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Register a new userNumerical convergence of hydrodynamical simulations of galaxy formation: the abundance and internal structure of galaxies and their cold dark matter haloes
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Aaron D. Ludlow
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We address the issue of numerical convergence in cosmological smoothed particle hydrodynamics simulations using a suite of runs drawn from the EAGLE project. Our simulations adopt subgrid models that produce realistic galaxy populations at a fiducial mass and force resolution, but systematically vary the latter in order to study their impact on galaxy properties. We provide several analytic criteria that help guide the selection of gravitational softening for hydrodynamical simulations, and present results from runs that both adhere to and deviate from them. Unlike dark matter-only simulations, hydrodynamical simulations exhibit a strong sensitivity to gravitational softening, and care must be taken when selecting numerical parameters. Our results--which focus mainly on star formation histories, galaxy stellar mass functions and sizes--illuminate three main considerations. First, softening imposes a minimum resolved escape speed, $v_epsilon$, due to the binding energy between gas particles. Runs that adopt such small softening lengths that $v_epsilon gt 10,{rm km s^{-1}}$ (the sound speed in ionised $sim 10^4,{rm K}$ gas) suffer from reduced effects of photo-heating. Second, feedback from stars or active galactic nuclei may suffer from numerical over-cooling if the gravitational softening length is chosen below a critical value, $epsilon_{rm eFB}$. Third, we note that small softening lengths exacerbate the segregation of stars and dark matter particles in halo centres, often leading to the counter-intuitive result that galaxy sizes {em increase} as softening is reduced. The structure of dark matter haloes in hydrodynamical runs respond to softening in a way that reflects the sensitivity of their galaxy populations to numerical parameters.
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We study the impact of numerical parameters on the properties of cold dark matter haloes formed in collisionless cosmological simulations. We quantify convergence in the median spherically-averaged circular velocity profiles for haloes of widely varying particle number, as well as in the statistics of their structural scaling relations and mass functions. In agreement with prior work focused on single haloes, our results suggest that cosmological simulations yield robust halo properties for a wide range of gravitational softening parameters, $epsilon$, provided: 1) $epsilon$ is not larger than a convergence radius, $r_{rm conv}$, which is dictated by 2-body relaxation and determined by particle number, and 2) a sufficient number of timesteps are taken to accurately resolve particle orbits with short dynamical times. Provided these conditions are met, median circular velocity profiles converge to within $approx 10$ per cent for radii beyond which the local 2-body relaxation timescale exceeds the Hubble time by a factor $kappaequiv t_{rm relax}/t_{rm H}gt 0.177$, with better convergence attained for higher $kappa$. We provide analytic estimates of $r_{rm conv}$ that build on previous attempts in two ways: first, by highlighting its explicit (but weak) softening-dependence and, second, by providing a simpler criterion in which $r_{rm conv}$ is determined entirely by the mean inter-particle spacing, $l$; for example, better than $10$ per cent convergence in circular velocity for $rgt 0.05,l$. We show how these analytic criteria can be used to assess convergence in structural scaling relations for dark matter haloes as a function of their mass or maximum circular speed.
We use cosmological hydrodynamical galaxy formation simulations from the NIHAO project to investigate the response of cold dark matter (CDM) haloes to baryonic processes. Previous work has shown that the halo response is primarily a function of the ratio between galaxy stellar mass and total virial mass, and the density threshold above which gas is eligible to form stars, $n [{rm cm}^{-3}]$. At low $n$ all simulations in the literature agree that dwarf galaxy haloes are cuspy, but at high $nge 100$ there is no consensus. We trace halo contraction in dwarf galaxies with $nge 100$ reported in some previous simulations to insufficient spatial resolution. Provided the adopted star formation threshold is appropriate for the resolution of the simulation, we show that the halo response is remarkably stable for $nge 5$, up to the highest star formation threshold that we test, $n=500$. This free parameter can be calibrated using the observed clustering of young stars. Simulations with low thresholds $nle 1$ predict clustering that is too weak, while simulations with high star formation thresholds $nge 5$, are consistent with the observed clustering. Finally, we test the CDM predictions against the circular velocities of nearby dwarf galaxies. Low thresholds predict velocities that are too high, while simulations with $nsim 10$ provide a good match to the observations. We thus conclude that the CDM model provides a good description of the structure of galaxies on kpc scales provided the effects of baryons are properly captured.
Dark matter-only simulations are able to produce the cosmic structure of a $Lambda$CDM universe, at a much lower computational cost than more physically motivated hydrodynamical simulations. However, it is not clear how well smaller substructure is reproduced by dark matter-only simulations. To investigate this, we directly compare the substructure of galaxy clusters and of surrounding galaxy groups in hydrodynamical and dark matter-only simulations. We utilise TheThreeHundred project, a suite of 324 simulations of galaxy clusters that have been simulated with hydrodynamics, and in dark matter-only. We find that dark matter-only simulations underestimate the number density of galaxies in the centres of groups and clusters relative to hydrodynamical simulations, and that this effect is stronger in denser regions. We also look at the phase space of infalling galaxy groups, to show that dark matter-only simulations underpredict the number density of galaxies in the centres of these groups by about a factor of four. This implies that the structure and evolution of infalling groups may be different to that predicted by dark matter-only simulations. Finally, we discuss potential causes for this underestimation, considering both physical effects, and numerical differences in the analysis.
Self-gravitating astronomical objects often show a central plateau in the density profile (core) whose physical origin is hotly debated. Cores are theoretically expected in N-body systems of maximum entropy, however, they are not present in the canonical N-body numerical simulations of cold dark matter (CDM). Our work shows that despite this apparent contradiction between theory and numerical simulations, they are fully consistent. Simply put, cores are characteristic of systems in thermodynamic equilibrium, but thermalizing collisions are purposely suppressed in CDM simulations. When collisions are allowed, N-body numerical simulations develop cored density profiles, in perfect agreement with the theoretical expectation. We compare theory and two types of numerical simulations: (1) when DM particles are self-interacting (SIDM) with enough cross-section, then the effective two-body relaxation timescale becomes shorter than the Hubble time resulting in cored DM haloes. The haloes thus obtained, with masses from dwarf galaxies to galaxy clusters, collapse to a single shape after normalization, and this shape agrees with the polytropic density profile theoretically expected. (2) The inner radii in canonical N-body numerical simulations are always discarded because the use of finite-mass DM particles artificially increases the two-body collision rate. We show that the discarded radii develop cores that are larger than the employed numerical softening and have polytropic shapes independently of halo mass. Our work suggests that the presence of cores in simulated (or observed) density profiles can used as evidence for systems in thermodynamic equilibrium.
A cutoff in the linear matter power spectrum at dwarf galaxy scales has been shown to affect the abundance, formation mechanism and age of dwarf haloes and their galaxies at high and low redshift. We use hydrodynamical simulations of galaxy formation within the ETHOS framework in a benchmark model that has such a cutoff, and that has been shown to be an alternative to the cold dark matter (CDM) model that alleviates its dwarf-scale challenges. We show how galaxies in this model form differently to CDM on a halo-by-halo basis, at redshifts $zge6$. We show that ETHOS haloes at the half-mode mass scale form with 50~per~cent less mass than their CDM counterparts due to their later formation times, yet they retain more of their gas reservoir due to the different behaviour of gas and dark matter during the monolithic collapse of the first haloes in models with a galactic-scale cutoff. As a result, galaxies in ETHOS haloes near the cutoff scale grow rapidly between $z=10-6$ and by $z=6$ end up having very similar stellar masses, higher gas fractions and higher star formation rates relative to their CDM counterparts. We highlight these differences by making predictions for how the number of galaxies with old stellar populations is suppressed in ETHOS for both $z=6$ galaxies and for gas-poor Local Group fossil galaxies. Interestingly, we find an age gradient in ETHOS between galaxies that form in high and low density environments.
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