Improved constraints on cosmic microwave background secondary anisotropies from the complete 2008 South Pole Telescope data

TL;DR

This work analyzes the complete 2008 South Pole Telescope data to measure the CMB power spectrum at small angular scales using a forward-model, multi-frequency approach that jointly fits lensed primary CMB, thermal and kinetic SZ effects, and foregrounds from DSFGs and radio sources. By combining the 150 and 220 GHz bandpowers with external low-ℓ CMB data, the authors constrain the SZ amplitudes and show a significant tension between the observed tSZ power and several theoretical templates, favoring lower tSZ power likely due to non-thermal pressure or other feedback processes in clusters. They demonstrate a strong degeneracy between tSZ and kSZ, constrain a linear combination D^{tSZ}_{3000} + 0.5 D^{kSZ}_{3000} = 4.5 ± 1.0 μK^2, and report 95% CL upper limits D^{tSZ}_{3000} < 5.3 μK^2 and D^{kSZ}_{3000} < 6.5 μK^2. Combining tSZ measurements with primary CMB data can halve the σ_8 uncertainty, but the exact σ_8 value depends strongly on the tSZ model, highlighting the need for improved modeling of intracluster gas physics to extract robust cosmological constraints from SZ power spectra.

Abstract

We report measurements of the cosmic microwave background (CMB) power spectrum from the complete 2008 South Pole Telescope (SPT) data set. We analyze twice as much data as the first SPT power spectrum analysis, using an improved cosmological parameter estimator which fits multi-frequency models to the SPT 150 and $220\,$GHz bandpowers. We find an excellent fit to the measured bandpowers with a model that includes lensed primary CMB anisotropy, secondary thermal (tSZ) and kinetic (kSZ) Sunyaev-Zel'dovich anisotropies, unclustered synchrotron point sources, and clustered dusty point sources. In addition to measuring the power spectrum of dusty galaxies at high signal-to-noise, the data primarily constrain a linear combination of the kSZ and tSZ anisotropy contributions at $150\,$GHz and $\ell=3000$: $D^{tSZ}_{3000} + 0.5\,D^{kSZ}_{3000} = 4.5\pm 1.0 \,μ{\rm K}^2$. The 95% confidence upper limits on secondary anisotropy power are $D^{tSZ}_{3000} < 5.3\,μ{\rm K}^2$ and $D^{kSZ}_{3000} < 6.5\,μ{\rm K}^2$. We also consider the potential correlation of dusty and tSZ sources, and find it incapable of relaxing the tSZ upper limit. These results increase the significance of the lower than expected tSZ amplitude previously determined from SPT power spectrum measurements. We find that models including non-thermal pressure support in groups and clusters predict tSZ power in better agreement with the SPT data. Combining the tSZ power measurement with primary CMB data halves the statistical uncertainty on $σ_8$. However, the preferred value of $σ_8$ varies significantly between tSZ models. Improved constraints on cosmological parameters from tSZ power spectrum measurements require continued progress in the modeling of the tSZ power.

Figures (16)

• Figure 1: Left axis: The measured SPT beam functions at $150\,$GHz ( black line) and $220\,$GHz ( blue line). Right axis: The fractional beam uncertainties at $150\,$GHz ( black dashed line) and $220\,$GHz ( blue dashed line). The beam uncertainty is parametrized by a three component model, the quadrature sum of which is plotted here.
• Figure 2: Jackknives for the SPT data set at $150\,$GHz ( blue circles) and $220\,$GHz ( black diamonds). For clarity, the $220\,$GHz jackknives have been shifted to the right by $\Delta\ell = 100$. Top panel: Bandpowers of the "first half - second half" jackknife compared to the expected error bars about zero signal. Disagreement with zero would indicate either a noise misestimate or a time-dependent systematic signal. Second panel: Power spectrum of the left-going minus right-going difference map. This test yields strong constraints on the accuracy of the detector transfer function deconvolution and on possible directional systematics. Third panel: Bandpowers for the difference map when the data are split based on the observed very large scale ($\ell < 100$) ground pickup as a function of azimuth. Signals fixed in azimuth, such as ground pickup on smaller scales, would produce non-zero power. We see no evidence for ground-based pickup across this $\ell$-range. The cumulative probability to exceed the $\chi^2$ observed in these three tests at 150 and $220\,$GHz is 55%. Bottom panel: The un-differenced SPT power spectra at each frequency for comparison.
• Figure 3: Top panel: From left to right, the SPT $150\,$GHz, $150\times220\,$GHz, and $220\,$GHz bandpowers. Overplotted is the best-fit model ( red line) with components shown individually. The lensed primary CMB anisotropy is marked by an orange line. The best-fit tSZ ( purple line) and predicted kSZ ( purple dashed line) power spectra are also shown. The predicted radio source term is represented by the blue dots. The DSFG Poisson term at each frequency is denoted by the green dashed line and the clustered DSFG component by the green dot-dash line. The damping tail of the primary CMB anisotropy is apparent below $\ell = 3000$. Above $\ell = 3000$, there is a clear excess with an angular scale dependence consistent with point sources. These sources have low flux (sources detected at $>$$\,5\,\sigma$ at $150\,$GHz have been masked) and a rising frequency spectrum, consistent with expectations for DSFGs. Bottom panel: Plot of the residual between the measured bandpowers and best-fit spectrum.
• Figure 4: The SPT $150\,$GHz bandpowers ( black circles), WMAP7 bandpowers ( purple squares), ACBAR bandpowers ( green triangles), QUaD bandpowers ( cyan diamonds), and ACT $150\,$GHz bandpowers ( orange circles) plotted against the best-fit lensed $\Lambda$CDM CMB spectrum. The damping tail of the primary CMB anisotropy is apparent below $\ell = 3000$. Above $\ell = 3000$, there is a clear excess due to secondary anisotropies and residual point sources that has now been measured by both SPT and ACT. Note that the source masking threshold in the SPT data ($6.4\,$mJy) is lower than that in the ACT data, so we expect less radio source power at high $\ell$. We have multiplied the SPT bandpowers by the best-fit calibration of 0.92 as determined in parameter fits.
• Figure 5: Templates used for the tSZ, kSZ, and clustered DSFG power discussed in §\ref{['sec:model']}. The top plot shows alternate tSZ templates. The black, solid line is the (baseline) S10 model. The blue, dashed line is the Shaw model. The red, dotted line is the Trac model. The teal dot-dash line is the Battaglia model. The bottom plot shows both kSZ and clustered DSFG templates. The black, solid line is the (baseline) S10 kSZ model. The red, dotted line is the patchy kSZ model. The blue, dashed line is the (baseline) power-law clustered DSFG template. The teal, dot-dash line is the linear-theory clustered DSFG template. The clustered DSFG templates have both been normalized to $1\;\mu {\rm K}^2$ at $\ell=3000$.