A unified pseudo- C ℓ framework

We study the problem of EB-leakage that is associated with incomplete polarized CMB sky. In the blind case that assumes no additional information about the statistical properties and amplitudes of the signal from the missing sky region, we prove that the recycling method gives the unique best estimate of the EB-leakage. Compared to the previous method, this method reduces the uncertainties in the BB power spectrum due to EB-leakage by more than one order of magnitude in the most interesting domain of multipoles, where is between 80 and 200. This work also provides a useful guideline for observational design of future CMB experiments.

Section: Conclusion and Discussionsupporting

confidence: 56%

Blind correction of the EB-leakage in the pixel domain

Liu¹,

Creswell²,

Dachlythra³

2019

“…We have described and generalized existing analytical approaches to estimate the covariance matrix for pseudo-C power spectrum estimators [34][35][36], and implemented them in the public code NaMaster [38], making it straightforward to fully account for the effects of survey geometry on the data uncertainties. With these approximation, computationally speaking, the problem of estimating a covariance matrix is as complex as that of computing the power spectrum itself, and scales with the number of pixels in the map as N 3/2 pix .…”

Section: Discussionmentioning

confidence: 99%

Disconnected pseudo-C_ℓ covariances for projected large-scale structure data

García-García

Alonso

Bellini

2019

Self Cite

The disconnected part of the power spectrum covariance matrix (also known as the "Gaussian" covariance) is the dominant contribution on large scales for galaxy clustering and weak lensing datasets. The presence of a complicated sky mask causes non-trivial correlations between different Fourier/harmonic modes, which must be accurately characterized in order to obtain reliable cosmological constraints. This is particularly relevant for galaxy survey data. Unfortunately, an exact calculation of these correlations involves O( 6 max ) operations that become computationally impractical very quickly. We present an implementation of approximate methods to estimate the Gaussian covariance matrix of power spectra involving spin-0 and spin-2 flat-and curved-sky fields, expanding on existing algorithms. These methods achieve an O( 3 max ) scaling, which makes the computation of the covariance matrix as fast as the computation of the power spectrum itself. We quantify the accuracy of these methods on large-scale structure and weak lensing data, making use of a large number of Gaussian but otherwise realistic simulations. We show that, using the approximate covariance matrix, we are able to recover the true posterior distribution of cosmological parameters to high accuracy. We also quantify the shortcomings of these methods, which become unreliable on the very largest scales, as well as for covariance matrix elements involving cosmic shear B modes. The algorithms presented here are implemented in the public code NaMaster https://github.com/LSSTDESC/NaMaster.

“…In the context of pseudo-C estimators this is achieved in practice by obtaining the best-fit value of A syst , subtracting the corresponding best-fit contaminant contribution from the maps and analytically accounting for the associated loss of modes when computing the angular power spectrum. Further details about this method can be found in [54,64]. We must note that star contamination is a special type of contaminant, since it is an additive contribution to the observed galaxy number density n g , not its overdensity.…”

Section: Angular Power Spectramentioning

confidence: 99%

Tomographic galaxy clustering with the Subaru Hyper Suprime-Cam first year public data release

Nicola

Alonso

Sánchez

et al. 2020

Self Cite

101

We analyze the clustering of galaxies in the first public data release of the Hyper Suprime-Cam Subaru Strategic Program. Despite the relatively small footprints of the observed fields, the data are an excellent proxy for the very deep photometric datasets that will be acquired by the Large Synoptic Survey Telescope, and are therefore an ideal test bed for the analysis methods being implemented by the LSST Dark Energy Science Collaboration. We select a magnitude limited sample with i < 24.5 and analyze it in four tomographic redshift bins covering the range 0.15 z 1.5. We carry out a Fourier-space analysis of the two-point clustering of this sample, including all auto-and cross-correlations between bins. We demonstrate the use of map-level deprojection methods to account for non-physical fluctuations in the galaxy number density caused by observational systematics. Through a halo occupation distribution analysis, we place constraints on the characteristic halo masses of this sample as a function of redshift, finding a good fit up to scales k max = 1 Mpc −1 , including both auto-and cross-correlations. Our results show monotonically decreasing average halo masses with increasing redshift, which can be interpreted in terms of the drop-out of red galaxies at high redshifts for a flux-limited sample, consistent with previous analyses. In terms of photometric redshift systematics, we show that additional care is needed in order to marginalize over uncertainties in the redshift distribution in galaxy clustering, even for samples of this small size, and that these uncertainties can be significantly constrained by including cross-bin correlations. We are able to make a ∼ 3σ detection of the effects of lensing magnification in the HSC data. Our results are stable to variations in the amplitude of density fluctuations σ 8 and the cold dark matter abundance Ω c and we find constraints that agree well with measurements from Planck and low-redshift probes. Finally, we use our analysis pipeline to study the clustering of galaxies as a function of limiting flux, and provide a simple fitting function for the linear galaxy bias for magnitude limited samples as a function of limiting magnitude and redshift. Discussion and Conclusions 50A Reconstructing depth from discrete sources 54