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arXiv · 2111.13702

The Information Content of Projected Galaxy Fields

Lucas Porth·Gary M. Bernstein·Robert E. Smith·Abigail J. Lee
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Abstract

The power spectrum of the nonlinearly evolved large-scale mass distribution recovers only a minority of the information available on the mass fluctuation amplitude. We investigate the recovery of this information in 2D "slabs" of the mass distribution averaged over $\approx100$~$h^{-1}$Mpc along the line of sight, as might be obtained from photometric redshift surveys. We demonstrate a Hamiltonian Monte Carlo (HMC) method to reconstruct the non-Gaussian mass distribution in slabs, under the assumption that the projected field is a point-transformed Gaussian random field, Poisson-sampled by galaxies. When applied to the \textit{Quijote} $N$-body suite at $z=0.5$ and at a transverse resolution of 2~$h^{-1}$Mpc, the method recovers $\sim 30$ times more information than the 2D power spectrum in the well-sampled limit, recovering the Gaussian limit on information. At a more realistic galaxy sampling density of $0.01$~$h^3$Mpc$^{-3}$, shot noise reduces the information gain to a factor of 5 improvement over the power spectrum at resolutions of 4~$h^{-1}$Mpc or smaller.

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Lucas Porth, Gary M. Bernstein, Robert E. Smith, Abigail J. Lee. 2022-12-12. The Information Content of Projected Galaxy Fields. https://doi.org/10.1093/mnras%2Fstac3225

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