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Register a new userNeutrinos in N-body simulations
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Caio Bastos De Senna Nascimento
Publication date
2021
fields
Physics
and research's language is
English
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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.
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We present a new method for generating initial conditions for numerical cosmological simulations in which massive neutrinos are treated as an extra set of N-body (collisionless) particles. It allows us to accurately follow the density field for both Cold Dark Matter (CDM) and neutrinos at both high and low redshifts. At high redshifts, the new method is able to reduce the shot noise in the neutrino power spectrum by a factor of more than $10^7$ compared to previous methods, where the power spectrum was dominated by shot noise at all scales. We find that our new approach also helps to reduce the noise on the total matter power spectrum on large scales, whereas on small scales the results agree with previous simulations. Our new method also allows for a systematic study of clustering of the low velocity tail of the distribution function of neutrinos. This method also allows for the study of the evolution of the overall velocity distribution as a function of the environment determined by the CDM field.
Cosmological $N$-body simulations are typically purely run with particles using Newtonian equations of motion. However, such simulations can be made fully consistent with general relativity using a well-defined prescription. Here, we extend the formalism previously developed for $Lambda$CDM cosmologies with massless neutrinos to include the effects of massive, but light neutrinos. We have implemented the method in two different $N$-body codes, CONCEPT and PKDGRAV, and demonstrate that they produce consistent results. We furthermore show that we can recover all appropriate limits, including the full GR solution in linear perturbation theory at the per mille level of precision.
Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for LambdaCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code. This space-time coincides with a simple N-body gauge for z<50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable forwards approach for such cases.
Many barred galaxies harbor small-scale secondary bars in the center. The evolution of such double-barred galaxies is still not well understood, partly because of a lack of realistic N-body models with which to study them. Here we report the generation of such systems in the presence of rotating pseudobulges. We demonstrate with high mass and force resolution collisionless N-body simulations that long-lived secondary bars can form spontaneously without requiring gas, contrary to previous claims. We find that secondary bars rotate faster than primary ones. The rotation is not rigid: the secondary bars pulsate, with their amplitude and pattern speed oscillating as they rotate through the primary bars. This self-consistent study supports previous work based on orbital analysis in the potential of two rigidly rotating bars. We also characterize the density and kinematics of the N-body simulations of the double-barred galaxies, compare with observations to achieve a better understanding of such galaxies. The pulsating nature of secondary bars may have important implications for understanding the central region of double-barred galaxies.
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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