http://arxiv.org/abs/2105.14489
We measure the dark matter power spectrum amplitude as a function of the overdensity $\delta_W$ in $N$-body simulation subsamples. We show that the response follows a power law form in terms of $(1+\delta_W)$, and we provide a fit in terms of the perturbation theory linear response $R_1$ and the variance $\sigma(L^3)$ of a subvolume of size $L$. Our fit, especially for low overdensities, is more accurate than linear or second order calculation from perturbation theory and can be predicted from cosmological parameters with standard tools. Furthermore, the lognormal nature of the overdensity distribution causes a “super-survey” bias, i.e. the power spectrum amplitude for a subsample with average density is typically underestimated by about $-2\sigma^2$. Although this bias becomes sub-percent above characteristic scales of $200 Mpc h^{-1}$, taking it account improves the accuracy of estimating power spectra from zoom-in simulations and smaller high resolution surveys embedded in larger low resolution volumes.
G. Rácz, I. Szapudi and I. Csabai
Tue, 1 Jun 21
20/72
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