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Towards optimal estimation of the galaxy power spectrum

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posted on 2023-06-09, 02:24 authored by Robert E SmithRobert E Smith, Laura Marian
The galaxy power spectrum encodes a wealth of information about cosmology and the matter fluctuations. Its unbiased and optimal estimation is therefore of great importance. In this paper, we generalize the framework of Feldman et al. (1994) to take into account the fact that galaxies are not simply a Poisson sampling of the underlying dark matter distribution. Besides finite survey-volume effects and flux limits, our optimal estimation scheme incorporates several of the key tenets of galaxy formation: galaxies form and reside exclusively in dark matter haloes; a given dark matter halo may host several galaxies of various luminosities; galaxies inherit part of their large-scale bias from their host halo. Under these broad assumptions, we prove that the optimal weights do not explicitly depend on galaxy luminosity, other than through defining the maximum survey volume and effective galaxy density at a given position. Instead, they depend on the bias associated with the host halo; the first and second factorial moments of the halo occupation distribution; a selection function, which gives the fraction of galaxies that can be observed in a halo of mass M at position {r} in the survey; and an effective number density of galaxies. If one wishes to reconstruct the matter power spectrum, then, provided the model is correct, this scheme provides the only unbiased estimator. The practical challenges with implementing this approach are also discussed.

Funding

TB002-46; Dept P&A

History

Publication status

  • Published

File Version

  • Published version

Journal

Monthly Notices of the Royal Astronomical Society

ISSN

0035-8711

Publisher

Oxford University Press

Issue

2

Volume

454

Page range

1266-1289

Department affiliated with

  • Physics and Astronomy Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-08-05

First Open Access (FOA) Date

2016-08-05

First Compliant Deposit (FCD) Date

2016-08-05

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