How to suppress the shot noise in galaxy surveys

TL;DR

This Letter explores the idea of weighting central halo galaxies by halo mass and finds that the resulting shot noise can be reduced dramatically relative to expectations, with a 10-30 suppression at n[over ] = 4x10(-3) (h/Mpc)(3).

Abstract

Galaxy surveys are one of the most powerful means to extract the cosmological information and for a given volume the attainable precision is determined by the galaxy shot noise sigma_n^2 relative to the power spectrum P. It is generally assumed that shot noise is white and given by the inverse of the number density n. In this paper we argue one may be able to considerably improve upon this: in the halo picture of cosmological structure all of the dark matter is in halos of varying mass and galaxies are formed inside these halos, but for the dark matter mass and momentum conservation guarantee that nonlinear effects cannot develop a white noise in the dark matter power spectrum on large scales. This suggests that with a suitable weighting a similar effect may be achieved for galaxies, suppressing their shot noise. We explore this idea with N-body simulations by weighting central halo galaxies by halo mass and find that the resulting shot noise can be reduced dramatically relative to expectations, with a 10-30 suppression at the highest number density of n=4*10^-3 (Mpc/h)^3 resolved in our simulations. For specific applications other weighting schemes may achieve even better results and for n=3*10^-4(Mpc/h)^3 we can reduce sigma_n^2/P by up to a factor of 10 relative to uniform weighting. These results open up new opportunities to extract cosmological information in galaxy surveys, such as the recently proposed multi-tracer approach to cancel sampling variance, and may have important consequences for the planning of future redshift surveys. Taking full advantage of these findings may require better understanding of galaxy formation process to develop accurate tracers of the halo mass.

Figures (3)

• Figure 1: Shot noise power spectrum $\sigma_n^2$ measured in simulations for uniform weighting of halos in a mass bin and mass threshold, mass weighting and $f(M)=M/(1+(M/10^{14}h^{-1}M_{\odot})^{0.5}$ weighting, for several different abundances, corresponding at $z=0$ to mass thresholds of $4\times 10^{13}h^{-1}M_{\odot}$, $1.4 \times 10^{13}h^{-1}M_{\odot}/h$, $6 \times 10^{12}h^{-1}M_{\odot}$ and $10^{12}h^{-1}M_{\odot}/h$, from the lowest to the highest abundance, respectively. Straight lines (same color/line style) are the expected shot noise $\sigma_e^2$ for each of the weightings (equal for the mass bin and mass threshold with uniform weighting).
• Figure 2: Same as figure \ref{['fig1']}, but for $\sigma_n^2/P$. Also shown are the bias values for the different cases.
• Figure 3: Effects of log-normal scatter $\sigma$ in halo mass observable on the shot noise $\sigma_n^2$ for mass and $f(M)=M/(1+(M/10^{14}h^{-1}M_{\odot})^{0.5})$ weights, for $\bar{n}=3\times 10^{-4}({\rm h/Mpc})^3$ and $\bar{n}=4\times 10^{-3}({\rm h/Mpc})^3$. Scatter hardly affects the bias, so the relative effects of scatter are the same for $\sigma_n^2/P$ and we do not show them here.