Prof. David Alonso

Abstract:

<jats:p>The study of third-order statistics in large-scale structure analyses has been hampered by the increased complexity of bispectrum estimators (compared to power spectra), the large dimensionality of the data vector, and the difficulty in estimating its covariance matrix. In this paper we present the filtered-squared bispectrum (FSB), an estimator of the projected bispectrum effectively consisting of the cross-correlation between the square of a field filtered on a range of scales and the original field. Within this formalism, we are able to recycle much of the infrastructure built around power spectrum measurement to construct an estimator that is both fast and robust against mode-coupling effects caused by incomplete sky observations. Furthermore, we demonstrate that the existing techniques for the estimation of analytical power spectrum covariances can be used within this formalism to calculate the bispectrum covariance at very high accuracy, naturally accounting for the most relevant Gaussian and non-Gaussian contributions in a model-independent manner.</jats:p>

Abstract:

<jats:title>Abstract</jats:title> <jats:p>We present a formalism to extract the angular power spectrum of fields sampled at a finite number of points with arbitrary positions — a common situation for several catalog-based astrophysical probes — through a simple extension of the standard pseudo-<jats:italic>C<jats:sub>ℓ</jats:sub> </jats:italic> algorithm. A key complication in this case is the need to handle the shot noise component of the associated discrete angular mask which, for sparse catalogs, can lead to strong coupling between very different angular scales. We show that this problem can be solved easily by estimating this contribution analytically and subtracting it. The resulting estimator is immune to small-scale pixelization effects and aliasing, and, most notably, unbiased against the contribution from measurement noise uncorrelated between different sources. We demonstrate the validity of the method in the context of cosmic shear datasets, and showcase its usage in the case of other spin-0 and spin-1 astrophysical fields of interest. We incorporate the method in the public <jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://github.com/LSSTDESC/NaMaster" xlink:type="simple">&lt;monospace&gt;NaMaster&lt;/monospace&gt;</jats:ext-link> code.</jats:p>