The Atacama Cosmology Telescope: A Measurement of the 600< ell <8000 Cosmic Microwave Background Power Spectrum at 148 GHz

TL;DR

This study presents a high-resolution measurement of the CMB temperature power spectrum at 148 GHz with ACT, covering $600<\ell<8000$ over 228 deg^2. It combines meticulous data reduction, planet-based absolute calibration, and a robust AMTM-based power-spectrum estimator to isolate the CMB signal from foregrounds and instrumental effects. The analysis yields a strong upper limit on SZ power, $A_{\rm SZ}<1.63$ (95% CL), translating to $\sigma_8^{\rm SZ}<0.86$ (95% CL), and detects residual point-source power $A_p=11.2$–$11.9\,\mu\mathrm{K}^2$ consistent with radio and IR source models. Joint ACT+WMAP analyses corroborate a $\Lambda$CDM cosmology while highlighting the importance of foreground modeling for precision small-scale CMB studies, with implications for future high-$\ell$ polarization measurements and multi-frequency foreground separation.

Abstract

We present a measurement of the angular power spectrum of the cosmic microwave background (CMB) radiation observed at 148 GHz. The measurement uses maps with 1.4' angular resolution made with data from the Atacama Cosmology Telescope (ACT). The observations cover 228 square degrees of the southern sky, in a 4.2-degree-wide strip centered on declination 53 degrees South. The CMB at arcminute angular scales is particularly sensitive to the Silk damping scale, to the Sunyaev-Zel'dovich (SZ) effect from galaxy clusters, and to emission by radio sources and dusty galaxies. After masking the 108 brightest point sources in our maps, we estimate the power spectrum between 600 < \ell < 8000 using the adaptive multi-taper method to minimize spectral leakage and maximize use of the full data set. Our absolute calibration is based on observations of Uranus. To verify the calibration and test the fidelity of our map at large angular scales, we cross-correlate the ACT map to the WMAP map and recover the WMAP power spectrum from 250 < ell < 1150. The power beyond the Silk damping tail of the CMB is consistent with models of the emission from point sources. We quantify the contribution of SZ clusters to the power spectrum by fitting to a model normalized at sigma8 = 0.8. We constrain the model's amplitude ASZ < 1.63 (95% CL). If interpreted as a measurement of sigma8, this implies sigma8^SZ < 0.86 (95% CL) given our SZ model. A fit of ACT and WMAP five-year data jointly to a 6-parameter LCDM model plus terms for point sources and the SZ effect is consistent with these results.

Figures (8)

• Figure 1: Recent measurements of the CMB power spectrum, including this work. Top: the measurements of WMAP nolta/etal:2009, Bolocam sayers/etal:2009, QUaD brown/etal:2009friedman/etal:2009, APEX-SZ reichardt/etal:2009a, ACBAR reichardt/etal:2009, SZA sharp/etal:prep, BIMA dawson/etal:2006, CBI sievers/etal:prep, and SPT lueker/etal:prep. For all the results, a radio point source contribution has been removed either by masking before computing the power spectrum (at 150 GHz), or by masking and modeling the residual (at 30 GHz and for WMAP). APEX-SZ additionally masks clusters and potential IR sources. Bottom: The ACT power spectrum from this work. The inset shows the cross-power spectrum between ACT and WMAP maps in the ACT southern field (see Section \ref{['sec:wmap_cal']}), which we use to check both the validity of the maps at larger scales and the absolute calibration. Only the ACT power spectrum is analyzed in this paper. In both panels and the inset, the solid curve (blue) is the $\Lambda$CDM model of dunkley/etal:2009 (including lensing). The SZ effect and foreground sources are expected to contribute additional power, as shown in Figure \ref{['fig:cl_binned']} and Table \ref{['tab:cls']}. For display purposes---and only in this figure---we scale our result by 0.96 in temperature relative to the Uranus calibration; this calibration factor best fits our data to the $\Lambda$CDM model and differs from the Uranus calibration by $0.7\sigma$. Recent WMAP observations of Uranus suggest the same rescaling factor (see footnote to Section \ref{['sec:calibration']}). ACT bandpowers for $\ell>4200$ have been combined into bins of $\Delta\ell=600$ for this figure; they are given in a note to Table \ref{['tab:cls']}.
• Figure 2: The map and a difference map of the ACT southern field at 150 GHz. The same filters used in the power spectrum analysis are applied to both maps: an isotropic high-pass filter suppresses power for $\ell\lesssim 300$ (Equation \ref{['eq:highpass']}), and all modes with $|\ell_x|<270$ are set to zero, as described in Section \ref{['sec:spectrum_single']}. Top: The ACT southern field. The intensity scale is $\micro \kelvin$ (CMB units). The $360\,\mathrm{deg}^2$ with lowest noise are shown. The squares 4$.\!\!^{\circ}$2 on a side indicate the 13 patches used for the CMB power spectrum analysis (228 deg$^2$ total). Middle: A difference map made from two halves of the same data set. Most of the remaining structure visible at large scales is well below the range of $\ell$ that we consider in the power spectrum analysis. Bottom: The rms temperature uncertainty for one square arcminute pixels.
• Figure 3: The total estimated error $\sigma$ on the power spectrum (blue) given by the analytic expression (Equations \ref{['eq:analyticPSVariance']} and \ref{['eq:analyticPSPoissonTerm']}). The uncertainty on $\sigma$ is found using simulations and is shown by the shaded blue band. The Gaussian sample variance (red line, labeled "S") dominates for $\ell\lesssim1200$, and atmospheric plus instrument noise (purple, "N") dominates at $\ell>2000$. The non-Gaussian term due to unmasked point sources and clusters of galaxies contributes about 15% of the variance at $2500<\ell<6000$ (green, "P"). The errors estimated using the scatter of the results from the thirteen patches (Equation \ref{['eq:binBinCovariance']} are shown for comparison (black points); they agree well with the analytic errors.
• Figure 4: The observed power spectrum in bandpowers at 150 GHz from ACT observations (points with error bars). At large angular scales there is good agreement with the lensed $\Lambda$CDM model of the primary CMB (light blue curve shown for $\ell<4700$). The $\chi^2$ of the model is 7.1 for 4 ACT data points in the range $600<\ell<1800$. The best-fitting model to the full dataset is shown (dark blue, the highest curve for all $\ell>2500$). The complete model includes the primary CMB model plus both a Poisson power from point sources and SZ power from clusters; both additional components have been allowed to vary. The complete model has been smoothed by convolution with a boxcar window function of width $\Delta\ell=300$; the primary CMB model has not been smoothed. The narrower, gold band shows the marginalized $95\%$ CL limits on the Poisson amplitude, while the curve indicates the best-fit amplitude $A_p = 11.9\,\micro \kelvin^2$. The wider pink band shows the $95\%$ CL upper bound on the SZ amplitude, $A_{\rm SZ} < 1.63$; the dark curve inside it shows the best-fit value of $A_{\rm SZ} = 0.63$. The Poisson and SZ power are consistent with higher frequency observations and with $\Lambda$CDM predictions. The fitting procedure is described in Section \ref{['sec:params']}.
• Figure 5: Convergence of the maps as a function of iteration. The mapmaking algorithm converges well by iteration 500. For signal-only simulations (top), the amplitude of fluctuations in the difference between the processed output map at iteration $i$ and the input map (denoted $({C^i_b})^{1/2}$), is less than 1% of the amplitude of fluctuations in the input map ($\sqrt{C_b}$) at all scales by $i=500$. Iterations $i=5,20,100,$ and 500 are shown. For simulations with noise and for the data (middle and bottom, respectively), convergence is tested by estimating the maximum change in power between the processed map at iteration $i$ and iteration $1000$, as a fraction of the uncertainty in the power in the final map. For iteration 500 this fraction $r_c$ (described in Section \ref{['sec:results']}) is sufficiently small, less than 0.5 at all scales.