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Register a new userApplication of Contour Minkowski Tensor and $mathcal{D}$ Statistic to the Planck $E$-mode data
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We test the statistical isotropy (SI) of the $E$-mode polarization of the Cosmic Microwave Background (CMB) radiation observed by the Planck satellite using two statistics, namely, the $alpha$ estimator that is derived from the contour Minkowski Tensor (CMT), and the Directional statistic ($mathcal{D}$ statistic). The $alpha$ estimator obtained from the CMT provides information about the alignment of structures and can be used to infer statistical properties such as Gaussianity and SI of random fields. The $mathcal{D}$ statistic is based on detecting preferred directionality shown by vectors defined by the field. We compute $alpha$ and $mathcal{D}$ statistic for the low resolution component separated SMICA $E$-mode map of CMB polarization, and compare with the values calculated using FFP10 SMICA simulations. We find good agreement between the Planck data and SMICA simulations for both $alpha$ estimator and $mathcal{D}$ statistic.
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We use morphological descriptors, Betti numbers and Contour Minkowski Tensor (CMT) on 21cm brightness temperature excursion sets, to study the ionization and heating history of the intergalactic medium (IGM) during and before the Epoch of Reionization (EoR). The ratio of eigenvalues of the CMT denoted by $beta$, gives shape information while its trace gives the contour length of holes and connected regions. We simulate the matter density, neutral hydrogen fraction, spin temperature and brightness temperature field using the publicly available code 21cmFAST in a redshift range of $z=20.22$ to $z=6$. We study the redshift evolution of three quantities - the Betti number counts $N_{con,hole}$, the characteristic size $r^{ch}_{con,hole}$ and shape anisotropy parameter $beta^{ch}_{con,hole}$ of connected regions and holes for these fields and investigate the different physical origins of their evolution. We make a qualitative comparison of different models of heating and ionization during the EoR. We obtain different regimes of morphological evolution of brightness temperature, depending upon how the shapes and sizes of connected regions and holes change with redshift for different astrophysical settings affecting the ionization and heating history of the IGM during and before the EoR. We find that the morphology of the brightness temperature field traces the morphology of ionized regions below a certain redshift value depending upon the model, where $Delta r^{ch}_{hole}<10 %$ and $Delta beta^{ch}_{hole}<1 %$ relative to the $x_{HI}$ field. This difference decreases with redshift. Therefore, the ionization history of the IGM can be reconstructed using the morphological description of $delta T_b$ in real space.
Testing deviations from the $Lambda$CDM model using the Cosmic Microwave Background (CMB) power spectra requires a pristine understanding of instrumental systematics. In this work we discuss the properties of a new observable ${cal R}^{TE}_{ell}$, the correlation coefficient of temperature and E modes. We find that this observable is mostly unaffected by systematics introducing multiplicative biases such as errors in calibration, polarisation efficiency, beam and transfer function measurements. We discuss the dependency of this observable on the cosmological model and derive its statistical properties. We then compute the T-E correlation coefficients of Planck legacy data and compare them with expectations from the Planck best-fit $Lambda$CDM and foreground model.
We present measurements of the $E$-mode ($EE$) polarization power spectrum and temperature-$E$-mode ($TE$) cross-power spectrum of the cosmic microwave background using data collected by SPT-3G, the latest instrument installed on the South Pole Telescope. This analysis uses observations of a 1500 deg$^2$ region at 95, 150, and 220 GHz taken over a four month period in 2018. We report binned values of the $EE$ and $TE$ power spectra over the angular multipole range $300 le ell < 3000$, using the multifrequency data to construct six semi-independent estimates of each power spectrum and their minimum-variance combination. These measurements improve upon the previous results of SPTpol across the multipole ranges $300 le ell le 1400$ for $EE$ and $300 le ell le 1700$ for $TE$, resulting in constraints on cosmological parameters comparable to those from other current leading ground-based experiments. We find that the SPT-3G dataset is well-fit by a $Lambda$CDM cosmological model with parameter constraints consistent with those from Planck and SPTpol data. From SPT-3G data alone, we find $H_0 = 68.8 pm 1.5 mathrm{km,s^{-1},Mpc^{-1}}$ and $sigma_8 = 0.789 pm 0.016$, with a gravitational lensing amplitude consistent with the $Lambda$CDM prediction ($A_L = 0.98 pm 0.12$). We combine the SPT-3G and the Planck datasets and obtain joint constraints on the $Lambda$CDM model. The volume of the 68% confidence region in six-dimensional $Lambda$CDM parameter space is reduced by a factor of 1.5 compared to Planck-only constraints, with only slight shifts in central values. We note that the results presented here are obtained from data collected during just half of a typical observing season with only part of the focal plane operable, and that the active detector count has since nearly doubled for observations made with SPT-3G after 2018.
We present constraints on the tensor-to-scalar ratio r using Planck data. We use the latest release of Planck maps (PR4), processed with the NPIPE code, which produces calibrated frequency maps in temperature and polarization for all Planck channels from 30 GHz to 857 GHz using the same pipeline. We computed constraints on r using the BB angular power spectrum, and we also discuss constraints coming from the TT spectrum. Given Plancks noise level, the TT spectrum gives constraints on r that are cosmic-variance limited (with $sigma$(r)=0.093), but we show that the marginalized posterior peaks towards negative values of r at about the 1.2$sigma$ level. We derived Planck constraints using the BB power spectrum at both large angular scales (the reionization bump) and intermediate angular scales (the recombination bump) from $ell$=2 to 150, and find a stronger constraint than that from TT, with $sigma$(r)=0.069. The Planck BB spectrum shows no systematic bias, and is compatible with zero, given both the statistical noise and the systematic uncertainties. The likelihood analysis using B modes yields the constraint r<0.158 at 95% confidence using more than 50% of the sky. This upper limit tightens to r<0.069 when Planck EE, BB, and EB power spectra are combined consistently, and it tightens further to r<0.056 when the Planck TT power spectrum is included in the combination. Finally, combining Planck with BICEP2/Keck 2015 data yields an upper limit of r<0.044.
We present measurements of $E$-mode polarization and temperature-$E$-mode correlation in the cosmic microwave background (CMB) using data from the first season of observations with SPTpol, the polarization-sensitive receiver currently installed on the South Pole Telescope (SPT). The observations used in this work cover 100~sqdeg of sky with arcminute resolution at $150,$GHz. We report the $E$-mode angular auto-power spectrum ($EE$) and the temperature-$E$-mode angular cross-power spectrum ($TE$) over the multipole range $500 < ell leq5000$. These power spectra improve on previous measurements in the high-$ell$ (small-scale) regime. We fit the combination of the SPTpol power spectra, data from planck, and previous SPT measurements with a six-parameter LCDM cosmological model. We find that the best-fit parameters are consistent with previous results. The improvement in high-$ell$ sensitivity over previous measurements leads to a significant improvement in the limit on polarized point-source power: after masking sources brighter than 50,mJy in unpolarized flux at 150,GHz, we find a 95% confidence upper limit on unclustered point-source power in the $EE$ spectrum of $D_ell = ell (ell+1) C_ell / 2 pi < 0.40 mu{mbox{K}}^2$ at $ell=3000$, indicating that future $EE$ measurements will not be limited by power from unclustered point sources in the multipole range $ell < 3600$, and possibly much higher in $ell.$
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