Optimal Representation of the Density Field From Redshift Surveys

Schumacher, Elke (2000) Optimal Representation of the Density Field From Redshift Surveys. MSc(R) thesis, University of Glasgow.

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Abstract

This thesis presents a method to reconstruct the density field in the local universe from flux limited nearly all-sky redshift surveys. As a first application we reconstruct the over-density field in redshift space up to redshifts of 20,000 km s-1 from the PSCz catalogue of [Saunders et al. 2000]. One of the most important issues that needs to be considered for this task is the impact of selection effects. So far no redshift catalogue contains all existing galaxies (up to a certain distance) but a subset that is chosen according to certain selection criteria. Usually the region close to the galactic plane is not observed because it is obscured by the Milky Way, and as the distance increases, more and more galaxies become too faint to be detected, so that at large distances only very luminous galaxies are included in the catalogue. The former selection criterion can be expressed as an angular mask, and the latter is described by the selection function, which can be interpreted as a radial mask. Due to the spherical symmetry of nearly all-sky redshift surveys it is an obvious choice to expand the density (and also the velocity and potential) field using Spherical Harmonics and Spherical Bessel Functions, which are a set of orthonormal basis functions on a completely observed spherical volume. This basis also allows a separation of angular and radial effects, e.g. the distortion due to the peculiar motions, which affects only the radial component. The calculation is complicated by the existence of the angular mask and the selection function. The difficulties arise because the volume is not observed completely, and these basis functions lose their orthogonality. Thus expansion coefficients are not independent. Therefore we construct a new set of basis functions that are orthonormal on the angular and radial masked space. They are linear combinations of the Spherical Harmonics and Spherical Bessel Functions. The method is an extension to three dimensions of the orthonor-malisation procedure of [Gorski 1994]. Due to the orthonormality the expansion coefficients of this basis can be computed independently and for any error analysis they can also be treated as statistically independent, which are both useful properties. The linear relation allows us to transform between the coefficients of the two bases. First of all we need to determine the selection function of the redshift catalogue. Therefore we apply a robust method that is related to the C- -Method of [Lynden-Bell 1971]. This method assumes a universal luminosity function, but makes no assumption about the spatial distribution of the galaxies or the parametric form of the luminosity function. Tests on mock catalogues yield an error in the selection function of 14% up to redshifts of 30,000 km s-1. The comparison of the derived selection function with the data of the PSCz catalogue shows a good agreement in the range of these uncertainties up to redshifts of 20,000 km s-1. We reconstruct the overdensity field in redshift space up to redshifts of 20,000 km s-1. The procedure involves the inversion of a large matrix, hence we invert the matrix via Singular Value Decomposition and apply a linear regularisation method. We tested the influence of the choice of the maximum redshift and of the truncation in the expansion series and did not find the results sensitive to them. We also replaced our selection function with the one of [Saunders et al. 2000], but only the amplitude of the density peaks was slightly affected. We find our reconstructed overdensity field in a good agreement with the data, and also with other recent results. In the final chapter we outline how the derived redshift space density field can be trans-formed to real space and how the results can be applied e.g. for power spectrum estimation.

Item Type: Thesis (MSc(R))
Qualification Level: Masters
Additional Information: Adviser: Martin Hendry
Keywords: Astronomy
Date of Award: 2000
Depositing User: Enlighten Team
Unique ID: glathesis:2000-76223
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 19 Nov 2019 16:26
Last Modified: 19 Nov 2019 16:26
URI: http://theses.gla.ac.uk/id/eprint/76223

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