The Atacama Cosmology Telescope: likelihood for small-scale CMB data

The Atacama Cosmology Telescope has measured the angular power spectra of microwave fluctuations to arcminute scales at frequencies of 148 and 218 GHz, from three seasons of data. At small scales the fluctuations in the primordial Cosmic Microwave Background (CMB) become increasingly obscured by extragalactic foregounds and secondary CMB signals. We present results from a nine-parameter model describing these secondary effects, including the thermal and kinematic Sunyaev-Zel'dovich (tSZ and kSZ) power; the clustered and Poisson-like power from Cosmic Infrared Background (CIB) sources, and their frequency scaling; the tSZ-CIB correlation coefficient; the extragalactic radio source power; and thermal dust emission from Galactic cirrus in two different regions of the sky. In order to extract cosmological parameters, we describe a likelihood function for the ACT data, fitting this model to the multi-frequency spectra in the multipole range 500 < l < 10000. We extend the likelihood to include spectra from the South Pole Telescope at frequencies of 95, 150, and 220 GHz. Accounting for different radio source levels and Galactic cirrus emission, the same model provides an excellent fit to both datasets simultaneously, with χ2/dof= 675/697 for ACT, and 96/107 for SPT. We then use the multi-frequency likelihood to estimate the CMB power spectrum from ACT in bandpowers, marginalizing over the secondary parameters. This provides a simplified `CMB-only' likelihood in the range 500 < l < 3500 for use in cosmological parameter estimation.

[1]  Edward J. Wollack,et al.  First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters , 2003, astro-ph/0302209.

[2]  H. Trac,et al.  REIONIZATION ON LARGE SCALES. III. PREDICTIONS FOR LOW-ℓ COSMIC MICROWAVE BACKGROUND POLARIZATION AND HIGH-ℓ KINETIC SUNYAEV–ZEL'DOVICH OBSERVABLES , 2012, 1211.2832.

[3]  Edward J. Wollack,et al.  THE ATACAMA COSMOLOGY TELESCOPE: EXTRAGALACTIC SOURCES AT 148 GHz IN THE 2008 SURVEY , 2010, 1007.5256.

[4]  Guilaine Lagache,et al.  IRIS : A NEW GENERATION OF IRAS MAPS , 2005 .

[5]  The Atacama Cosmology Telescope: Calibration with WMAP Using Cross-Correlations , 2010, 1009.0777.

[6]  D. Spergel,et al.  The kinetic Sunyaev–Zel’dovich signal from inhomogeneous reionization: a parameter space study , 2011, 1112.1820.

[7]  J. R. Bond,et al.  Cosmological Results from Five Years of 30 GHz CMB Intensity Measurements with the Cosmic Background Imager , 2009, 0901.4540.

[8]  J. Richard Bond,et al.  Cosmic microwave background snapshots: pre-WMAP and post-WMAP , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Jeremiah P. Ostriker,et al.  Generation of microwave background fluctuations from nonlinear perturbations at the era of galaxy formation , 1986 .

[10]  M. Halpern,et al.  First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: The Angular Power Spectrum , 2003, astro-ph/0302217.

[11]  Benjamin D. Wandelt,et al.  Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling , 2004 .

[12]  R. B. Barreiro,et al.  Planck early results. XVIII. The power spectrum of cosmic infrared background anisotropies , 2011, 1101.2028.

[13]  Satoshi Nozawa,et al.  Relativistic corrections to the Sunyaev-Zel'dovich effects for clusters of galaxies , 1999 .

[14]  O. Zahn,et al.  SHARPENING THE PRECISION OF THE SUNYAEV–ZEL'DOVICH POWER SPECTRUM , 2009, 0903.5322.

[15]  A. Lewis,et al.  Cosmic Microwave Background and Inflation Parameters , 2004, astro-ph/0406195.

[16]  Self-regulated reionization , 2006, astro-ph/0607517.

[17]  Edward J. Wollack,et al.  POWER-LAW TEMPLATE FOR INFRARED POINT-SOURCE CLUSTERING , 2011, 1108.4614.

[18]  W. B. Burton,et al.  TENTATIVE DETECTION OF A COSMIC FAR-INFRARED BACKGROUND WITH COBE , 1996 .

[19]  Edward J. Wollack,et al.  OVERVIEW OF THE ATACAMA COSMOLOGY TELESCOPE: RECEIVER, INSTRUMENTATION, AND TELESCOPE SYSTEMS , 2011 .

[20]  J. R. Bond,et al.  Accepted for publication in The Astrophysical Journal Preprint typeset using L ATEX style emulateapj v. 3/3/03 COSMOLOGICAL PARAMETERS FROM COSMIC BACKGROUND IMAGER OBSERVATIONS AND COMPARISONS WITH BOOMERANG, DASI, AND MAXIMA , 2003 .

[21]  M. Lueker,et al.  A MEASUREMENT OF THE COSMIC MICROWAVE BACKGROUND DAMPING TAIL FROM THE 2500-SQUARE-DEGREE SPT-SZ SURVEY , 2012, 1210.7231.

[22]  Uros Seljak,et al.  The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters , 2002 .

[23]  G. Lagache,et al.  Implications of the cosmic infrared background for light production and the star formation history in the Universe , 2000 .

[24]  C. H. Anderson,et al.  Application of Monte Carlo Algorithms to the Bayesian Analysis of the Cosmic Microwave Background , 2002, astro-ph/0209560.

[25]  A. Hu,et al.  Secondary Cosmic Microwave Background Anisotropies in a Universe Reionized in Patches , 1998, astro-ph/9803188.

[26]  M. Halpern,et al.  FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: LIKELIHOODS AND PARAMETERS FROM THE WMAP DATA , 2008, 0803.0586.

[27]  Edward J. Wollack,et al.  FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION , 2008, 0803.0547.

[28]  H. Trac,et al.  TEMPLATES FOR THE SUNYAEV–ZEL’DOVICH ANGULAR POWER SPECTRUM , 2010, 1006.2828.

[29]  T. Rodet,et al.  Correlated Anisotropies in the Cosmic Far-Infrared Background Detected by the Multiband Imaging Photometer for Spitzer: Constraint on the Bias , 2007, 0707.2443.

[30]  Edward J. Wollack,et al.  THE ATACAMA COSMOLOGY TELESCOPE: COSMOLOGICAL PARAMETERS FROM THE 2008 POWER SPECTRUM , 2010, 1009.0866.

[31]  Jeremiah P. Ostriker,et al.  SIMULATIONS OF THE MICROWAVE SKY , 2009, 0908.0540.

[32]  Satoshi Nozawa,et al.  Relativistic corrections to the Sunyaev-Zel'dovich effects for clusters of galaxies , 1999 .

[33]  C. B. Netterfield,et al.  Planck early results - I. The Planck mission , 2011, 1101.2022.

[34]  M. Lueker,et al.  COSMIC MICROWAVE BACKGROUND CONSTRAINTS ON THE DURATION AND TIMING OF REIONIZATION FROM THE SOUTH POLE TELESCOPE , 2011, 1111.6386.

[35]  P. A. R. Ade,et al.  MEASUREMENTS OF SECONDARY COSMIC MICROWAVE BACKGROUND ANISOTROPIES WITH THE SOUTH POLE TELESCOPE , 2009, 0912.4317.

[36]  M. Lueker,et al.  A MEASUREMENT OF THE DAMPING TAIL OF THE COSMIC MICROWAVE BACKGROUND POWER SPECTRUM WITH THE SOUTH POLE TELESCOPE , 2011, 1105.3182.

[37]  G. Efstathiou,et al.  A Simple Empirically Motivated Template for the Unresolved Thermal Sunyaev-Zeldovich Effect , 2011, 1106.3208.

[38]  T. Cullen,et al.  Global existence of solutions for the relativistic Boltzmann equation on the flat Robertson-Walker space-time for arbitrarily large intial data , 2005, gr-qc/0507035.

[39]  D. Nagai,et al.  IMPACT OF CLUSTER PHYSICS ON THE SUNYAEV–ZEL'DOVICH POWER SPECTRUM , 2010, 1006.1945.

[40]  M. Halpern,et al.  FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: ANGULAR POWER SPECTRA , 2008, The Astrophysical Journal Supplement Series.

[41]  M. Halpern,et al.  Five-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Galactic Foreground Emission , 2008 .

[42]  J. R. Bond,et al.  ON THE CLUSTER PHYSICS OF SUNYAEV–ZEL'DOVICH AND X-RAY SURVEYS. II. DECONSTRUCTING THE THERMAL SZ POWER SPECTRUM , 2011, 1109.3711.

[43]  P. A. R. Ade,et al.  ANGULAR POWER SPECTRA OF THE MILLIMETER-WAVELENGTH BACKGROUND LIGHT FROM DUSTY STAR-FORMING GALAXIES WITH THE SOUTH POLE TELESCOPE , 2009, 0912.4315.

[44]  J. Silk.  COSMIC BLACK-BODY RADIATION AND GALAXY FORMATION. , 1968 .

[45]  Adrian T. Lee,et al.  EXTRAGALACTIC MILLIMETER-WAVE SOURCES IN SOUTH POLE TELESCOPE SURVEY DATA: SOURCE COUNTS, CATALOG, AND STATISTICS FOR AN 87 SQUARE-DEGREE FIELD , 2009, 0912.2338.

[46]  A. Lewis,et al.  Cosmological parameters from CMB and other data: A Monte Carlo approach , 2002, astro-ph/0205436.

[47]  M. Lueker,et al.  A MEASUREMENT OF SECONDARY COSMIC MICROWAVE BACKGROUND ANISOTROPIES WITH TWO YEARS OF SOUTH POLE TELESCOPE OBSERVATIONS , 2011, 1111.0932.

[48]  M. Dickinson,et al.  The Angular Clustering of Lyman-Break Galaxies at Redshift z ~ 3 , 1998, astro-ph/9802318.

[49]  Edward J. Wollack,et al.  THE ATACAMA COSMOLOGY TELESCOPE: CALIBRATION WITH THE WILKINSON MICROWAVE ANISOTROPY PROBE USING CROSS-CORRELATIONS , 2010, 1009.0777.

[50]  The angular correlation function of galaxies from POSS-II , 1991 .

[51]  Peter A. R. Ade,et al.  THE ATACAMA COSMOLOGY TELESCOPE: DATA CHARACTERIZATION AND MAPMAKING , 2012, 1208.0050.

[52]  Edward J. Wollack,et al.  SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: POWER SPECTRA AND WMAP-DERIVED PARAMETERS , 2010, 1001.4635.

[53]  THE KINETIC SUNYAEV-ZEL'DOVICH EFFECT FROM REIONIZATION , 2005, astro-ph/0504189.

[54]  J. R. Bond,et al.  Radical Compression of Cosmic Microwave Background Data , 2000 .

[55]  Daisuke Nagai,et al.  DECONSTRUCTING THE KINETIC SZ POWER SPECTRUM , 2011, 1109.0553.

[56]  P. A. R. Ade,et al.  THE ATACAMA COSMOLOGY TELESCOPE: A MEASUREMENT OF THE 600 < ℓ < 8000 COSMIC MICROWAVE BACKGROUND POWER SPECTRUM AT 148 GHz , 2010, 1001.2934.

[57]  Edward J. Wollack,et al.  OVERVIEW OF THE ATACAMA COSMOLOGY TELESCOPE: RECEIVER, INSTRUMENTATION, AND TELESCOPE SYSTEMS , 2010, 1007.0290.

[58]  James J. Bock,et al.  BLAST: CORRELATIONS IN THE COSMIC FAR-INFRARED BACKGROUND AT 250, 350, AND 500 μm REVEAL CLUSTERING OF STAR-FORMING GALAXIES , 2009, 0904.1200.

[59]  Peter A. R. Ade,et al.  THE ATACAMA COSMOLOGY TELESCOPE: A MEASUREMENT OF THE COSMIC MICROWAVE BACKGROUND POWER SPECTRUM AT 148 AND 218 GHz FROM THE 2008 SOUTHERN SURVEY , 2010, 1009.0847.

[60]  J. Dunkley,et al.  Modelling the correlation between the thermal Sunyaev Zel'dovich effect and the cosmic infrared background , 2012, 1204.5927.

[61]  P. A. R. Ade,et al.  IMPROVED CONSTRAINTS ON COSMIC MICROWAVE BACKGROUND SECONDARY ANISOTROPIES FROM THE COMPLETE 2008 SOUTH POLE TELESCOPE DATA , 2010, 1012.4788.

[62]  A. Melchiorri,et al.  Analytic marginalization over CMB calibration and beam uncertainty , 2002 .

[63]  J. Dunkley,et al.  Constraining thermal dust emission in distant galaxies with number counts and angular power spectra , 2012, 1210.6697.

[64]  A. Lewis,et al.  Efficient computation of CMB anisotropies in closed FRW models , 1999, astro-ph/9911177.

[65]  David J. Schlegel,et al.  Extrapolation of Galactic Dust Emission at 100 Microns to Cosmic Microwave Background Radiation Frequencies Using FIRAS , 1999, astro-ph/9905128.

[66]  V. Narayanan,et al.  The Angular Correlation Function of Galaxies from Early Sloan Digital Sky Survey Data , 2001, astro-ph/0107417.

[67]  Fast and reliable MCMC for cosmological parameter estimation , 2004, astro-ph/0405462.

[68]  Edward J. Wollack,et al.  CORRELATIONS IN THE (SUB)MILLIMETER BACKGROUND FROM ACT × BLAST , 2011, 1101.1517.

[69]  Amber D. Miller,et al.  A MEASUREMENT OF ARCMINUTE ANISOTROPY IN THE COSMIC MICROWAVE BACKGROUND WITH THE SUNYAEV–ZEL’DOVICH ARRAY , 2009, 0901.4342.

[70]  Y. Zeldovich,et al.  Small-scale fluctuations of relic radiation , 1970, Astrophysics and Space Science.

[71]  Calibration of Nonthermal Pressure in Global Dark Matter Simulations of Clusters of Galaxies , 2012, 1204.1762.

[72]  C. B. Netterfield,et al.  Planck early results. XIX. All-sky temperature and dust optical depth from Planck and IRAS. Constraints on the "dark gas" in our Galaxy , 2011, 1101.2029.

[73]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[74]  J. R. Bond,et al.  SIMULATIONS OF THE SUNYAEV–ZEL'DOVICH POWER SPECTRUM WITH ACTIVE GALACTIC NUCLEUS FEEDBACK , 2010, 1003.4256.