We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the bispectrum, taking advantage of a 2D-FFTlog algorithm. As a preliminary test of its accuracy, we consider the toy model of a spherical window function in real space. This setup provides an analytical evaluation of the 3-point function of the window, and therefore it allows to isolate and quantify possible systematic errors of the method. We find that our implementation of the convolution in terms of a mixing matrix shows differences at the percent level in comparison to the measurements from a very large set of mock halo catalogs. It is also able to recover unbiased constraints on halo bias parameters in a likelihood analysis of a set of numerical simulations with a total volume of 100 h -3 Gpc3. For the level of accuracy required by these tests, the multiplication with the mixing matrix is performed in the time of one second or less.
Bispectrum-window convolution via Hankel transform / Pardede, Kevin; Rizzo, Federico; Biagetti, Matteo; Castorina, Emanuele; Sefusatti, Emiliano; Monaco, Pierluigi. - In: JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS. - ISSN 1475-7516. - 2022:10(2022), pp. 1-36. [10.1088/1475-7516/2022/10/066]
Bispectrum-window convolution via Hankel transform
Pardede, Kevin;Biagetti, Matteo;Castorina, Emanuele;
2022-01-01
Abstract
We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the bispectrum, taking advantage of a 2D-FFTlog algorithm. As a preliminary test of its accuracy, we consider the toy model of a spherical window function in real space. This setup provides an analytical evaluation of the 3-point function of the window, and therefore it allows to isolate and quantify possible systematic errors of the method. We find that our implementation of the convolution in terms of a mixing matrix shows differences at the percent level in comparison to the measurements from a very large set of mock halo catalogs. It is also able to recover unbiased constraints on halo bias parameters in a likelihood analysis of a set of numerical simulations with a total volume of 100 h -3 Gpc3. For the level of accuracy required by these tests, the multiplication with the mixing matrix is performed in the time of one second or less.File | Dimensione | Formato | |
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