An empirical nonlinear power spectrum overdensity-response

Abstract

Context. The overdensity inside a cosmological sub-volume and the tidal fields from its surroundings affect the matter distribution of the region. The resulting difference between the local and global power spectra is characterized by the response function. Aims. Our aim is to provide a new, simple, and accurate formula for the power spectrum overdensity response at highly nonlinear scales based on the results of cosmological simulations and paying special attention to the lognormal nature of the density field. Methods. We measured 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 new fit in terms of the variance, $\sigma (L)$, of a sub-volume of size $L$. Results. Our fit has a similar accuracy and a comparable complexity to second-order standard perturbation theory on large scales, but it is also valid for nonlinear (smaller) scales, where perturbation theory needs higher-order terms for a comparable precision. Furthermore, we show that the lognormal nature of the overdensity distribution causes a previously unidentified bias: the power spectrum amplitude for a subsample with an average density is typically underestimated by about $-2{\sigma }^2$. Although this bias falls to the sub-percent level above characteristic scales of $200Mpc{h}^{-1}$, taking it into account improves the accuracy of estimating power spectra from zoom-in simulations and smaller high-resolution surveys embedded in larger low-resolution volumes.

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