Applying a star formation model calibrated on high-resolution interstellar medium simulations to cosmological simulations of galaxy formation

TL;DR

The paper develops a physics-based subgrid ISM model for cosmological galaxy formation by calibrating a TIGRESS-classic equation of state and a TIGRESS/Schmidt star-formation law against high-resolution ISM simulations. It implements these in isolated disk tests and innovative multi-zoom cosmological simulations to compare against SH and IllustrisTNG prescriptions. The TIGRESS-based models yield substantially thinner gas and stellar disks and a steeper SFR–gas relation, while total stellar masses show limited sensitivity to the EOS thanks to large-scale inflows/outflows and wind feedback. The work demonstrates a pathway to more physically grounded subgrid treatments in large-volume simulations, while identifying birth-velocity and disk-heating effects as important factors for future refinement and companion analyses.

Abstract

Modern high-resolution simulations of the interstellar medium (ISM) have shown that key factors in governing star formation are the competing influences of radiative dissipation, pressure support driven by stellar feedback, and the relentless pull of gravity. Cosmological simulations of galaxy formation, such as IllustrisTNG or ASTRID, are however not able to resolve this physics in detail and therefore need to rely on approximate treatments. These have often taken the form of empirical subgrid models of the ISM expressed in terms of an effective equation of state (EOS) that relates the mean ISM pressure to the mean gas density. Here we seek to improve these heuristic models by directly fitting their key ingredients to results of the high-resolution TIGRESS simulations, which have shown that the dynamical equilibrium of the ISM can be understood in terms of a pressure-regulated, feedback modulated (PRFM) model for star formation. Here we explore a simple subgrid model that draws on the PRFM concept but uses only local quantities. It accurately reproduces PRFM for pure gas disks, while it predicts slightly less star formation than PRFM in the presence of an additional thin stellar disk. We compare the properties of this model with the older Springel and Hernquist and TNG prescriptions, and apply all three to isolated simulations of disk galaxies as well as to a set of high-resolution zoom-in simulations carried out with a novel 'multi-zoom' technique that we introduce in this study. The softer EOS implied by TIGRESS produces substantially thinner disk galaxies, which has important ramifications for disk stability and galaxy morphology. The total stellar mass of galaxies is however hardly modified at low redshift, reflecting the dominating influence of large-scale gaseous inflows and outflows to galaxies, which are not sensitive to the EOS itself

Figures (21)

• Figure 1: The predicted relation (red solid line) between mid-plane pressure and star formation surface density for our TIGRESS/Schmidt model where equation (\ref{['prfmsfrlaw']}) is adopted as 3D star formation law combined with the equation of state model of equation (\ref{['prfmeqs']}). We compare to the power-law fit obtained by Ostriker2022 for the TIGRESS-classic simulations (grey thick line). We also include results when an additional stellar disk is present, and show cases where the gas disk is equal in mass to the stellar disk (blue), or is substantially lighter so that the gas only makes up 10% of the total disk mass (green). In both cases, we consider different ratios of the heights of stellar and gas disks, $H_\star / H_g =1$, 2, and 5, as labelled. Note that this plots shows the mid-plane pressure as a function of prescribed star-formation surface density; the models with different stellar disks exhibit different gas surface densities for a given star formation surface density.
• Figure 2: Top panel: Pressure as a function of hydrogen number density for three different equation-of-state models, SH, TNG, and TIGRESS-classic, as labelled. The vertical dashed line marks the common star formation threshold density adopted for the models. Below this density, the gas energy equation is solved explicitly, subject to normal radiative cooling and heating. The dotted lines mark the pressure for gas at temperature $10^4\,{\rm K}$ that is either fully ionized (upper line) or fully neutral (lower line). Gas at these densities typically has cooled down to this temperature, with an intermediate ionization state, depending on redshift. Bottom panel: Logarithmic slope of the different equations of state. The horizontal dotted line marks the critical slope of $4/3$ below which the Jeans mass becomes smaller with higher density.
• Figure 3: Pressure versus density in the regime around the onset of star formation, with individual cells from simulations with TNG (green) and TIGRESS/Schmidt (red) drawn as small circles. At densities above the star formation threshold (dashed vertical line), the pressure follows the equation of state model. The panel on the left shows the default treatment where the equation of state is sharply switched on at the star formation threshold, whereas the right panel shows our new variant where the pressure of the EOS model is faded in smoothly below the star formation threshold, so that pressure discontinuities can be avoided. In both cases, the star formation threshold is identical.
• Figure 4: Expected scale-height of gas layers in plane-parallel symmetry for the Springel & Hernquist model (blue), the equation of state adopted for IllustrisTNG (green), and the TIGRESS-classic fit. Below the star formation threshold, an isothermal gas at $10^4\,{\rm K}$ is assumed in all three scenarios. The feedback from star formation leads to a thickening of the gaseous layer beyond the isothermal $h_z\propto \Sigma_{\rm gas}^{-1}$ scaling. The dotted line shows the cell size of TNG50 (with mass resolution $m_{\rm gas} = 8.5\times 10^4\,{\rm M}_\odot$) at the corresponding mid-plane gas densities.
• Figure 5: Expected surface density of star formation as a function of gas surface density for the three different EOS models. The star formation threshold induces a cut-off of the star formation at gas densities around $\Sigma_{\rm gas}\simeq 10\,{\rm M}_\odot {\rm pc}^{-2}$, consistent with observations. The TNG model produces a higher star formation rate density as SH due to its thinner scale height, even though the star formation consumption timescale is the same in SH and TNG, modulo at high density, where TNG adopts an accelerated star formation timescale. TIGRESS/Schmidt on the other has a still softer equation of state, and its star formation timescale depends more steeply on density. As a result, the relation between $\Sigma_{\rm SFR}$ and $\Sigma_{\rm gas}$ is notably steeper. The dotted lines in the background are power-law fits, yielding slopes of 1.64, 1.74 and 2.40 for SH, TNG, and TIGRESS/Schmidt, respectively.