arXiv subjects

D. Luong-Van

Publications and source records attributed to D. Luong-Van.

At least 19 recordsLinked to original sources

arXiv2023

SPT-SZ MCMF: An extension of the SPT-SZ catalog over the DES region

We present an extension to a Sunyaev-Zel'dovich Effect (SZE) selected cluster catalog based on observations from the South Pole Telescope (SPT); this catalog extends to lower signal-to-noise than the previous SPT-SZ catalog and therefore includes lower mass clusters. Optically derived redshifts, centers, richnesses and morphological parameters together with catalog contamination and completeness statistics are extracted using the multi-component matched filter algorithm (MCMF) applied to the S/N>4 SPT-SZ candidate list and the Dark Energy Survey (DES) photometric galaxy catalog. The main catalog contains 811 sources above S/N=4, has 91% purity and is 95% complete with respect to the original SZE selection. It contains 50% more total clusters and twice as many clusters above z=0.8 in comparison to the original SPT-SZ sample. The MCMF algorithm allows us to define subsamples of the desired purity with traceable impact on catalog completeness. As an example, we provide two subsamples with S/N>4.25 and S/N>4.5 for which the sample contamination and cleaning-induced incompleteness are both as low as the expected Poisson noise for samples of their size. The subsample with S/N>4.5 has 98% purity and 96% completeness, and will be included in a combined SPT cluster and DES weak-lensing cosmological analysis. We measure the number of false detections in the SPT-SZ candidate list as function of S/N, finding that it follows that expected from assuming Gaussian noise, but with a lower amplitude compared to previous estimates from simulations.

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arXiv2022

Mapping gas around massive galaxies: cross-correlation of DES Y3 galaxies and Compton-$y$-maps from SPT and Planck

We cross-correlate positions of galaxies measured in data from the first three years of the Dark Energy Survey with Compton-$y$-maps generated using data from the South Pole Telescope (SPT) and the {\it Planck} mission. We model this cross-correlation measurement together with the galaxy auto-correlation to constrain the distribution of gas in the Universe. We measure the hydrostatic mass bias or, equivalently, the mean halo bias-weighted electron pressure $\langle b_{h}P_{e}\rangle$, using large-scale information. We find $\langle b_{h}P_{e}\rangle$ to be $[0.16^{+0.03}_{-0.04},0.28^{+0.04}_{-0.05},0.45^{+0.06}_{-0.10},0.54^{+0.08}_{-0.07},0.61^{+0.08}_{-0.06},0.63^{+0.07}_{-0.08}]$ meV cm$^{-3}$ at redshifts $z \sim [0.30, 0.46, 0.62,0.77, 0.89, 0.97]$. These values are consistent with previous work where measurements exist in the redshift range. We also constrain the mean gas profile using small-scale information, enabled by the high-resolution of the SPT data. We compare our measurements to different parametrized profiles based on the cosmo-OWLS hydrodynamical simulations. We find that our data are consistent with the simulation that assumes an AGN heating temperature of $10^{8.5}$K but are incompatible with the model that assumes an AGN heating temperature of $10^{8.0}$K. These comparisons indicate that the data prefer a higher value of electron pressure than the simulations within $r_{500c}$ of the galaxies' halos.

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arXiv2022

Combining Planck and SPT cluster catalogs: cosmological analysis and impact on Planck scaling relation calibration

We provide the first combined cosmological analysis of South Pole Telescope (SPT) and Planck cluster catalogs. The aim is to provide an independent calibration for Planck scaling relations, exploiting the cosmological constraining power of the SPT-SZ cluster catalog and its dedicated weak lensing (WL) and X-ray follow-up observations. We build a new version of the Planck cluster likelihood. In the $νΛ$CDM scenario, focusing on the mass slope and mass bias of Planck scaling relations, we find $α_{\text{SZ}} = 1.49_{-0.10}^{+0.07}$ and $(1-b)_{\text{SZ}} = 0.69_{-0.14}^{+0.07}$ respectively. The results for the mass slope show a $\sim 4 \, σ$ departure from the self-similar evolution, $α_{\text{SZ}} \sim 1.8$. This shift is mainly driven by the matter density value preferred by SPT data, $Ω_m = 0.30 \pm 0.03$, lower than the one obtained by Planck data alone, $Ω_m = 0.37_{-0.06}^{+0.02}$. The mass bias constraints are consistent both with outcomes of hydrodynamical simulations and external WL calibrations, $(1-b) \sim 0.8$, and with results required by the Planck cosmic microwave background cosmology, $(1-b) \sim 0.6$. From this analysis, we obtain a new catalog of Planck cluster masses $M_{500}$. We estimate the ratio between the published Planck $M_{\text{SZ}}$ masses and our derived masses $M_{500}$, as a "measured mass bias", $(1-b)_M$. We analyse the mass, redshift and detection noise dependence of $(1-b)_M$, finding an increasing trend towards high redshift and low mass. These results mimic the effect of departure from self-similarity in cluster evolution, showing different dependencies for the low-mass high-mass, low-z high-z regimes.

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arXiv2022

Shocks in the Stacked Sunyaev-Zel'dovich Profiles of Clusters II: Measurements from SPT-SZ + Planck Compton-y Map

We search for the signature of cosmological shocks in stacked gas pressure profiles of galaxy clusters using data from the South Pole Telescope (SPT). Specifically, we stack the latest Compton-y maps from the 2500 deg^2 SPT-SZ survey on the locations of clusters identified in that same dataset. The sample contains 516 clusters with mean mass = 1e14.9 msol and redshift = 0.55. We analyze in parallel a set of zoom-in hydrodynamical simulations from The Three Hundred project. The SPT-SZ data show two features: (i) a pressure deficit at R/R200m = $1.08 \pm 0.09$, measured at $3.1σ$ significance and not observed in the simulations, and; (ii) a sharp decrease in pressure at R/R200m = $4.58 \pm 1.24$ at $2.0σ$ significance. The pressure deficit is qualitatively consistent with a shock-induced thermal non-equilibrium between electrons and ions, and the second feature is consistent with accretion shocks seen in previous studies. We split the cluster sample by redshift and mass, and find both features exist in all cases. There are also no significant differences in features along and across the cluster major axis, whose orientation roughly points towards filamentary structure. As a consistency test, we also analyze clusters from the Planck and Atacama Cosmology Telescope Polarimeter surveys and find quantitatively similar features in the pressure profiles. Finally, we compare the accretion shock radius (Rsh_acc) with existing measurements of the splashback radius (Rsp) for SPT-SZ and constrain the lower limit of the ratio, Rsh_acc/Rsp > $2.16 \pm 0.59$.

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arXiv2021

CMB/kSZ and Compton-$y$ Maps from 2500 square degrees of SPT-SZ and Planck Survey Data

We present component-separated maps of the primary cosmic microwave background/kinematic Sunyaev-Zel'dovich (SZ) amplitude and the thermal SZ Compton-$y$ parameter, created using data from the South Pole Telescope (SPT) and the Planck satellite. These maps, which cover the $\sim$2500 square degrees of the Southern sky imaged by the SPT-SZ survey, represent a significant improvement over previous such products available in this region by virtue of their higher angular resolution (1.25 arcminutes for our highest resolution Compton-$y$ maps) and lower noise at small angular scales. In this work we detail the construction of these maps using linear combination techniques, including our method for limiting the correlation of our lowest-noise Compton-$y$ map products with the cosmic infrared background. We perform a range of validation tests on these data products to test our sky modeling and combination algorithms, and we find good performance in all of these tests. Recognizing the potential utility of these data products for a wide range of astrophysical and cosmological analyses, including studies of the gas properties of galaxies, groups, and clusters, we make these products publicly available at http://pole.uchicago.edu/public/data/sptsz_ymap and on the NASA/LAMBDA website.

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arXiv2021

Improving cosmological constraints from galaxy cluster number counts with CMB-cluster-lensing data: Results from the SPT-SZ survey and forecasts for the future

We show the improvement to cosmological constraints from galaxy cluster surveys with the addition of CMB-cluster lensing data. We explore the cosmological implications of adding mass information from the 3.1$σ$ detection of gravitational lensing of the cosmic microwave background (CMB) by galaxy clusters to the Sunyaev-Zel'dovich (SZ) selected galaxy cluster sample from the 2500 deg$^2$ SPT-SZ survey and targeted optical and X-ray followup data. In the $Λ$CDM model, the combination of the cluster sample with the Planck power spectrum measurements prefers $σ_8 \left(Ω_m/0.3 \right)^{0.5} = 0.831 \pm 0.020$. Adding the cluster data reduces the uncertainty on this quantity by a factor of 1.4, which is unchanged whether or not the 3.1$σ$ CMB-cluster lensing measurement is included. We then forecast the impact of CMB-cluster lensing measurements with future cluster catalogs. Adding CMB-cluster lensing measurements to the SZ cluster catalog of the on-going SPT-3G survey is expected to improve the expected constraint on the dark energy equation of state $w$ by a factor of 1.3 to $σ(w) = 0.19$. We find the largest improvements from CMB-cluster lensing measurements to be for $σ_8$, where adding CMB-cluster lensing data to the cluster number counts reduces the expected uncertainty on $σ_8$ by factors of 2.4 and 3.6 for SPT-3G and CMB-S4 respectively.

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arXiv2020

Millimeter-wave Point Sources from the 2500-square-degree SPT-SZ Survey: Catalog and Population Statistics

We present a catalog of emissive point sources detected in the SPT-SZ survey, a contiguous 2530-square-degree area surveyed with the South Pole Telescope (SPT) from 2008 - 2011 in three bands centered at 95, 150, and 220 GHz. The catalog contains 4845 sources measured at a significance of 4.5 sigma or greater in at least one band, corresponding to detections above approximately 9.8, 5.8, and 20.4 mJy in 95, 150, and 220 GHz, respectively. Spectral behavior in the SPT bands is used for source classification into two populations based on the underlying physical mechanisms of compact, emissive sources that are bright at millimeter wavelengths: synchrotron radiation from active galactic nuclei and thermal emission from dust. The latter population includes a component of high-redshift sources often referred to as submillimeter galaxies (SMGs). In the relatively bright flux ranges probed by the survey, these sources are expected to be magnified by strong gravitational lensing. The survey also contains sources consistent with protoclusters, groups of dusty galaxies at high redshift undergoing collapse. We cross-match the SPT-SZ catalog with external catalogs at radio, infrared, and X-ray wavelengths and identify available redshift information. The catalog splits into 3980 synchrotron-dominated and 865 dust-dominated sources and we determine a list of 506 SMGs. Ten sources in the catalog are identified as stars. We calculate number counts for the full catalog, and synchrotron and dusty components, using a bootstrap method and compare our measured counts with models. This paper represents the third and final catalog of point sources in the SPT-SZ survey.

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arXiv2020

An Improved Measurement of the Secondary Cosmic Microwave Background Anisotropies from the SPT-SZ + SPTpol Surveys

We report new measurements of millimeter-wave power spectra in the angular multipole range $2000 \le \ell \le 11,000$ (angular scales $5^\prime \gtrsim θ\gtrsim 1^\prime$). By adding 95 and 150\,GHz data from the low-noise 500 deg$^2$ SPTpol survey to the SPT-SZ three-frequency 2540 deg$^2$ survey, we substantially reduce the uncertainties in these bands. These power spectra include contributions from the primary cosmic microwave background, cosmic infrared background, radio galaxies, and thermal and kinematic Sunyaev-Zel'dovich (SZ) effects. The data favor a thermal SZ (tSZ) power at 143\,GHz of $D^{\rm tSZ}_{3000} = 3.42 \pm 0.54~ μ{\rm K}^2$ and a kinematic SZ (kSZ) power of $D^{\rm kSZ}_{3000} = 3.0 \pm 1.0~ μ{\rm K}^2$. This is the first measurement of kSZ power at $\ge 3\,σ$. We study the implications of the measured kSZ power for the epoch of reionization, finding the duration of reionization to be $Δz_{re} = 1.0^{+1.6}_{-0.7}$ ($Δz_{re}< 4.1$ at 95% confidence), when combined with our previously published tSZ bispectrum measurement.

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arXiv2020

Fractional Polarisation of Extragalactic Sources in the 500-square-degree SPTpol Survey

We study the polarisation properties of extragalactic sources at 95 and 150 GHz in the SPTpol 500 deg$^2$ survey. We estimate the polarised power by stacking maps at known source positions, and correct for noise bias by subtracting the mean polarised power at random positions in the maps. We show that the method is unbiased using a set of simulated maps with similar noise properties to the real SPTpol maps. We find a flux-weighted mean-squared polarisation fraction $\langle p^2 \rangle= [8.9\pm1.1] \times 10^{-4}$ at 95 GHz and $[6.9\pm1.1] \times 10^{-4}$ at 150~GHz for the full sample. This is consistent with the values obtained for a sub-sample of active galactic nuclei. For dusty sources, we find 95 per cent upper limits of $\langle p^2 \rangle_{\rm 95}<16.9 \times 10^{-3}$ and $\langle p^2 \rangle_{\rm 150}<2.6 \times 10^{-3}$. We find no evidence that the polarisation fraction depends on the source flux or observing frequency. The 1-$σ$ upper limit on measured mean squared polarisation fraction at 150 GHz implies that extragalactic foregrounds will be subdominant to the CMB E and B mode polarisation power spectra out to at least $\ell\lesssim5700$ ($\ell\lesssim4700$) and $\ell\lesssim5300$ ($\ell\lesssim3600$), respectively at 95 (150) GHz.

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arXiv2019

Consistency of cosmic microwave background temperature measurements in three frequency bands in the 2500-square-degree SPT-SZ survey

We present an internal consistency test of South Pole Telescope (SPT) measurements of the cosmic microwave background (CMB) temperature anisotropy using three-band data from the SPT-SZ survey. These measurements are made from observations of ~2500 deg^2 of sky in three frequency bands centered at 95, 150, and 220 GHz. We combine the information from these three bands into six semi-independent estimates of the CMB power spectrum (three single-frequency power spectra and three cross-frequency spectra) over the multipole range 650 < l < 3000. We subtract an estimate of foreground power from each power spectrum and evaluate the consistency among the resulting CMB-only spectra. We determine that the six foreground-cleaned power spectra are consistent with the null hypothesis, in which the six cleaned spectra contain only CMB power and noise. A fit of the data to this model results in a chi-squared value of 236.3 for 235 degrees of freedom, and the probability to exceed this chi-squared value is 46%.

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arXiv2019

Cosmological lensing ratios with DES Y1, SPT and Planck

Correlations between tracers of the matter density field and gravitational lensing are sensitive to the evolution of the matter power spectrum and the expansion rate across cosmic time. Appropriately defined ratios of such correlation functions, on the other hand, depend only on the angular diameter distances to the tracer objects and to the gravitational lensing source planes. Because of their simple cosmological dependence, such ratios can exploit available signal-to-noise down to small angular scales, even where directly modeling the correlation functions is difficult. We present a measurement of lensing ratios using galaxy position and lensing data from the Dark Energy Survey, and CMB lensing data from the South Pole Telescope and Planck, obtaining the highest precision lensing ratio measurements to date. Relative to the concordance $Λ$CDM model, we find a best fit lensing ratio amplitude of $A = 1.1 \pm 0.1$. We use the ratio measurements to generate cosmological constraints, focusing on the curvature parameter. We demonstrate that photometrically selected galaxies can be used to measure lensing ratios, and argue that future lensing ratio measurements with data from a combination of LSST and Stage-4 CMB experiments can be used to place interesting cosmological constraints, even after considering the systematic uncertainties associated with photometric redshift and galaxy shear estimation.

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arXiv2019

Measurements of the Cross Spectra of the Cosmic Infrared and Microwave Backgrounds from 95 to 1200 GHz

We present measurements of the power spectra of cosmic infrared background (CIB) and cosmic microwave background (CMB) fluctuations in six frequency bands. Maps at the lower three frequency bands, 95, 150, and 220 GHz (3330, 2000, 1360 $μ$m) are from the South Pole Telescope, while the upper three frequency bands, 600, 857, and 1200 GHz (500, 350, 250 $μ$m) are observed with Herschel/SPIRE. From these data, we produce 21 angular power spectra (six auto- and fifteen cross-frequency) spanning the multipole range $600 \le \ell \le 11,000$. Our measurements are the first to cross-correlate measurements near the peak of the CIB spectrum with maps at 95 GHz, complementing and extending the measurements from Planck Collaboration et al. (2014) at 218, 550, and 857 GHz. The observed fluctuations originate largely from clustered, infrared-emitting, dusty star-forming galaxies, the CMB, and to a lesser extent radio galaxies, active galactic nuclei, and the Sunyaev-Zel'dovich effect.

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arXiv2019

Cluster Cosmology Constraints from the 2500 deg$^2$ SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope

We derive cosmological constraints using a galaxy cluster sample selected from the 2500~deg$^2$ SPT-SZ survey. The sample spans the redshift range $0.25< z<1.75$ and contains 343 clusters with SZ detection significance $ξ>5$. The sample is supplemented with optical weak gravitational lensing measurements of 32 clusters with $0.29<z<1.13$ (from Magellan and HST) and X-ray measurements of 89 clusters with $0.25<z<1.75$ (from Chandra). We rely on minimal modeling assumptions: i) weak lensing provides an accurate means of measuring halo masses, ii) the mean SZ and X-ray observables are related to the true halo mass through power-law relations in mass and dimensionless Hubble parameter $E(z)$ with a-priori unknown parameters, iii) there is (correlated, lognormal) intrinsic scatter and measurement noise relating these observables to their mean relations. We simultaneously fit for these astrophysical modeling parameters and for cosmology. Assuming a flat $νΛ$CDM model, in which the sum of neutrino masses is a free parameter, we measure $Ω_\mathrm{m}=0.276\pm0.047$, $σ_8=0.781\pm0.037$, and $σ_8(Ω_\mathrm{m}/0.3)^{0.2}=0.766\pm0.025$. The redshift evolution of the X-ray $Y_\mathrm{X}$-mass and $M_\mathrm{gas}$-mass relations are both consistent with self-similar evolution to within $1σ$. The mass-slope of the $Y_\mathrm{X}$-mass relation shows a $2.3σ$ deviation from self-similarity. Similarly, the mass-slope of the $M_\mathrm{gas}$-mass relation is steeper than self-similarity at the $2.5σ$ level. In a $νw$CDM cosmology, we measure the dark energy equation of state parameter $w=-1.55\pm0.41$ from the cluster data. We perform a measurement of the growth of structure since redshift $z\sim1.7$ and find no evidence for tension with the prediction from General Relativity. We provide updated redshift and mass estimates for the SPT sample. (abridged)

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arXiv2018

Maps of the Southern Millimeter-wave Sky from Combined 2500 deg$^2$ SPT-SZ and Planck Temperature Data

We present three maps of the millimeter-wave sky created by combining data from the South Pole Telescope (SPT) and the Planck satellite. We use data from the SPT-SZ survey, a survey of 2540 deg$^2$ of the the sky with arcminute resolution in three bands centered at 95, 150, and 220 GHz, and the full-mission Planck temperature data in the 100, 143, and 217 GHz bands. A linear combination of the SPT-SZ and Planck data is computed in spherical harmonic space, with weights derived from the noise of both instruments. This weighting scheme results in Planck data providing most of the large-angular-scale information in the combined maps, with the smaller-scale information coming from SPT-SZ data. A number of tests have been done on the maps. We find their angular power spectra to agree very well with theoretically predicted spectra and previously published results.

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arXiv2018

Dark Energy Survey Year 1 Results: Joint Analysis of Galaxy Clustering, Galaxy Lensing, and CMB Lensing Two-point Functions

We perform a joint analysis of the auto and cross-correlations between three cosmic fields: the galaxy density field, the galaxy weak lensing shear field, and the cosmic microwave background (CMB) weak lensing convergence field. These three fields are measured using roughly 1300 sq. deg. of overlapping optical imaging data from first year observations of the Dark Energy Survey and millimeter-wave observations of the CMB from both the South Pole Telescope Sunyaev-Zel'dovich survey and Planck. We present cosmological constraints from the joint analysis of the two-point correlation functions between galaxy density and galaxy shear with CMB lensing. We test for consistency between these measurements and the DES-only two-point function measurements, finding no evidence for inconsistency in the context of flat $Λ$CDM cosmological models. Performing a joint analysis of five of the possible correlation functions between these fields (excluding only the CMB lensing autospectrum) yields $S_{8}\equiv σ_8\sqrt{Ω_{\rm m}/0.3} = 0.782^{+0.019}_{-0.025}$ and $Ω_{\rm m}=0.260^{+0.029}_{-0.019}$. We test for consistency between these five correlation function measurements and the Planck-only measurement of the CMB lensing autospectrum, again finding no evidence for inconsistency in the context of flat $Λ$CDM models. Combining constraints from all six two-point functions yields $S_{8}=0.776^{+0.014}_{-0.021}$ and $Ω_{\rm m}= 0.271^{+0.022}_{-0.016}$. These results provide a powerful test and confirmation of the results from the first year DES joint-probes analysis.

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arXiv2018

Dark Energy Survey Year 1 Results: tomographic cross-correlations between DES galaxies and CMB lensing from SPT+Planck

We measure the cross-correlation between redMaGiC galaxies selected from the Dark Energy Survey (DES) Year-1 data and gravitational lensing of the cosmic microwave background (CMB) reconstructed from South Pole Telescope (SPT) and Planck data over 1289 sq. deg. When combining measurements across multiple galaxy redshift bins spanning the redshift range of $0.15<z<0.90$, we reject the hypothesis of no correlation at 19.9$σ$ significance. When removing small-scale data points where thermal Sunyaev-Zel'dovich signal and nonlinear galaxy bias could potentially bias our results, the detection significance is reduced to 9.9$σ$. We perform a joint analysis of galaxy-CMB lensing cross-correlations and galaxy clustering to constrain cosmology, finding $Ω_{\rm m} = 0.276^{+0.029}_{-0.030}$ and $S_{8}=σ_{8}\sqrt{\mathstrut Ω_{\rm m}/0.3} = 0.800^{+0.090}_{-0.094}$. We also perform two alternate analyses aimed at constraining only the growth rate of cosmic structure as a function of redshift, finding consistency with predictions from the concordance $Λ$CDM model. The measurements presented here are part of a joint cosmological analysis that combines galaxy clustering, galaxy lensing and CMB lensing using data from DES, SPT and Planck.

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arXiv2018

Dark Energy Survey Year 1 Results: Cross-correlation between DES Y1 galaxy weak lensing and SPT+Planck CMB weak lensing

We cross-correlate galaxy weak lensing measurements from the Dark Energy Survey (DES) year-one (Y1) data with a cosmic microwave background (CMB) weak lensing map derived from South Pole Telescope (SPT) and Planck data, with an effective overlapping area of 1289 deg$^{2}$. With the combined measurements from four source galaxy redshift bins, we reject the hypothesis of no lensing with a significance of $10.8σ$. When employing angular scale cuts, this significance is reduced to $6.8σ$, which remains the highest signal-to-noise measurement of its kind to date. We fit the amplitude of the correlation functions while fixing the cosmological parameters to a fiducial $Λ$CDM model, finding $A = 0.99 \pm 0.17$. We additionally use the correlation function measurements to constrain shear calibration bias, obtaining constraints that are consistent with previous DES analyses. Finally, when performing a cosmological analysis under the $Λ$CDM model, we obtain the marginalized constraints of $Ω_{\rm m}=0.261^{+0.070}_{-0.051}$ and $S_{8}\equiv σ_{8}\sqrt{Ω_{\rm m}/0.3} = 0.660^{+0.085}_{-0.100}$. These measurements are used in a companion work that presents cosmological constraints from the joint analysis of two-point functions among galaxies, galaxy shears, and CMB lensing using DES, SPT and Planck data.

astro-ph.CO↗

arXiv2018

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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