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

TL;DR

The paper develops a comprehensive multi-frequency likelihood for ACT small-scale CMB data that jointly models primary CMB and nine secondary components (tSZ, kSZ, CIB-P, CIB-C, tSZ-CIB, radio, and Galactic cirrus). It extends the framework to incorporate SPT data and, via Gibbs sampling, produces a CMB-only bandpower likelihood that marginalizes over foregrounds, enabling efficient cosmological parameter estimation while preserving information in the damping tail. The authors demonstrate excellent fits to ACT and SPT data, show consistency with the WMAP7 LCDM model, and provide a validated, compressed likelihood for use in broader cosmological analyses. The approach yields robust constraints on foregrounds and a practical pathway to integrate high-resolution CMB measurements into cosmological inference.

Abstract

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<ell<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 chi2/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<ell<3500 for use in cosmological parameter estimation.

Figures (12)

• Figure 1: Summary of small-scale mm-wave data measured by the Atacama Cosmology Telescope das/etal:prep and the South Pole Telescope keisler/etal:2011reichardt/etal:2012, in the angular range used for measuring the damping tail of the CMB. The ACT and SPT data are independently calibrated to WMAP. The vertical axis is $\ell^4 C_\ell$ instead of the conventional $\ell^2 C_\ell$ to highlight the features at these angular scales. The primary CMB signal corresponding to the best-fitting $\Lambda$CDM model sievers/etal:prep is indicated (dashed), together with the total signal at 148 GHz (red, lower solid curve) and 217 GHz (black, upper solid curve), including secondary effects from SZ and foregrounds. Modeling the secondary contributions from SZ and foregrounds is vital to allow extraction of the primordial signal at small scales.
• Figure 2: Regions of the sky used for ACT power spectra das/etal:prep in the Equatorial plane (ACT-E, 300 deg$^2$), and at -55$^\circ$ declination (ACT-S, 292 deg$^2$). The 800 deg$^2$ used for SPT power spectra keisler/etal:2011reichardt/etal:2012 is indicated, with 54 deg$^2$ overlap with ACT-S. The color scales with Galactic cirrus intensity finkbeiner/davis/schlegel:1999.
• Figure 3: Template power spectra for the thermal and kinetic Sunyaev-Zel'dovich effects battaglia/etal:2012battaglia/etal:2010, clustered CIB sources scaling as $\ell^{0.8}$addison/etal:2012, the cross-correlation between tSZ and CIB addison/dunkley/spergel:2012, and Galactic cirrus miville-deschenes/lagache:2005. They are normalized at $\ell=3000$ and 150 GHz, and the tSZ-CIB is shown for a perfectly correlated signal. Poisson CIB and radio source power (not shown) scale as $\ell^2$.
• Figure 4: (Top) Power spectra measured by ACT das/etal:prep at 148 and 218 GHz, and their cross-spectrum, coadded over ACT-E and ACT-S. We show the primary (lensed CMB in dotted black line) and secondary contributions (dotted lines) to the best-fitting model. (Bottom) Residual power in the ACT cross-frequency spectra, after subtracting the best-fitting model, at 148 (left), 148x218 (center), and 218 GHz (right). The errors at small scales are correlated due to beam uncertainty. The model is a good fit simultaneously to ACT-E and ACT-S, with no sigificant residual features.
• Figure 5: Distributions for secondary parameters from ACT and SPT, for best-fitting $\Lambda$CDM model. Parameters {$a_{\rm tSZ}$, $a_{\rm kSZ}$, $a_p$, $a_c$, $a_{\rm gs}$, $a_{\rm ge}$, $a_s$} are the $\ell(\ell+1)C_\ell/2\pi$ power in $\mu \rm{K}^2$ at $\ell=3000$ and frequency $150~$GHz. The tSZ-CIB correlation parameter $\xi$ is also defined at $\ell=3000$. The dust emissivity index $\beta_c$ is in flux units, for a modified blackbody with effective temperature $9.7~\rm{K}$. Conversions to power at each frequency are given in Table \ref{['table:sec_params']}. Strong priors, described in §\ref{['subsec:sec_param']}, are imposed on {$\xi$, $a_{\rm ge}$, $a_{\rm gs}$, $a_s$}.