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K. T. Story

Publications and source records attributed to K. T. Story.

At least 37 records · Page 2Linked to original sources

Broadband anti-reflective coatings for cosmic microwave background experiments

The desire for higher sensitivity has driven ground-based cosmic microwave background (CMB) experiments to employ ever larger focal planes, which in turn require larger reimaging optics. Practical limits to the maximum size of these optics motivates the development of quasi-optically-coupled (lenslet-coupled), multi-chroic detectors. These detectors can be sensitive across a broader bandwidth compared to waveguide-coupled detectors. However, the increase in bandwidth comes at a cost: the lenses (up to $\sim$700 mm diameter) and lenslets ($\sim$5 mm diameter, hemispherical lenses on the focal plane) used in these systems are made from high-refractive-index materials (such as silicon or amorphous aluminum oxide) that reflect nearly a third of the incident radiation. In order to maximize the faint CMB signal that reaches the detectors, the lenses and lenslets must be coated with an anti-reflective (AR) material. The AR coating must maximize radiation transmission in scientifically interesting bands and be cryogenically stable. Such a coating was developed for the third generation camera, SPT-3G, of the South Pole Telescope (SPT) experiment, but the materials and techniques used in the development are general to AR coatings for mm-wave optics. The three-layer polytetrafluoroethylene-based AR coating is broadband, inexpensive, and can be manufactured with simple tools. The coating is field tested; AR coated focal plane elements were deployed in the 2016-2017 austral summer and AR coated reimaging optics were deployed in 2017-2018.

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

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 ($σ_8 = 0.77 \pm 0.02$).

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A Comparison of Maps and Power Spectra Determined from South Pole Telescope and Planck Data

We study the consistency of 150 GHz data from the South Pole Telescope (SPT) and 143 GHz data from the Planck satellite over the patch of sky covered by the SPT-SZ survey. We first visually compare the maps and find that the residuals appear consistent with noise after accounting for differences in angular resolution and filtering. We then calculate (1) the cross-spectrum between two independent halves of SPT data, (2) the cross-spectrum between two independent halves of Planck data, and (3) the cross-spectrum between SPT and Planck data. We find the three cross-spectra are well-fit (PTE = 0.30) by the null hypothesis in which both experiments have measured the same sky map up to a single free calibration parameter---i.e., we find no evidence for systematic errors in either data set. As a by-product, we improve the precision of the SPT calibration by nearly an order of magnitude, from 2.6% to 0.3% in power. Finally, we compare all three cross-spectra to the full-sky Planck power spectrum and find marginal evidence for differences between the power spectra from the SPT-SZ footprint and the full sky. We model these differences as a power law in spherical harmonic multipole number. The best-fit value of this tilt is consistent among the three cross-spectra in the SPT-SZ footprint, implying that the source of this tilt is a sample variance fluctuation in the SPT-SZ region relative to the full sky. The consistency of cosmological parameters derived from these datasets is discussed in a companion paper.

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Constraints on Cosmological Parameters from the Angular Power Spectrum of a Combined 2500 deg$^2$ SPT-SZ and Planck Gravitational Lensing Map

We report constraints on cosmological parameters from the angular power spectrum of a cosmic microwave background (CMB) gravitational lensing potential map created using temperature data from 2500 deg$^2$ of South Pole Telescope (SPT) data supplemented with data from Planck in the same sky region, with the statistical power in the combined map primarily from the SPT data. We fit the corresponding lensing angular power spectrum to a model including cold dark matter and a cosmological constant ($Λ$CDM), and to models with single-parameter extensions to $Λ$CDM. We find constraints that are comparable to and consistent with constraints found using the full-sky Planck CMB lensing data. Specifically, we find $σ_8 Ω_{\rm m}^{0.25}=0.598 \pm 0.024$ from the lensing data alone with relatively weak priors placed on the other $Λ$CDM parameters. In combination with primary CMB data from Planck, we explore single-parameter extensions to the $Λ$CDM model. We find $Ω_k = -0.012^{+0.021}_{-0.023}$ or $M_ν< 0.70$eV both at 95% confidence, all in good agreement with results that include the lensing potential as measured by Planck over the full sky. We include two independent free parameters that scale the effect of lensing on the CMB: $A_{L}$, which scales the lensing power spectrum in both the lens reconstruction power and in the smearing of the acoustic peaks, and $A^{ϕϕ}$, which scales only the amplitude of the CMB lensing reconstruction power spectrum. We find $A^{ϕϕ} \times A_{L} =1.01 \pm 0.08$ for the lensing map made from combined SPT and Planck temperature data, indicating that the amount of lensing is in excellent agreement with what is expected from the observed CMB angular power spectrum when not including the information from smearing of the acoustic peaks.

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A Comparison of Cosmological Parameters Determined from CMB Temperature Power Spectra from the South Pole Telescope and the Planck Satellite

The Planck cosmic microwave background (CMB) temperature data are best fit with a LCDM model that is in mild tension with constraints from other cosmological probes. The South Pole Telescope (SPT) 2540 $\text{deg}^2$ SPT-SZ survey offers measurements on sub-degree angular scales (multipoles $650 \leq \ell \leq 2500$) with sufficient precision to use as an independent check of the Planck data. Here we build on the recent joint analysis of the SPT-SZ and Planck data in \citet{hou17} by comparing LCDM parameter estimates using the temperature power spectrum from both data sets in the SPT-SZ survey region. We also restrict the multipole range used in parameter fitting to focus on modes measured well by both SPT and Planck, thereby greatly reducing sample variance as a driver of parameter differences and creating a stringent test for systematic errors. We find no evidence of systematic errors from such tests. When we expand the maximum multipole of SPT data used, we see low-significance shifts in the angular scale of the sound horizon and the physical baryon and cold dark matter densities, with a resulting trend to higher Hubble constant. When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky data but keep the multipole range restricted, we find differences in the parameters $n_s$ and $A_se^{-2τ}$. We perform further checks, investigating instrumental effects and modeling assumptions, and we find no evidence that the effects investigated are responsible for any of the parameter shifts. Taken together, these tests reveal no evidence for systematic errors in SPT or Planck data in the overlapping sky coverage and multipole range and, at most, weak evidence for a breakdown of LCDM or systematic errors influencing either the Planck data outside the SPT-SZ survey area or the SPT data at $\ell >2000$.

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CMB Polarization B-mode Delensing with SPTpol and Herschel

We present a demonstration of delensing the observed cosmic microwave background (CMB) B-mode polarization anisotropy. This process of reducing the gravitational-lensing generated B-mode component will become increasingly important for improving searches for the B modes produced by primordial gravitational waves. In this work, we delens B-mode maps constructed from multi-frequency SPTpol observations of a 90 deg$^2$ patch of sky by subtracting a B-mode template constructed from two inputs: SPTpol E-mode maps and a lensing potential map estimated from the $\textit{Herschel}$ $500\,μm$ map of the CIB. We find that our delensing procedure reduces the measured B-mode power spectrum by 28% in the multipole range $300 < \ell < 2300$; this is shown to be consistent with expectations from theory and simulations and to be robust against systematics. The null hypothesis of no delensing is rejected at $6.9 σ$. Furthermore, we build and use a suite of realistic simulations to study the general properties of the delensing process and find that the delensing efficiency achieved in this work is limited primarily by the noise in the lensing potential map. We demonstrate the importance of including realistic experimental non-idealities in the delensing forecasts used to inform instrument and survey-strategy planning of upcoming lower-noise experiments, such as CMB-S4.

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A 2500 square-degree CMB lensing map from combined South Pole Telescope and Planck data

We present a cosmic microwave background (CMB) lensing map produced from a linear combination of South Pole Telescope (SPT) and \emph{Planck} temperature data. The 150 GHz temperature data from the $2500\ {\rm deg}^{2}$ SPT-SZ survey is combined with the \emph{Planck} 143 GHz data in harmonic space, to obtain a temperature map that has a broader $\ell$ coverage and less noise than either individual map. Using a quadratic estimator technique on this combined temperature map, we produce a map of the gravitational lensing potential projected along the line of sight. We measure the auto-spectrum of the lensing potential $C_{L}^{ϕϕ}$, and compare it to the theoretical prediction for a $Λ$CDM cosmology consistent with the \emph{Planck} 2015 data set, finding a best-fit amplitude of $0.95_{-0.06}^{+0.06}({\rm Stat.})\! _{-0.01}^{+0.01}({\rm Sys.})$. The null hypothesis of no lensing is rejected at a significance of $24\,σ$. One important use of such a lensing potential map is in cross-correlations with other dark matter tracers. We demonstrate this cross-correlation in practice by calculating the cross-spectrum, $C_{L}^{ϕG}$, between the SPT+\emph{Planck} lensing map and Wide-field Infrared Survey Explorer (\emph{WISE}) galaxies. We fit $C_{L}^{ϕG}$ to a power law of the form $p_{L}=a(L/L_{0})^{-b}$ with $a=2.15 \times 10^{-8}$, $b=1.35$, $L_{0}=490$, and find $η^{ϕG}=0.94^{+0.04}_{-0.04}$, which is marginally lower, but in good agreement with $η^{ϕG}=1.00^{+0.02}_{-0.01}$, the best-fit amplitude for the cross-correlation of \emph{Planck}-2015 CMB lensing and \emph{WISE} galaxies over $\sim67\%$ of the sky. The lensing potential map presented here will be used for cross-correlation studies with the Dark Energy Survey (DES), whose footprint nearly completely covers the SPT $2500\ {\rm deg}^2$ field.

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Maps of the Magellanic Clouds from Combined South Pole Telescope and Planck Data

We present maps of the Large and Small Magellanic Clouds from combined South Pole Telescope (SPT) and Planck data. The Planck satellite observes in nine bands, while the SPT data used in this work were taken with the three-band SPT-SZ camera, The SPT-SZ bands correspond closely to three of the nine Planck bands, namely those centered at 1.4, 2.1, and 3.0 mm. The angular resolution of the Planck data ranges from 5 to 10 arcmin, while the SPT resolution ranges from 1.0 to 1.7 arcmin. The combined maps take advantage of the high resolution of the SPT data and the long-timescale stability of the space-based Planck observations to deliver robust brightness measurements on scales from the size of the maps down to ~1 arcmin. In each band, we first calibrate and color-correct the SPT data to match the Planck data, then we use noise estimates from each instrument and knowledge of each instrument's beam to make the inverse-variance-weighted combination of the two instruments' data as a function of angular scale. We create maps assuming a range of underlying emission spectra and at a range of final resolutions. We perform several consistency tests on the combined maps and estimate the expected noise in measurements of features in the maps. We compare maps from this work to maps from the Herschel HERITAGE survey, finding general consistency between the datasets. All data products described in this paper are available for download from the NASA Legacy Archive for Microwave Background Data Analysis server.

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SPT-GMOS: A Gemini/GMOS-South Spectroscopic Survey of Galaxy Clusters in the SPT-SZ Survey

We present the results of SPT-GMOS, a spectroscopic survey with the Gemini Multi-Object Spectrograph (GMOS) on Gemini South. The targets of SPT-GMOS are galaxy clusters identified in the SPT-SZ survey, a millimeter-wave survey of 2500 squ. deg. of the southern sky using the South Pole Telescope (SPT). Multi-object spectroscopic observations of 62 SPT-selected galaxy clusters were performed between January 2011 and December 2015, yielding spectra with radial velocity measurements for 2595 sources. We identify 2243 of these sources as galaxies, and 352 as stars. Of the galaxies, we identify 1579 as members of SPT-SZ galaxy clusters. The primary goal of these observations was to obtain spectra of cluster member galaxies to estimate cluster redshifts and velocity dispersions. We describe the full spectroscopic dataset and resulting data products, including galaxy redshifts, cluster redshifts and velocity dispersions, and measurements of several well-known spectral indices for each galaxy: the equivalent width, W, of [O II] 3727,3729 and H-delta, and the 4000A break strength, D4000. We use the spectral indices to classify galaxies by spectral type (i.e., passive, post-starburst, star-forming), and we match the spectra against photometric catalogs to characterize spectroscopically-observed cluster members as a function of brightness (relative to m*). Finally, we report several new measurements of redshifts for ten bright, strongly-lensed background galaxies in the cores of eight galaxy clusters. Combining the SPT-GMOS dataset with previous spectroscopic follow-up of SPT-SZ galaxy clusters results in spectroscopic measurements for >100 clusters, or ~20% of the full SPT-SZ sample.

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Millimeter Transient Point Sources in the SPTpol 100 Square Degree Survey

The millimeter transient sky is largely unexplored, with measurements limited to follow-up of objects detected at other wavelengths. High-angular-resolution telescopes designed for measurement of the cosmic microwave background offer the possibility to discover new, unknown transient sources in this band, particularly the afterglows of unobserved gamma-ray bursts. Here we use the 10-meter millimeter-wave South Pole Telescope, designed for the primary purpose of observing the cosmic microwave background at arcminute and larger angular scales, to conduct a search for such objects. During the 2012-2013 season, the telescope was used to continuously observe a 100 square degree patch of sky centered at RA 23h30m and declination -55 degrees using the polarization-sensitive SPTpol camera in two bands centered at 95 and 150 GHz. These 6000 hours of observations provided continuous monitoring for day- to month-scale millimeter-wave transient sources at the 10 mJy level. One candidate object was observed with properties broadly consistent with a gamma-ray burst afterglow, but at a statistical significance too low (p=0.01) to confirm detection.

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Detection of the kinematic Sunyaev-Zel'dovich effect with DES Year 1 and SPT

We detect the kinematic Sunyaev-Zel'dovich (kSZ) effect with a statistical significance of $4.2 σ$ by combining a cluster catalogue derived from the first year data of the Dark Energy Survey (DES) with CMB temperature maps from the South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) Survey. This measurement is performed with a differential statistic that isolates the pairwise kSZ signal, providing the first detection of the large-scale, pairwise motion of clusters using redshifts derived from photometric data. By fitting the pairwise kSZ signal to a theoretical template we measure the average central optical depth of the cluster sample, $\barτ_e = (3.75 \pm 0.89)\cdot 10^{-3}$. We compare the extracted signal to realistic simulations and find good agreement with respect to the signal-to-noise, the constraint on $\barτ_e$, and the corresponding gas fraction. High-precision measurements of the pairwise kSZ signal with future data will be able to place constraints on the baryonic physics of galaxy clusters, and could be used to probe gravity on scales $ \gtrsim 100$ Mpc.

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Joint Measurement of Lensing-Galaxy Correlations Using SPT and DES SV Data

We measure the correlation of galaxy lensing and cosmic microwave background lensing with a set of galaxies expected to trace the matter density field. The measurements are performed using pre-survey Dark Energy Survey (DES) Science Verification optical imaging data and millimeter-wave data from the 2500 square degree South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) survey. The two lensing-galaxy correlations are jointly fit to extract constraints on cosmological parameters, constraints on the redshift distribution of the lens galaxies, and constraints on the absolute shear calibration of DES galaxy lensing measurements. We show that an attractive feature of these fits is that they are fairly insensitive to the clustering bias of the galaxies used as matter tracers. The measurement presented in this work confirms that DES and SPT data are consistent with each other and with the currently favored $Λ$CDM cosmological model. It also demonstrates that joint lensing-galaxy correlation measurement considered here contains a wealth of information that can be extracted using current and future surveys.

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Cosmological Constraints from Galaxy Clusters in the 2500 square-degree SPT-SZ Survey

(abridged) We present cosmological constraints obtained from galaxy clusters identified by their Sunyaev-Zel'dovich effect signature in the 2500 square degree South Pole Telescope Sunyaev Zel'dovich survey. We consider the 377 cluster candidates identified at z>0.25 with a detection significance greater than five, corresponding to the 95% purity threshold for the survey. We compute constraints on cosmological models using the measured cluster abundance as a function of mass and redshift. We include additional constraints from multi-wavelength observations, including Chandra X-ray data for 82 clusters and a weak lensing-based prior on the normalization of the mass-observable scaling relations. Assuming a LCDM cosmology, where the species-summed neutrino mass has the minimum allowed value (mnu = 0.06 eV) from neutrino oscillation experiments, we combine the cluster data with a prior on H0 and find sigma_8 = 0.797+-0.031 and Omega_m = 0.289+-0.042, with the parameter combination sigma_8(Omega_m/0.27)^0.3 = 0.784+-0.039. These results are in good agreement with constraints from the CMB from SPT, WMAP, and Planck, as well as with constraints from other cluster datasets. Adding mnu as a free parameter, we find mnu = 0.14+-0.08 eV when combining the SPT cluster data with Planck CMB data and BAO data, consistent with the minimum allowed value. Finally, we consider a cosmology where mnu and N_eff are fixed to the LCDM values, but the dark energy equation of state parameter w is free. Using the SPT cluster data in combination with an H0 prior, we measure w = -1.28+-0.31, a constraint consistent with the LCDM cosmological model and derived from the combination of growth of structure and geometry. When combined with primarily geometrical constraints from Planck CMB, H0, BAO and SNe, adding the SPT cluster data improves the w constraint from the geometrical data alone by 14%, to w = -1.023+-0.042.

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CMB lensing tomography with the DES Science Verification galaxies

We measure the cross-correlation between the galaxy density in the Dark Energy Survey (DES) Science Verification data and the lensing of the cosmic microwave background (CMB) as reconstructed with the Planck satellite and the South Pole Telescope (SPT). When using the DES main galaxy sample over the full redshift range $0.2 < z < 1.2$, a cross-correlation signal is detected at $6 σ$ and $4σ$ with SPT and Planck respectively. We then divide the DES galaxies into five photometric redshift bins, finding significant ($>$$2 σ$) detections in all bins. Comparing to the fiducial Planck cosmology, we find the redshift evolution of the signal matches expectations, although the amplitude is consistently lower than predicted across redshift bins. We test for possible systematics that could affect our result and find no evidence for significant contamination. Finally, we demonstrate how these measurements can be used to constrain the growth of structure across cosmic time. We find the data are fit by a model in which the amplitude of structure in the $z<1.2$ universe is $0.73 \pm 0.16$ times as large as predicted in the LCDM Planck cosmology, a $1.7σ$ deviation.

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Cross-correlation of gravitational lensing from DES Science Verification data with SPT and Planck lensing

We measure the cross-correlation between weak lensing of galaxy images and of the cosmic microwave background (CMB). The effects of gravitational lensing on different sources will be correlated if the lensing is caused by the same mass fluctuations. We use galaxy shape measurements from 139 deg$^{2}$ of the Dark Energy Survey (DES) Science Verification data and overlapping CMB lensing from the South Pole Telescope (SPT) and Planck. The DES source galaxies have a median redshift of $z_{\rm med} {\sim} 0.7$, while the CMB lensing kernel is broad and peaks at $z{\sim}2$. The resulting cross-correlation is maximally sensitive to mass fluctuations at $z{\sim}0.44$. Assuming the Planck 2015 best-fit cosmology, the amplitude of the DES$\times$SPT cross-power is found to be $A = 0.88 \pm 0.30$ and that from DES$\times$Planck to be $A = 0.86 \pm 0.39$, where $A=1$ corresponds to the theoretical prediction. These are consistent with the expected signal and correspond to significances of $2.9 σ$ and $2.2 σ$ respectively. We demonstrate that our results are robust to a number of important systematic effects including the shear measurement method, estimator choice, photometric redshift uncertainty and CMB lensing systematics. Significant intrinsic alignment of galaxy shapes would increase the cross-correlation signal inferred from the data; we calculate a value of $A = 1.08 \pm 0.36$ for DES$\times$SPT when we correct the observations with a simple IA model. With three measurements of this cross-correlation now existing in the literature, there is not yet reliable evidence for any deviation from the expected LCDM level of cross-correlation, given the size of the statistical uncertainties and the significant impact of systematic errors, particularly IAs. We provide forecasts for the expected signal-to-noise of the combination of the five-year DES survey and SPT-3G.

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A Measurement of the Cosmic Microwave Background Gravitational Lensing Potential from 100 Square Degrees of SPTpol Data

We present a measurement of the cosmic microwave background (CMB) gravitational lensing potential using data from the first two seasons of observations with SPTpol, the polarization-sensitive receiver currently installed on the South Pole Telescope (SPT). The observations used in this work cover 100 deg$^2$ of sky with arcminute resolution at 150 GHz. Using a quadratic estimator, we make maps of the CMB lensing potential from combinations of CMB temperature and polarization maps. We combine these lensing potential maps to form a minimum-variance (MV) map. The lensing potential is measured with a signal-to-noise ratio of greater than one for angular multipoles between $100< L <250$. This is the highest signal-to-noise mass map made from the CMB to date and will be powerful in cross-correlation with other tracers of large-scale structure. We calculate the power spectrum of the lensing potential for each estimator, and we report the value of the MV power spectrum between $100< L <2000$ as our primary result. We constrain the ratio of the spectrum to a fiducial $Λ$CDM model to be $A_{\rm MV}=0.92 \pm 0.14 {\rm\, (Stat.)} \pm 0.08 {\rm\, (Sys.)}$. Restricting ourselves to polarized data only, we find $A_{\rm POL}=0.92 \pm 0.24 {\rm\, (Stat.)} \pm 0.11 {\rm\, (Sys.)}$. This measurement rejects the hypothesis of no lensing at $5.9 σ$ using polarization data alone, and at $14 σ$ using both temperature and polarization data.

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A Measurement of Gravitational Lensing of the Cosmic Microwave Background by Galaxy Clusters Using Data from the South Pole Telescope

Clusters of galaxies are expected to gravitationally lens the cosmic microwave background (CMB) and thereby generate a distinct signal in the CMB on arcminute scales. Measurements of this effect can be used to constrain the masses of galaxy clusters with CMB data alone. Here we present a measurement of lensing of the CMB by galaxy clusters using data from the South Pole Telescope (SPT). We develop a maximum likelihood approach to extract the CMB cluster lensing signal and validate the method on mock data. We quantify the effects on our analysis of several potential sources of systematic error and find that they generally act to reduce the best-fit cluster mass. It is estimated that this bias to lower cluster mass is roughly $0.85σ$ in units of the statistical error bar, although this estimate should be viewed as an upper limit. We apply our maximum likelihood technique to 513 clusters selected via their SZ signatures in SPT data, and rule out the null hypothesis of no lensing at $3.1σ$. The lensing-derived mass estimate for the full cluster sample is consistent with that inferred from the SZ flux: $M_{200,\mathrm{lens}} = 0.83_{-0.37}^{+0.38}\, M_{200,\mathrm{SZ}}$ (68% C.L., statistical error only).

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Measurements of Sub-degree B-mode Polarization in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data

We present a measurement of the $B$-mode polarization power spectrum (the $BB$ spectrum) from 100 $\mathrm{deg}^2$ of sky observed with SPTpol, a polarization-sensitive receiver currently installed on the South Pole Telescope. The observations used in this work were taken during 2012 and early 2013 and include data in spectral bands centered at 95 and 150 GHz. We report the $BB$ spectrum in five bins in multipole space, spanning the range $300 \le \ell \le 2300$, and for three spectral combinations: 95 GHz $\times$ 95 GHz, 95 GHz $\times$ 150 GHz, and 150 GHz $\times$ 150 GHz. We subtract small ($< 0.5 σ$ in units of statistical uncertainty) biases from these spectra and account for the uncertainty in those biases. The resulting power spectra are inconsistent with zero power but consistent with predictions for the $BB$ spectrum arising from the gravitational lensing of $E$-mode polarization. If we assume no other source of $BB$ power besides lensed $B$ modes, we determine a preference for lensed $B$ modes of $4.9 σ$. After marginalizing over tensor power and foregrounds, namely polarized emission from galactic dust and extragalactic sources, this significance is $4.3 σ$. Fitting for a single parameter, $A_\mathrm{lens}$, that multiplies the predicted lensed $B$-mode spectrum, and marginalizing over tensor power and foregrounds, we find $A_\mathrm{lens} = 1.08 \pm 0.26$, indicating that our measured spectra are consistent with the signal expected from gravitational lensing. The data presented here provide the best measurement to date of the $B$-mode power spectrum on these angular scales.

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