Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data

TL;DR

This work delivers high-sensitivity measurements of the CMB EE and TE power spectra from 150 GHz SPTpol data over 500 deg^2, extending the multipole range to ℓ ≤ 8000 and revealing nine EE acoustic peaks. It leverages cross-spectra from 125 map bundles, MASTER-based deconvolution, detailed beam and calibration handling (including Venus-based beams and Planck cross-calibration), T→P deprojection, and a robust nuisance-foreground treatment to constrain ΛCDM and several high-ℓ extensions. The results indicate mild tension with ΛCDM (≈2.1σ) and show that including high-ℓ polarization information shifts H0 upward and σ8 downward, with Planck+SPTpol jointly reducing parameter-volume substantially. The analysis demonstrates the power of polarized damping-tail measurements to tighten constraints on fundamental physics (Y_p, N_eff) and to inform future CMB polarization efforts, including delensing prospects with SPTpol and upcoming experiments. The polarization measurements provide complementary scrutiny of the damping tail and contribute to the broader effort to understand possible tensions between CMB and low-redshift determinations of cosmological parameters.

Abstract

We present measurements of the $E$-mode polarization angular auto-power spectrum ($EE$) and temperature-$E$-mode cross-power spectrum ($TE$) of the cosmic microwave background (CMB) using 150 GHz data from three seasons of SPTpol observations. We report the power spectra over the spherical harmonic multipole range $50 < \ell \leq 8000$, and detect nine acoustic peaks in the $EE$ spectrum with high signal-to-noise ratio. These measurements are the most sensitive to date of the $EE$ and $TE$ power spectra at $\ell > 1050$ and $\ell > 1475$, respectively. The observations cover 500 deg$^2$, a fivefold increase in area compared to previous SPTpol analyses, which increases our sensitivity to the photon diffusion damping tail of the CMB power spectra enabling tighter constraints on \LCDM model extensions. After masking all sources with unpolarized flux $>50$ mJy we place a 95% confidence upper limit on residual polarized point-source power of $D_\ell = \ell(\ell+1)C_\ell/2π<0.107\,μ{\rm K}^2$ at $\ell=3000$, suggesting that the $EE$ damping tail dominates foregrounds to at least $\ell = 4050$ with modest source masking. We find that the SPTpol dataset is in mild tension with the $ΛCDM$ model ($2.1\,σ$), and different data splits prefer parameter values that differ at the $\sim 1\,σ$ level. When fitting SPTpol data at $\ell < 1000$ we find cosmological parameter constraints consistent with those for $Planck$ temperature. Including SPTpol data at $\ell > 1000$ results in a preference for a higher value of the expansion rate ($H_0 = 71.3 \pm 2.1\,\mbox{km}\,s^{-1}\mbox{Mpc}^{-1}$ ) and a lower value for present-day density fluctuations ($σ_8 = 0.77 \pm 0.02$).

Figures (17)

• Figure 1: SPTpol 500 $\mathrm{deg}^2$$T$ signal (top) and noise (bottom) maps. The noise maps are obtained by subtracting data of the first half from data of the second half of the set of bundles and dividing by 2 to reflect the effective noise level of the entire dataset.
• Figure 2: Top: map of Stokes $Q$. Bottom: map of Stokes $U$. The clear striping along lines of constant right ascension and declination in $Q$ and $\pm45^{\circ}$ striping in $U$ are indicative of high signal-to-noise ratio $E$ modes. The maps have been smoothed by a $4^\prime$ FWHM Gaussian.
• Figure 3: SPTpol 500 $\mathrm{deg}^2$$E$-mode signal (top) and noise (bottom) maps. The Fourier transforms of the $Q$ and $U$ maps shown in Figure \ref{['fig:coadd_qu']} are combined to form $E$ modes, which are inverse Fourier transformed to generate an $E$-mode map. Both maps have been smoothed by a $4^\prime$ FWHM Gaussian.
• Figure 4: SPTpol 500 $\mathrm{deg}^2$$TT$ (blue) and $EE$ (red) noise spectra. The left-hand labels give the noise in units of $\mu{\rm K}^2$ while the right-hand labels give the equivalent map depth in $\mu\hbox{K}-\hbox{arcmin}$.
• Figure 5: (a) 2D Fourier-space filtering transfer function, which we calculate from simulated maps with the Sanson-Flamsteed projection. Note that we have not corrected the 2D transfer function for mode coupling. (b) Zoom-in of the 2D transfer function at low $\ell_x$ and $\ell_y$. (c) Geometric mean of the $TT$ and $EE$ 1D filtering transfer functions corrected for mode coupling, which we calculate from maps using the oblique Lambert azimuthal equal-area projection.