Michael Y. Grudić

FIRE-2 Simulations: Physics versus Numerics in Galaxy Formation

The Feedback In Realistic Environments (FIRE) project explores feedback in cosmological galaxy formation simulations. Previous FIRE simulations used an identical source code (“FIRE-1”) for consistency. Motivated by the development of more accurate numerics – including hydrodynamic solvers, gravitational softening, and supernova coupling algorithms – and exploration of new physics (e.g. magnetic fields), we introduce “FIRE-2”, an updated numerical implementation of FIRE physics for the GIZMO code. We run a suite of simulations and compare against FIRE-1: overall, FIRE-2 improvements do not qualitatively change galaxy-scale properties. We pursue an extensive study of numerics versus physics. Details of the star-formation algorithm, cooling physics, and chemistry have weak effects, provided that we include metal-line cooling and star formation occurs at higher-than-mean densities. We present new resolution criteria for high-resolution galaxy simulations. Most galaxy-scale properties are robust to numerics we test, provided: (1) Toomre masses are resolved; (2) feedback coupling ensures conservation, and (3) individual supernovae are time-resolved. Stellar masses and profiles are most robust to resolution, followed by metal abundances and morphologies, followed by properties of winds and circum-galactic media (CGM). Central (∼kpc) mass concentrations in massive (>L*) galaxies are sensitive to numerics (via trapping/recycling of winds in hot halos). Multiple feedback mechanisms play key roles: supernovae regulate stellar masses/winds; stellar mass-loss fuels late star formation; radiative feedback suppresses accretion onto dwarfs and instantaneous star formation in disks. We provide all initial conditions and numerical algorithms used.

When Feedback Fails: The Scaling and Saturation of Star Formation Efficiency

We present a suite of 3D multiphysics MHD simulations following star formation in isolated turbulent molecular gas discs ranging from 5 to 500 parsecs in radius. These simulations are designed to survey the range of surface densities between those typical of Milky Way giant molecular clouds (GMCs) (∼10^2M⊙pc^(−2)) and extreme ultraluminous infrared galaxy environments (∼10^4M⊙pc^(−2)) so as to map out the scaling of the cloud-scale star formation efficiency (SFE) between these two regimes. The simulations include prescriptions for supernova, stellar wind, and radiative feedback, which we find to be essential in determining both the instantaneous per-freefall (e_(ff)) and integrated (e_(int)) star formation efficiencies. In all simulations, the gas discs form stars until a critical stellar surface density has been reached and the remaining gas is blown out by stellar feedback. We find that surface density is a good predictor of e_(int), as suggested by analytic force balance arguments from previous works. SFE eventually saturates to ∼1 at high surface density. We also find a proportional relationship between e_(ff) and e_(int), implying that star formation is feedback-moderated even over very short time-scales in isolated clouds. These results have implications for star formation in galactic discs, the nature and fate of nuclear starbursts, and the formation of bound star clusters. The scaling of e_(ff) with surface density is not consistent with the notion that e_(ff) is always ∼ 1 per cent on the scale of GMCs, but our predictions recover the ∼ 1 per cent value for GMC parameters similar to those found in spiral galaxies, including our own.

Formation of globular cluster candidates in merging proto-galaxies at high redshift: a view from the FIRE cosmological simulations

Using a state-of-the-art cosmological simulation of merging proto-galaxies at high redshift from the FIRE project, with explicit treatments of star formation and stellar feedback in the interstellar medium, we investigate the formation of star clusters and examine one of the formation hypotheses of present-day metal-poor globular clusters. We find that frequent mergers in high-redshift proto-galaxies could provide a fertile environment to produce long-lasting bound star clusters. The violent merger event disturbs the gravitational potential and pushes a large gas mass of ≳ 10^(5–6) M⊙ collectively to high density, at which point it rapidly turns into stars before stellar feedback can stop star formation. The high dynamic range of the reported simulation is critical in realizing such dense star-forming clouds with a small dynamical time-scale, t_(ff)≲ 3 Myr, shorter than most stellar feedback time-scales. Our simulation then allows us to trace how clusters could become virialized and tightly bound to survive for up to ∼420 Myr till the end of the simulation. Because the clusters tightly bound core was formed in one short burst, and the nearby older stars originally grouped with the cluster tend to be preferentially removed, at the end of the simulation the cluster has a small age spread.

From the top down and back up again: star cluster structure from hierarchical star formation

Young massive star clusters spanning ~104-108M⊙ in mass have been observed to have similar surface brightness profiles. We show that recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that initial profiles of finite maximum density will tend to produce successively shallower power-law profiles under hierarchical merging, owing to certain conservation constraints on the phase-space distribution. We perform N-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically clustered mass distribution constructed from an idealized fragmentation model. Assuming only power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus, we bolster the physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This could have important implications for the structure and dynamics of nascent globular clusters.

Universal scaling relations in scale-free structure formation

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution dN/dM ∝ M^(−2) which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters, and even dark matter haloes. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to M^(−2) and a column density distribution with a power-law tail of dA/dln Σ ∝ Σ^(−1). In the case where structure formation is controlled by gravity the two-point correlation becomes ξ2D ∝ R^(−1). Furthermore, structures formed by such processes (e.g. young star clusters, DM haloes) tend to a ρ ∝ R^(−3) density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation, and detailed ‘full physics’ hydrodynamical simulations. We find that these power laws are good first-order descriptions in all cases.

Isothermal Fragmentation: Is there a low-mass cut-off?

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo monolithic collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating monolithic collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number M_(infall) ∼ √GM/(Rc^2_s ), equivalent to the number of Jeans masses in the initial cloud NJ. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if M_(infall) ≫ 1, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass.