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Register a new userRenormalisation of linear halo bias in N-body simulations
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The interpretation of redshift surveys requires modeling the relationship between large-scale fluctuations in the observed number density of tracers, $delta_mathrm{h}$, and the underlying matter density, $delta$. Bias models often express $delta_mathrm{h}$ as a truncated series of integro-differential operators acting on $delta$, each weighted by a bias parameter. Due to the presence of `composite operators (obtained by multiplying fields evaluated at the same spatial location), the linear bias parameter measured from clustering statistics does not coincide with that appearing in the bias expansion. This issue can be cured by re-writing the expansion in terms of `renormalised operators. After providing a pedagogical and comprehensive review of bias renormalisation in perturbation theory, we generalize the concept to non-perturbative dynamics and successfully apply it to dark-matter haloes extracted from a large suite of N-body simulations. When comparing numerical and perturbative results, we highlight the effect of the window function employed to smooth the random fields. We then measure the bias parameters as a function of halo mass by fitting a non-perturbative bias model (both before and after applying renormalisation) to the cross spectrum $P_{delta_mathrm{h}delta}(k)$. Finally, we employ Bayesian model selection to determine the optimal operator set to describe $P_{delta_mathrm{h}delta}(k)$ for $k<0.2,h$ Mpc$^{-1}$ at redshift $z=0$. We find that it includes $delta, abla^2delta, delta^2$ and the square of the traceless tidal tensor, $s^2$. Considering higher-order terms (in $delta$) leads to overfitting as they cannot be precisely constrained by our data. We also notice that next-to-leading-order perturbative solutions are inaccurate for $kgtrsim 0.1,h$ Mpc$^{-1}$.
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The description of the abundance and clustering of halos for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially yield constraints of order unity on the non-Gaussianity parameter f_{NL}. We present tests on N-body simulations of analytical formulae describing the halo abundance and clustering for non-Gaussian initial conditions. We calibrate the analytic non-Gaussian mass function of Matarrese et al.(2000) and LoVerde et al.(2008) and the analytic description of clustering of halos for non-Gaussian initial conditions on N-body simulations. We find excellent agreement between the simulations and the analytic predictions if we make the corrections delta_c --> delta_c X sqrt{q} and delta_c --> delta_c X q where q ~ 0.75, in the density threshold for gravitational collapse and in the non-Gaussian fractional correction to the halo bias, respectively. We discuss the implications of this correction on present and forecasted primordial non-Gaussianity constraints. We confirm that the non-Gaussian halo bias offers a robust and highly competitive test of primordial non-Gaussianity.
We derive a simple prescription for including beyond-linear halo bias within the standard, analytical halo-model power spectrum calculation. This results in a corrective term that is added to the usual two-halo term. We measure this correction using data from $N$-body simulations and demonstrate that it can boost power in the two-halo term by a factor of $sim2$ at scales $ksim0.7,h Mpc^{-1}$, with the exact magnitude of the boost determined by the specific pair of fields in the two-point function. How this translates to the full power spectrum depends on the relative strength of the one-halo term, which can mask the importance of this correction to a greater or lesser degree, again depending on the fields. Generally we find that our correction is more important for signals that arise from lower-mass haloes. When comparing our calculation to simulated data we find that the under-prediction of power in the transition region between the two- and one-halo terms, which typically plagues halo-model calculations, is almost completely eliminated when including the full non-linear halo bias. We show improved results for the auto and cross spectra of galaxies, haloes and matter. In the specific case of matter-matter or matter-halo power we note that a large fraction of the improvement comes from the non-linear biasing between low- and high-mass haloes. We envisage our model being useful in the analytical modelling of cross correlation signals. Our non-linear bias halo-model code is available at https://github.com/alexander-mead/BNL
In the next decade, cosmological surveys will have the statistical power to detect the absolute neutrino mass scale. N-body simulations of large-scale structure formation play a central role in interpreting data from such surveys. Yet these simulations are Newtonian in nature. We provide a quantitative study of the limitations to treating neutrinos, implemented as N-body particles, in N-body codes, focusing on the error introduced by neglecting special relativistic effects. Special relativistic effects are potentially important due to the large thermal velocities of neutrino particles in the simulation box. We derive a self-consistent theory of linear perturbations in Newtonian and non-relativistic neutrinos and use this to demonstrate that N-body simulations overestimate the neutrino free-streaming scale, and cause errors in the matter power spectrum that depend on the initial redshift of the simulations. For $z_{i} lesssim 100$, and neutrino masses within the currently allowed range, this error is $lesssim 0.5%$, though represents an up to $sim 10%$ correction to the shape of the neutrino-induced suppression to the cold dark matter power spectrum. We argue that the simulations accurately model non-linear clustering of neutrinos so that the error is confined to linear scales.
We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a $rm {Lambda CDM}$ Universe, can be meaningfully identified for galaxy clusters, in the presence of full three-dimensional effects. We use The Dark Sky Simulations and Illustris-TNG dark-matter--only cosmological runs to calculate radial velocity profiles around collapsed structures, extending out to many times the virial radius $R_{200}$. There, the turnaround radius can be unambiguously identified as the largest non-expanding scale around a center of gravity. We find that: (a) Indeed, a single turnaround scale can meaningfully describe strongly non-spherical structures. (b) For halos of masses $M_{200}>10^{13}M_odot$, the turnaround radius $R_{ta}$ scales with the enclosed mass $M_{ta}$ as $M_{ta}^{1/3}$, as predicted by the spherical collapse model. (c) The deviation of $R_{ta}$ in simulated halos from the spherical collapse model prediction is insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when such are present. (d) Halos exhibit a characteristic average density within the turnaround scale. This characteristic density is dependent on cosmology and redshift. For the present cosmic epoch and for concordance cosmological parameters ($Omega_m sim 0.7$; $Omega_Lambda sim 0.3$) turnaround structures exhibit an average matter density contrast with the background Universe of $delta sim 11$. Thus $R_{ta}$ is equivalent to $R_{11}$ -- in a way analogous to defining the virial radius as $R_{200}$ -- with the advantage that $R_{11}$ is shown in this work to correspond to a kinematically relevant scale in N-body simulations.
We perform a series of high-resolution N-body simulations of cosmological structure formation starting from Gaussian and non-Gaussian initial conditions. We adopt the best-fitting cosmological parameters of WMAP (3rd- and 5th-year) and we consider non-Gaussianity of the local type parameterised by 8 different values of the non-linearity parameter F_NL. Building upon previous work based on the Gaussian case, we show that, expressed in terms of suitable variables, the mass function of friends-of-friends haloes is approximately universal (i.e. independent of redshift, cosmology, and matter transfer function) to good precision (nearly 10 per cent) also in non-Gaussian scenarios. We provide fitting formulae for the high-mass end (M>10^13 M_sol/h) of the universal mass function in terms of F_NL, and we also present a non-universal fit in terms of both F_NL and z to be used for applications requiring higher accuracy. In the Gaussian case, we extend our fit to a wider range of halo masses (M>2.4 x 10^10 M_sol/h) and we also provide a consistent fit of the linear halo bias. We show that, for realistic values of F_NL, the matter power-spectrum in non-Gaussian cosmologies departs from the Gaussian one by up to 2 per cent on the scales where the baryonic- oscillation features are imprinted on the 2-point statistics. We confirm the strong k-dependence of the halo bias on large scales (k<0.05 h Mpc^-1) which was already detected in previous studies. However, we find that commonly used parameterisations based on the peak-background split do not provide an accurate description of our simulations which present extra dependencies on the wavenumber, the non-linearity parameter and, possibly, the clustering strength. We provide an accurate fit of the simulation data that can be used as a benchmark for future determinations of F_NL with galaxy surveys.
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