps of temperature fuctuations at 148 GHz and 218 GHz, three cross-spectra are estimated in bands in the range 500 < < for 148GHz, and 1500 < < for both the 218GHz and the GHz cross-spectrum (see Das et a. 2010). A ikeihood function is constructed to estimate parameters from these

3 ACT 2008 Parameters 3 spectra. The function returns the ikeihood of the data, p(d C CMB, Θ), given a theoretica ensed CMB spectrum, C CMB, and a set of secondary parameters describing the additiona sma-scae power, Θ. In this anaysis we consider two ikeihoods: the ikeihood, which returns the ikeihood of a three spectra given a mode, and the 148-ony ikeihood, which returns the ikeihood of just the 148GHz spectrum given a mode. The temperature fuctuations in the ACT maps are expected to be the sum of fuctuations from ensed CMB, therma and kinetic SZ, radio point sources, infrared point sources, and therma dust emission from the Gaaxy(seee.g.,Sehgaeta.2010a). Thesevaryasfunctions of frequency. The ensed CMB and the kinetic SZ are backbody emission, and so are constant as a function of frequency in thermodynamic units. The therma SZ emission has a known frequency dependence (Sunyaev & Ze dovich 1970) and has negigibe contribution at 218 GHz. The radio point sources emit synchrotron, and the IR sources emit thermay, so both can be modeed as foowing power aw emission in fux given a narrow enough frequency range. For frequency ν and direction ˆn the signa in the maps can be modeed in therma units as T(ν,ˆn) = T CMB (ˆn)+ T SZ (ν,ˆn)+ T fg (ν,ˆn), (1) with ensedcmb fuctuations T CMB (ˆn). The SZsigna is the sum of therma and kinetic components T SZ (ν,ˆn) = f(ν) f(ν 0 ) TtSZ 0 (ˆn)+ T ksz (ˆn), (2) where the factor f(ν) = 2 (x/2)/tanh(x/2), for x = hν/k B T CMB, converts the expected SZ emission from the Rayeigh-Jeans (RJ) imit to thermodynamic units, and T0 tsz is the expected signa at frequency ν 0. At 218 GHz there is negigibe therma SZ signa, with f(218) = 0. The point source and Gaactic components are modeed as T fg (ν,ˆn)= g(ν) g(ν 0 ) { T IR 0 ( ν ν 0 ) αd 2 ( ) αs 2 ν + T0 rad ν 0 ( ) } αg 2 ν + T0 Ga, (3) ν 0 assuming that the IR and radio source emission in antenna temperature, T IR,rad 0, scae with goba power aws α d 2 and α s 2, respectivey, where α is the index in fux units. The factor g(ν) = (e x 1) 2 /x 2 e x converts from antenna to CMB thermodynamic temperature at frequency ν. The factors are g = [1.71,3.02] for 148GHz and 218GHz. Power aw behavior is aso assumed for the Gaactic dust emission T0 Ga. This behavior is expected to be a goodapproximationbetween 148GHz and 218 GHz, but breaks down over arger frequency ranges. To compute the ikeihood one coud first estimate the CMB map, by subtracting off the foreground and SZ components. This is commony done in CMB anayses for subtracting Gaactic components (e.g., Bennett et a. 2003), and has aso been used for subtracting the IR point sources (Ha et a. 2010; Lueker et a. 2009). However, for the ACT frequencies and noise eves the radio sources cannot be negected, so a inear combination of the 148GHz and 218GHz maps wi not remove a the source contamination. Instead, we choose to construct a mode for the cross power spectra between frequency ν i and ν j, C ij = T (ν i ) T (ν j ), (4) where T is the Fourier transform of T(ˆn). For ACT anaysis we use a fat-sky approximation, described in Das et a. (2010). The individua components are assumed to be uncorreated, so the theoretica crossspectrum B th,ij is modeed from Eq. 1 as B th,ij = B CMB +B tsz,ij +B ksz,ij +B IR,ij +B rad,ij +B Ga,ij, (5) where B (+1)C /2π. The first term, B CMB, is the ensed primary CMB power spectrum and is the same at a frequencies. The therma SZ (tsz) power is modeed as B tsz,ij f(ν i ) = A tsz f(ν 0 ) f(ν j ) f(ν 0 ) BtSZ 0,, (6) where B0, tsz is a tempate power spectrum corresponding tothepredictedtszemissionatν 0 =148GHzforamode with σ 8 = 0.8, to be described in Section 2.1.2, and A tsz is an ampitude parameter. The kinetic SZ (ksz) power is modeed as B ksz,ij = A ksz B ksz 0,, (7) where B ksz 0, is a tempate spectrum for the predicted backbody ksz emission for a mode with σ 8 = 0.8, aso described in Section The tota SZ power is then given by B SZ,ij f(ν i ) f(ν j ) = A tsz f(ν 0 ) f(ν 0 ) BtSZ 0, +A ksz B0, ksz. (8) The infrared point sources are expected to be custered, and their power is modeed as B IR,ij = [ ( ) ] 2 A d +A c B0, cust g(ν i ) g(ν j ) 3000 g(ν 0 ) g(ν 0 ) ( ) αd 2 νi ν j (9) ν 0 ν 0 where A d and A c are the vaues of B3000 IR at 148GHz for Poisson and custered dust terms respectivey, assuming a normaized tempate spectrum B0, cust. This wi be described in Section This mode assumes the same spectra index for the custered and Poisson IR power. The radio sources are not expected to be significanty custered (see, e.g., Sharp et a. 2010; Ha et a. 2010), and so can be described by Poisson scae-free power, with ( ) 2 ( ) αs 2 B rad,ij g(ν i ) g(ν j ) νi ν j = A s, (10) 3000 g(ν 0 ) g(ν 0 ) ν 0 ν 0 with ampitude A s normaized at ν 0 =148GHz and = Though we have described the pivot frequency as ν 0 =148GHz for a components in Eqs. 6-10, in practice we use the band-centers for SZ, radio and dusty sources given in Tabe 4 of Swetz et a. (2010). The Gaactic emission, B Ga,ij, isexpectedtobe sub-dominantonact scaes, as demonstrated in Das et a. (2010) using the

4 4 J. Dunkey et a. FDS dust map (Finkbeiner et a. 1999) as a Gaactic dust tempate, so is negected in this anaysis. Given SZ and custered source tempates, aside from parameters constrained by B CMB, this mode has 7 free parameters: five ampitudes A tsz, A ksz, A d, A c, A s, and two spectra indices, α d, α s. As we wi describe in Sec 2.2.1, we impose priors on some of these and constrain others. We refer to these parameters as secondary parameters, to distinguish them from primary cosmoogica parameters describing the primordia fuctuations. In part of the anaysis we wi estimate parameters from the 148GHz spectrum aone. In this case i = j and ν i = ν 0. The mode in Eq. 5 then simpifies to +A tsz B tsz B th =BCMB 0, +A kszb0, ksz ( +(A s +A d ) 3000 This can be further simpified to ) 2 +A c B cust 0,. (11) ( ) 2 B th = B CMB +A SZ B0,+A SZ p +A c B0, cust, (12) 3000 where A p = A s + A d is the tota Poisson power at = 3000, and A SZ = A ksz = A tsz measures the tota SZ power, B0, SZ = BtSZ 0, +BkSZ 0,. This is the same parameterization considered in Fower et a. (2010), and has just three secondary parameters: A SZ, A p and A c. Using this mode, we can compute the theoretica spectra for a given set of secondary parameters Θ, and for a given theoretica CMB temperature power spectrum. The data power spectra are not measured at every mutipoe, so bandpower theoretica spectra are computed using C th,ij b = w ij b Cth,ij, where w ij b is the bandpowerwindow function in band b for cross-spectrum ij, described in Das et a. (2010). 1 The data power spectra have caibration uncertainties (to be described in Sec 2.1.1). To account for these uncertainties we incude two caibration parametersy(ν i ), foreachmapi,thatscaetheestimated data power spectra, Ĉ ij b, and their uncertainties, as C ij b = y(ν i)y(ν j )Ĉij b. (13) The ikeihood of the caibrated data is then given by 2nL = (Cb th C b ) T Σ 1 (Cb th C b )+ndetσ, (14) assuming Gaussian uncertainties on the measured bandpowers with covariance matrix Σ. For the ikeihood the mode and data vectors Cb th and C b contain three spectra, C b = [C 148,148 b,c 148,218 b,c 218,218 b ]. For the 148-ony ikeihood, C b = C 148,148 b. We use the data between 500 < < for the GHz autospectrum, but restrict the range to 1500 < < for the GHz and the GHz spectra. This range is chosen since for 148GHz at scaes arger than = 500 the signa cannot be accuratey separated from atmospheric noise, and for 218GHz the maps do not converge beow = 1500, described in Das et a. (2010). The bandpower covariance matrix Σ is described in the Appendix of Das et a. (2010), and incudes correations between the three spectra. Das et a. (2010) demonstrates with Monte-Caro simuations that the covariance is we modeed by a Gaussian distribution with negigibe correation between bands. 1 Here we use the notation w b for the bandpower window functions; Das et a. (2010) uses B b Caibration and beam uncertainty The ACT caibration is described in Hajian et a. (2010). The 148 GHz maps are caibrated using WMAP, resuting in a 2% map caibration error in temperature units, at effective = 700. The 218GHz maps are caibrated using observations of Uranus, with a 7% caibration error at = The two caibration errors have negigibe covariance, and are treated as independent errors. For anayses using 148GHz data aone we marginaize over the caibration uncertainty anayticay foowinggangaeta.(1996)andbrideeta.(2002). For joint anayses with the 148GHz and 218GHz data we expicity sampe the caibration parameters y(ν i ) with Gaussian priors of y(148) = 1.00 ± 0.02 and y(218) = 1.00 ± We check that the anaytic and numerica marginaization methods give the same resuts for 148 GHz. The beam window functions are described in Das et a. (2010), and are estimated using maps of Saturn. The maps are made with an independent pipeine to the initia ACT beam estimates made in Hincks et a. (2009), but produce consistent resuts. The uncertainties on the beam window functions are of order 0.7% for the 148GHz band and1.5%at 218GHz. Uncertainties in the measured beams are incorporated using a ikeihood approximation described in Appendix A; the magnitude of the derived uncertainties is consistent with Hincks et a. (2009) and the uncertainties used in the parameter estimation in Fower et a. (2010) SZ tempates The therma SZ tempate B tsz 0, describes the power from tsz temperature fuctuations from a custers, normaized for a universe with ampitude of matter fuctuations σ 8 = 0.8. There is uncertainty in the expected shape and ampitude of this signa, arising due to incompete knowedge of the detaied gas physics that affects the integrated pressure of the custers. Previous cosmoogica studies, e.g., the ACBAR and CBI experiments, have used tempates derived from hydrodynamica simuations (Bond et a. 2005). The anaysis for WMAP used the anaytic Komatsu-Sejak (K-S) spectrum derived from a hao mode (Komatsu & Sejak 2001). Recent studies for SPT have considered simuations and anaytic tempates from Sehga et a. (2010a) and Shaw et a. (2009). In this anaysis we consider four therma SZ tempates, from Sehga et a. (2010a), Trac, Bode, & Ostriker (2010), Battagia et a. (2010), and Shaw et a. (2010). Trac, Bode, & Ostriker (2010) constructed severa tempates by processing a dark matter simuation to incude gas in dark matter haos and in the fiamentary intergaactic medium. Their standard mode, which was first described in Sehga et a. (2010a), is referred to here as TBO-1. It is based on the gas mode in Bode, Ostriker, & Vikhinin (2009), with the hot gas modeed with a poytropic equation of state and in hydrostatic equiibrium, with star formation and feedback caibrated against observations of oca custers. This is the tempate considered in the ACT anaysis by Fower et a. (2010), and has a simiar ampitude and shape to the K-S spectrum. Recent state-of-the-art simuations described in

5 ACT 2008 Parameters 5 Battagia et a. (2010) have been used to predict the SZ spectrum (referred to as Battagia ). Fu hydrodynamica SPH simuations were made of arge scae cosmic structure, incuding radiative cooing, star formation, feedback from AGN and supernovae, and non-therma pressure support. The predicted spectrum has 2/3 the powercomparedtothetbo-1spectrumandismoreconsistent with SZ measurements from SPT (Lueker et a. 2009). It is aso compatibe with predictions made that AGN heating woud decrease the expected SZ power (Roychowdhury et a. 2005). These hydrodynamica simuations pre-date the SPT observations, but there have aso been recent deveopments in simuating and modeing the expected SZ effect in ight of the SPT resuts in Lueker et a. (2009), and motivated by recent observations of the intra-custer medium (see Trac, Bode, & Ostriker (2010) for a discussion). In a second mode described in Trac, Bode, & Ostriker (2010), the nontherma20 mode referred to here as TBO-2, there is 20% non-therma pressure support, with increased star formation and reduced feedback, which has the effect of owering the predicted SZ power. The Shaw mode, described in Shaw et a. (2010), takes an anaytic hao mode approach, assuming hydrostatic equiibrium and a poytropic equation of state, with star formation, feedback from supernova and AGN, and energy transfer from dark matter to gas during mergers. It incudes non-therma pressure support. The spectra from each of these modes are shown in Figure 1, with a modes normaized to σ 8 = 0.8. We study constraints on a four tempates. Apart from the TBO-1 tempate, ahavesimiarampitudes ofb µK 2 at = 3000, athough the modes have different amounts of star formation, feedback, and non-therma support. The shape and ampitude of the expected kinetic SZ power spectrum is highy uncertain. We use the ksz tempate described in Sehga et a. (2010a), aso shown in Figure 1. The corresponding tempate for the nontherma20 mode in Trac, Bode, & Ostriker (2010) has a simiar ampitude. It is aso consistent with predictions from second order perturbation theory(hernández- Monteagudo& Ho 2009). In this anaysis the contamination of the SZ signa by point sources is negected, which is shown in Lin et a. (2009) to be a good approximation for radio gaaxies. Lueker et a. (2009) show it is aso a good assumption for IR sources for the current eves of sensitivity Custered source tempates The shape and ampitude of the power spectrum of custered dusty gaaxies are not yet we characterized (Knox et a. 2001; Fernandez-Conde et a. 2008; Viero et a. 2009; Ha et a. 2010), athough there have been measurements made by Viero et a. (2009) from the BLAST experiment. In Fower et a. (2010) we adopted a simpe power aw mode, with B. In this anaysis we move beyond this simpe parameterization to consider two aternative mode tempates. The first, Src-1, is obtained from the infrared source mode described in Section of Sehga et a. (2010a). This mode assumes that the IR emission traces star formation in haos at z < 3, and that the number of IR gaaxies in a given hao is proportiona to its mass. For the spectra energy distribution (SED) of the gaaxies, the mode uses an ef- Fig. 1. Therma SZ tempates for four different modes considered in this anaysis, and a singe ksz tempate, normaized at 148GHz for cosmoogies with σ 8 = 0.8. The TBO-1 tempate is from Sehga et a. (2010a), described further in Trac, Bode, & Ostriker (2010) together with TBO-2, derived from N-body simuations. The Battagia mode is derived from hydrodynamic SPH simuations (Battagia et a. 2010). The Shaw mode is based on an anaytic hao mode (Shaw et a. 2010). The ksz tempate is the kinetic SZ tempate in Sehga et a. (2010a). Two custered IR source tempates considered ( Src-1 and Src-2 ) are described in Sec and normaized at = The IR source curves are mutipied by ten for carity. fective graybody aw in which the dust temperature is a function of the CMB temperature, but its vaue at z = 0 is a free parameter. The dust emissivity spectra index and the typica IR uminosity and characteristic masses of the haos hosting IR gaaxies are free parameters of the mode. The mode incudes ony the two-hao power spectrum given in Eq. 24 of Sehga et a. (2010a), with contributions from pairs of gaaxies in different haos. The parameters of the mode have been updated from Sehga et a. (2010a) to better fit the observed BLAST power spectra at µm. 2 This updated tempate is shown in Figure 1, normaized to unity at = The shape is simiar to the custered mode used in the SPT anaysis by Ha et a. (2010), peaking at We aso consider the effect on our resuts of using an aternative tempate, Src-2, that has both one-hao and two-hao power, foowing a hao mode prescription simiar to Viero et a. (2009). Dark matter haos are popuated using gaaxy source counts from the source mode presented in Lagache, Doe, & Puget (2003), and hao occupation distribution parameters are tuned to fit the BLAST power spectra. This normaized tempate is aso showninfigure1. Atargescaesthishasasimiarshape to the Src-1 tempate, but at sma scaes tends approximatey to the B scaing adopted in Fower et a. (2010), which was motivated by observations of gaaxy custering at sma anges with typica correation function C(θ) θ 0.8 (Peebes 1980). The two tempates differ at > 3000, but at these anguar scaes the Poisson power is expected to dominate over the custering term Likeihood prescription 2 The updated parametersare β = 1.4, T 0 = 25.5, M 1 = , M 2 = , M coo = , L = , with definitions in Sehga et a. (2010a).

6 6 J. Dunkey et a. To summarize the methods, an anaysis with the ikeihood foows these steps to return the ACT ikeihood for a given mode: Seect primary cosmoogica parameters, and compute a theoretica ensed CMB power spectrum B CMB using the CAMB numerica Botzmann code (Lewis et a. 2000). Seect vaues for secondary parameters Θ = {A tsz, A ksz, A d, A c, A s, α d, α s }, and compute the tota theoretica power spectra B th,ij for , and using Eq. 5. Compute the bandpower theoretica power spectra C th,ij b = w ij b Cth,ij. Seect vaues for the caibration factors for 148 GHz and 218 GHz, and compute the ikeihood using Eq. 14 for 500 < < for and 1500 < < for and Add the ikeihood term due to beam uncertainty, described in Appendix A. Aargepartofouranaysisusesonythe148GHzspectrum. An anaysis done with this 148-ony ikeihood foows these steps: Seect primary cosmoogica parameters, and compute a theoretica ensed CMB power spectrum using CAMB. B CMB Seect vaues for secondary parameters Θ = {A SZ, A p, A c } and compute the tota theoretica power spectrum B th at 148GHz using Eq. 5. Compute the bandpower theoretica power spectrum Cb th = w b C th. Compute the ikeihood using Eq. 14 for 500 < < for 148GHz. Add the ikeihood term due to beam uncertainty, described in Appendix A, and anayticay marginaize over the caibration uncertainty Parameter estimation methods We use the ACT ikeihood for two separate parameter investigations. The first uses the ikeihood to constrain the secondary parameters, as our initia goa is to characterize the sma-scae behavior, and investigate whether this simpe mode sufficienty describes the observed emission. The second uses the 148-ony ikeihood to constrain primary and secondary parameters Secondary parameters from 148 and 218 GHz For most of the investigation with the ikeihood we fix the primary cosmoogica parameters to the best-fit ΛCDM parameters estimated from WMAP, as our goa is to characterize the sma-scae power observed by ACT, and check the goodness of fit of this simpe mode. To map out the probabiity distribution for these parameters we use an MCMC method. This uses the Metropois agorithm to sampe parameters (Metropois et a. 1953), foowing the methodoogy described in Dunkey et a. (2005). There are seven possibe secondary parameters, but we donotaowthematovaryfreey. Theradiosourcesdetected at 148 GHz, described in Marriage et a. (2010b), are observed to have typica spectra index S(ν) ν 0.5 in fux units. By fitting a scaed source mode from Toffoatti et a. (1998) to the detected sources, and using it to extrapoate to fainter sources, Marriage et a. (2010b) predict a residua radio source power of C = 2.8±0.3 nk 2. Converting units, we use these measurements to impose a Gaussian prior of A s = 4.0±0.4 µk 2, and we fix α s = 0.5. We aso fix A ksz = A tsz, as the ksz component is subdominant at 148GHz and the SZ modes predict them to be the same for a given cosmoogy. The other parameters (A tsz, A d, A c, and α d ) have uniform priors with positivity imposed on the ampitudes. Parameter resuts are quoted using the means and 68% confidence imits of the marginaized distributions, with 95% upper or ower imits given when the distribution is one-taied. We aso quote derived parameters to indicate the power in different components at 148GHz and 218GHz, for exampe the tota power in SZ at = 3000, B3000 SZ (B ksz +B tsz ) Parameters from 148 GHz In order to expore the probabiity distributions for a set of cosmoogica modes, we use the 148-ony ikeihood for parameter estimation. The focus is on using the 1000 < < 3000 spectrum to improve constraints on primary cosmoogica parameters. It is important that the SZ and foregound contribution be marginaized over, but we excude the more contaminated 218 GHz data given the current uncertainties in the foreground mode. To map out the distribution for cosmoogica parameters we use MCMC methods to expore the probabiity distributions for various cosmoogica modes. We parameterize cosmoogica modes using {Ω b h 2,Ω c h 2,Ω Λ, 2 R,n s,τ}. (15) These are the basic ΛCDM parameters, describing a fat universe with baryon density Ω b h 2, cod dark matter (CDM) density Ω c h 2, and a cosmoogica constant Ω Λ. Primordia perturbations are assumed to be scaar, adiabatic, and Gaussian, described by a power-aw with spectra tit n s, and ampitude 2 R, defined at pivot scae k 0 = 0.002/Mpc. We assume instantaneous reionization, where the universe transitions from neutra to ionized overaredshift range z = 0.5, with optica depth τ. Reionization ikey takes pace more sowy (e.g., Gnedin 2000; Trac et a. 2008), but current CMB measurements are insensitive to this choice (Larson et a. 2010). We aso consider an additiona set of primary parameters {dn s /dnk,r,n eff,y P,Gµ}, (16) that describe primordia perturbations with a running scaar spectra index dn s /dnk, a tensor contribution with tensor-to-scaar ratio r, a varying number of reativistic species N eff, varying primordia Heium fraction Y P, and cosmic strings with tension Gµ, using the Nambu string tempate described in Battye & Moss (2010). These parameters are added individuay to the ΛCDM mode in order to ook for possibe deviations from the concordance cosmoogy. Apart from Gµ these parameters a take uniform priors, with positivity priors on r, N eff, and Y P. The tensor spectra index is fixed at

7 ACT 2008 Parameters 7 Fig. 2. The anguar power spectrum measured by ACT at 148GHz and 218GHz (Das et a. 2010), with the theoretica mode for CMB, SZ, and point sources best-fit to the three spectra. The ensed CMB corresponds to the ΛCDM mode with parameters derived from WMAP (Komatsu et a. 2010). It dominates at arge scaes, but fas exponentiay due to Sik damping. The majority of power at > 3000 comes from extragaactic point sources beow a 20 mjy fux cut after masking. The radio sources are sub-dominant, and are constrained by a source mode fit to detected sources at 148GHz (Marriage et a. 2010b). The infrared source emission, assumed to foow a power aw, is dominated by Poisson power at sma scae, but about 1/3 of the IR power at = 3000 is attributed to custered source emission, assuming a tempate described in the text. The best-fit SZ (therma and kinetic) contribution at 148 GHz (assuming the TBO-1 tempate, Sehga et a. (2010a)) is 7µK 2 at = 3000; the subdominant kinetic SZ aso contributes at 218GHz. The data spectra and errors have been scaed by best-fit caibration factors of , and for the , , and spectra respectivey. n t = r/8, andboth theindex andratioaredefinedasin e.g., Komatsu et a. (2009). The CMB power spectrum from cosmic strings is expected to scae as (Gµ) 2, so we foow Sievers et a. (2009) and Battye & Moss (2010) by parameterizing the string power using q str (Gµ) 2. Limits on Gµ are then derived from q str. We generate the ensed theoretica CMB spectra using CAMB 3, and for computationa efficiency set the CMB to zero above = 4000 where the contribution is subdominant, ess than 5% of the tota power. To use the 148-ony ACT ikeihood there are three secondary parameters, A SZ,A p, and A c. For this part of the anaysis we use the TBO-1 and Src-1 SZ and custered source tempates, checking the effect on the primary parameters of substituting aternative tempates. We aso impose positivity priors on these parameters. We do not use any information expicity from the 218 GHz spectrum in this part of the anaysis, using just the 148- ony ikeihood, athough resuts are checked using the ikeihood. The ACT ikeihood is combined with the seven-year WMAP data and other cosmoogica data sets. We use the MCMC code and methodoogy described in Appendix C of Dunkey et a. (2009), with the convergence test described in Dunkey et a. (2005). A subset of resuts are cross-checked against the pubicy avaiabe CosmoMC code. To pace constraints on cosmoogica parameters we use the 7-year WMAP data in combination with ACT, using the WMAP ikeihood package v4.1 described in Larson eta.(2010). WMAPmeasurestheCMBoverthefusky to 0.2 scaes. A WMAP-ony resuts shown for comparison use MCMC chains from LAMBDA 4, described in Larson et a. (2010). We foow the methodoogy described in Komatsu et a. (2010) to consider the addition of distance measurements from astrophysica observations, on the anguar diameter distances measured from Baryon Acoustic Osciations (BAO) at z = 0.2 and 0.35, and on the Hubbe constant. The Gaussian priors on the distance ratios, r s /D V (z = 0.2) = ± andr s /D V (z = 0.35) = ±0.0036,arederivedfrom measurements from the Two-Degree Fied Gaaxy Redshift Survey (2dFGRS) and the Soan Digita Sky Survey Data Reease 7 (SDSS DR7), using a combined anaysis ofthe twodata-setsbypercivaeta.(2010). Theparameter r s is the comoving sound horizon size at the baryon drag epoch, and D V (z) [(1 + z) 2 D 2 A (z)cz/h(z)]1/3 is the effective distance measure for anguar diameter distance D A, and Hubbe parameter H(z). The inverse covariance matrix is given by Eq. 5 of Perciva et a. (2010). The Gaussian prior on the Hubbe con- 3 Version Feb 2010, with Recfast

8 8 J. Dunkey et a. TABLE 1 Parameters describing SZ and extragaactic source mode at 148GHz and 218GHz Parameter a GHz 148GHz -ony A tsz b 0.62±0.26 < 0.77 (95% CL) A d (µk 2 ) 7.8± ±1.9 A c (µk 2 ) 4.6±0.9 < 7.4 (95% CL) A s (µk 2 ) c 4.1± ±0.4 α d d 3.69±0.14 χ 2 /dof 78/106 29/46 a The ksz and tsz coefficients are setequa, A ksz = A tsz. A d, A c and A s are the B 3000 power for Poisson infrared gaaxies, custered infrared gaaxies, and Poisson radio gaaxies at 148GHz respectivey. The ΛCDM parameters are not varied here. b For the TBO-1 tempate. See Tabe 2 for other tempates and conversion to SZ power. c A Gaussian prior A s = 4.0±0.4 is imposed, and index α s = 0.5 assumed. d The 148GHz-ony data cannot constrain the IR point source index α d. stant, H 0 = 74.2 ± 3.6 km s 1 Mpc 1, comes from the magnitude-redshift reation from HST observations of 240 ow-z Type Ia supernovae at z < 0.1 by Riess et a. (2009). The error incudes both statistica and systematic errors. 3. HIGH-ELL SZ AND POINT SOURCE MODEL In this section we determine the goodness of fit of the SZandpoint sourcemodedescribedin Section2.1tothe ACT 148GHz and 218GHz power spectra, and estimate its parameters. This uses the ikeihood summarized in Sec 2.1.4, initiay hoding the ΛCDM mode fixed to the primary CMB with parameters given in Komatsu et a. (2010). The best-fit mode is a good fit to the three ACT power spectra over the fu anguar range 500 < < (χ 2 = 78 for 106 degrees of freedom), with constraints on parameters given in Tabe 1 for the TBO-1 SZ tempate and Src-1 source tempate. The spectra are shown in Figure 2, with the estimated components indicated at each frequency. The mean caibration factors, defined in Eq. 13, are 1.02 and 1.09 for 148GHz and 218 GHz respectivey. These are consistent with the expected vaues at the 1-1.2σ eve. The best-fitting 1.09 factor is driven by the < 2500 part of the cross-spectrum, where the primary CMB dominates. At = 3000, about haf the power at 148GHz is from the primary CMB (27 out of 50 µk 2 ), with the remainder divided among SZ, IR Poisson and custered power, and radio Poisson power (4-8 µk 2 in each component). At 218GHz, ony about 15% of the power comes from the primary CMB at = 3000 (27 out of 170 µk 2 ). Haf of the power is attributed to Poisson IR sources, the remaining approximatey 35% to power from custered IR sources. The mode fits the cross-spectrum, indicating that a simiar popuation of gaaxies is contributing at both frequencies Constraints on SZ power Using the muti-frequency spectra, power from SZ fuctuations is detected at more than 95% CL, with estimated A tsz for each tempate (TBO-1, TBO-2, Battagia, and Shaw) given in Tabe 2 and shown in Figure 3, marginaized over point source parameters. The estimated SZ power at = 3000 is robust to varying the SZ tempate, with tota SZ power (tsz pus ksz) esti- TABLE 2 Constraints on SZ emission Tempate a A b tsz B3000 SZ σ SZ,7 8 σ SZ,9 8 (µk 2 ) 0.8 (A 1/7 tsz ) 0.8 (A1/9 tsz ) TBO ± ± ± ±0.04 TBO ± ± ± ±0.04 Battagia 0.85 ± ± ± ± 0.04 Shaw 0.87± ± ± ±0.04 a Tempates are from Sehga et a. (2010a), Trac, Bode, & Ostriker (2010), Battagia et a. (2010), and Shaw et a. (2010). b We required A ksz = A tsz, as defined in Eqs c Tota tsz and ksz power at 148GHz, as defined in Eq. 8. Fig. 3. One-dimensiona marginaized distributions for the estimated therma SZ power in the ACT power spectra. There is evidence at the 95% CL eve for non-zero SZ power. The vaue A tsz = 1 corresponds to the predicted therma SZ ampitude in a universe with σ 8 = 0.8. The four curves correspond to the four SZ tempates shown in Figure 1; the TBO-1 tempate resuts in a ower vaue, athough a are consistent with A tsz = 1 at the 95% CL. The tota SZ power (incuding ksz) at 148GHz and = 3000 for a the tempates is consistent, with (+1)C SZ /2π = 7±3 µk 2. mated to be B3000 SZ = 6.8±2.9 µk 2. (17) The estimated tempate ampitude, A tsz, varies from 0.62±0.26for the TBO-1 tempate, to 0.96±0.43for the TBO-2 tempate. Note that A ksz is fixed equa to A tsz in these cases, with ampitudes defined in Eqs For the TBO-1 tempate, the mean ampitude is ower than expected for a universe with σ 8 = 0.8 (A tsz = 1), but not significanty. This is consistent with observations by SPT (Lueker et a. 2009), and is an improvement over the initia estimate of A tsz < 1.6 at 95% CL from the ACT power spectrum presented in Fower et a. (2010). Assuming that σ 8 is within the imits estimated fromprimary CMB data, e.g. from Komatsu et a. (2010), the ampitude is somewhat more consistent for the TBO-2, Battagia, and Shaw tempates, that incude more detaied gas physics, with A tsz = 1 within the 68% CL for these tempates. In a these cases we have hed the primary CMB parameters fixed. For a singe test case we marginaize over the 6 primary ΛCDM parameters in addition to the secondary parameters. This marginaization resuts in an increase in the mean vaue of B3000 SZ of

9 ACT 2008 Parameters 9 Fig. 4. Marginaized distributions (68% and 95% CL) for parameters describing the SZ and point source emission in the ACT power spectra. Left and center: The degeneracies between the tota SZ power, B SZ (+1)C SZ, and the infrared point source power, B IR, at 148GHz and = 3000 (soid unfied contours), are broken with the addition of 218GHz data (soid fied contours). Both the Poisson and custered IR power are shown, for two different custered source tempates (soid and dashed contours). A custered source component is required to fit the muti-frequency data at 5σ significance. Right: The Poisson dust power and the index α d = 3.69 ± 0.14 (power aw in fux between 148 GHz and 218 GHz, and unconstrained from 148 GHz aone) are anti-correated; the index indicates a dust emissivity of β µk 2 (a 0.2σ change), but a negigibe increase in the uncertainty. The number of custers, and therefore the expected SZ power, is a strong function of the ampitude of matter fuctuations, quantified by σ 8 (Komatsu & Kitayama 1999). In our mode we scae the SZ tempates by an overa ampitude, and woud ike to infer an estimate for σ 8 from A tsz. In Fower et a. (2010) we assumed a seventh power scaing, with A tsz σ8 7 (Komatsu & Sejak 2002),givingan upper imit ofσ8 SZ < 0.84at 95%CL, for A tsz < 1.6. However, the exact scaing of the shape and ampitude with cosmoogy, and in particuar with σ 8, is mode dependent and not precisey known (Lueker et a. 2009; Battagia et a. 2010; Trac et a. 2010). For the TBO tempates the combined tsz and ksz signa scaes cose to the 7th power, with the tsz varying approximatey as the 8th power (Trac, Bode, & Ostriker 2010). To bound the possibe range we compute two imits, assuming the tsz part of the tempate varies as either σ8 7 or σ8 9. The estimated vaues for σsz 8 in these cases are given in Tabe 2. No detections have yet been made of the kinetic SZ power spectrum. From SPT observations a 95% upper imit on B3000 ksz of 13µK 2 was estimated (Ha et a. 2010). If we aow the ksz ampitude to be varied independenty ofthe therma SZ ampitude, we find an upper imit from the ACT data on the kinetic SZ contribution of B ksz 3000 < 8µK2 (95% CL). (18) This is consistent with predictions by Iiev et a.(2008) of a 2µK 2 Ostriker-Vishniac signa at = 3000 and a 3µK 2 post-reionization ksz signa, but woud excude modes with higher eves of ksz from patchy reionization. The estimated SZ power is a sma signa, ess than 10 µk 2, and is correated with other parameters. We therefore investigate the dependence of the constraint on the priors imposed on other parameters. The SZ power is not strongy correated with the IR point source parameters when the 218GHz data are incuded, as shown in Figure 4, and so using the Src-2 custered source tempate in pace of Src-1 has a negigibe effect. There is some correation with the radio source power, as this term aso contributes predominanty at 148 GHz. Changing the radio index to α s = 0 has itte effect, but broadening the radiopriorto A s = 4±2 does reduce the significance of the SZ detection to 0.48±0.27 using the TBO-1 tempate; the SZ is anti-correated with the radio power, and reaxing the prior aows a arger radio component at 148GHz. This indicates the importance of the radio source characterization in Marriage et a. (2010b) for estimating the SZ power at 148GHz. A modest increase in the prior to A s = 4±0.8 has a negigibe effect. If we restrict the anaysis to 148GHz aone we find consistent resuts, with B3000 SZ < 7.8 µk2 at 95% CL. The best-fit mode has χ 2 = 29 for 46 degrees of freedom. In this case we cannot distinguish between the SZ and custered source components; the joint constraint shown in Figure 4 shows that simiar = 3000 power imits are paced on both components; marginaizing over a custered term has itte effect on the estimated SZ ampitude. The mean IR Poisson term is higher in this case, as there are more modes fitting the 148GHz data aone with ow SZ and custered source power. The mutifrequency information then breaks this degenerecy and more tighty constrains the Poisson power Unresoved point source emission The power spectrum measures fuctuations due to point sources beow a fux cut of approximatey 20 mjy. This is not an exact imit since the point source mask is constructed from sources with signa-to-noise ratio greater than 5 (Marriage et a. 2010b). The point source power observed at 148GHz and 218GHz has both synchrotron emission from radio gaaxies, and IR emission from dusty gaaxies. At 148 GHz the point source power, after remova of 5σ sources, is inferred to be spit in ratio roughy 1:2 between radio and IR gaaxies. Since we impose a prior on the residua radio power from Marriage et a. (2010b), we do not earn new information about this component from the power spectrum. At 218 GHz the point source power is dominated by IR dust emis-

10 10 J. Dunkey et a. Fig. 5. The power spectrum measured by ACT at 148GHz, scaed by 4, over the range dominated by primordia CMB ( < 3000). The spectrum is consistent with the WMAP power spectrum over the scaes 500 < < 1000, and gives a measure of the third to seventh acoustic peaks. The best-fit ΛCDM cosmoogica mode is shown, and is a good fit to the two datasets. At > 2000 the contribution from point soures and SZ becomes significant (dashed shows the tota best-fit theoretica spectrum; soid is ensed CMB). Three additiona theoretica modes for the primordia CMB are shown with N eff =10 reativistic species, 4 He fraction Y p = 0.5, and running of the spectra index dn s/dnk = They are consistent with WMAP but are excuded at east at the 95% eve by the ACT data. TABLE 3 Derived constraints on unresoved IR source emission a 148 GHz 218 GHz Poisson B 3000 (µk 2 ) b 7.8±0.7±0.7 90±5±10 C (nk 2 ) 5.5±0.5± ±3±6 C (Jy 2 sr 1 ) 0.85±0.08± ±0.7±1.8 Custered B 3000 (µk 2 ) c 4.6±0.9±0.6 54±12 ±5 Tota IR B 3000 (µk 2 ) 12.5± ±13 a The two errors indicate statistica uncertainty and a systematic error due to custered tempate uncertainty. b Equivaent to the parameter A d for 148GHz. c Equivaent to the parameter A c for 148GHz. sion. The IR Poisson power is estimated to be A d = 7.8±0.7µK 2, with derived Poisson IR power at 148GHz and 218GHz given in Tabe 3. A custered component is required to fit the data, with A c = 4.6±0.9 µk 2, corresponding to power at 218GHz of B = 54±12 µk2. A mode with no custered component has a poorer fit to the data by χ 2 = 28, indicating a detection of custering at the 5σ eve. It is the 218GHz power spectrum that provides this detection; the 148GHz spectrum is consistent with no custered component. In fux units, the effective index of unresoved IR emission is α d = 3.69±0.14 (19) between 148GHz and 218GHz, where S(ν) ν α. The dust index and Poisson ampitude are anti-correated, shown in Figure 4. This index estimate agrees with observations by SPT, who find α = 3.9±0.3 for the Poisson component, and 3.8 ± 1.2 for the custered component over the same frequency range (Ha et a. 2010). A property that can be derived from the effective index, α, is the dust emissivity index, β. For gaaxies at redshift z = 0 the dust emission can be described by a modified backbody, S(ν) ν β B ν (T d ), for dust temperature T d. In the Rayeigh-Jeans (RJ) imit the fux then approximates to S(ν) ν β+2 T d, with β = α 2. Using this reation gives a dust emissivity index measured by ACT of β = 1.7 ± 0.14, consistent with modes (e.g., Draine 2003). However, the RJ imit is not expected to be as good an approximation for redshifted graybodies (e.g., Ha et a. 2010), adding an uncertainty to β of up to 0.5. This shoud aso be considered an effective index, given the ikey temperature variation within each gaaxy. We test the dependence of these constraints on choices made in the ikeihood, using the same set of tests described in Sec 3.1. The estimated IR source parameters do not depend strongy on the SZ tempate chosen, with ess than 0.1σ change if we use the Battagia or TBO-1 SZ tempate. If the radio source index is set to α s = 0 insteadof 0.5thereisa 0.3σ reductionintheirpoisson source power at 148GHz, and a 0.2σ increase in the spectra index. As found in Sec 3.1, if the radio source