A Turbulent Framework for Star Formation in High-Redshift Galaxies

TL;DR

The paper introduces a turbulence-driven analytic framework to model star formation in high-redshift, bursty SFGs that lack clear ISM–CGM boundaries and are not well described by equilibrium disks. It treats halo gas as a supersonically turbulent medium with a lognormal density distribution, where star formation arises from the high-density tail above a threshold, yielding SFRs and radial profiles consistent with FIRE-2 simulations. Calibration against simulations fixes turbulence parameters and validates that the density PDF and density-threshold criterion reproduce observed halo-mass–dependent SFRs, halo sizes, and SFE trends, while predicting modest instantaneous galaxy-scale SFE (~10% or less) despite locally high efficiencies. This turbulence-centric view offers a physically grounded alternative to disk-based models for the bursty, early phases of galaxy formation and provides a framework adaptable to future refinements and broader mass/redshift regimes.

Abstract

Observations of distant galaxies suggest that the physics of galaxy formation at high redshifts differs significantly from later times. In contrast to large, steady disk galaxies like the Milky Way, high-redshift galaxies are often characterized by clumpy, disturbed morphologies and bursty star formation histories. These differences between low-mass, bursty galaxies and higher-mass, steady star-forming galaxies have recently been studied in galaxy formation simulations with resolved multiphase ISM. These simulation studies indicate that while steady disk galaxies can be well-modeled as "equilibrium disks" embedded in a distinct, hot CGM, bursty galaxies are much more dynamic and their star formation occurs in a dispersion-dominated medium that extends to halo scales, with no clear boundary between the ISM and the CGM. We develop an analytic framework to model star formation in bursty galaxies that are not adequately modeled as equilibrium disks. The framework approximates the gas in low-mass halos as a continuous, supersonically turbulent medium with large density fluctuations. Star formation occurs locally in the high-density tail of a roughly lognormal density distribution. This is analogous to turbulent models of star formation in molecular clouds, but here applied on inner CGM scales. By comparing with galaxy formation simulations from the FIRE project, we show that this framework can be used to understand star formation efficiencies and radial profiles in halos. The turbulent framework shows explicitly how the instantaneous galaxy-averaged star formation efficiency can be relatively low even if the local efficiency in dense gas approaches unity.

Figures (17)

• Figure 1: A schematic diagram of the turbulent framework presented in this work. In the early, bursty stage of their formation, low-mass/high-$z$ SFGs do not form stable, rotationally supported gas disks surrounded by a quasi-static hot CGM. Instead, stellar feedback and gas accretion drive strong supersonic turbulence extending out to the host halo, which does not thermalize due to the short cooling times especially the inner half halo where the majority of star formation takes place. In this regime, there is no clear distinction between ISM and CGM flows. Star formation across the halo can thus be approximated by combining the mean gas density profile and the gas density contrast distribution set by the turbulence properties with criteria for star formation in the high-density tail of the distribution.
• Figure 2: The mass fraction of gas above a given density threshold $\rho$ at different halo radii predicted by our analytic model for log-normal density contrast distribution. Marked by the vertical lines are the virial density $\rho_\mathrm{vir}=\Delta_\mathrm{vir}(z)\rho_\mathrm{c}(z)$ at $z=8$ and the critical density $\epsilon_\mathrm{SF}$ above which the SFE per free-fall time jumps from 0 to 1 (corresponding to $n_\mathrm{crit}=10^3\,\mathrm{cm^{-3}}$). Only a small fraction of the total gas mass can form stars and the fraction decreases with the radial distance.
• Figure 3: Gas temperature, number density, and line-of-sight velocity projections of the simulation $\texttt{z5m11h}$ in two snapshots at $z\sim5$ and 6, respectively. For temperature and density, the mass-averaged logarithmic values are shown along each projection, whereas for velocity the linear mass-averaged values are shown. The temperature and density distributions are characterized by large spatial fluctuations. A mixture of cold ($T_\mathrm{gas}<10^3\,$K), warm ($10^3<T_\mathrm{gas}<10^5\,$K), and hot ($T_\mathrm{gas}>10^5\,$K) gas extends to large halo radii, with no clear boundary between the ISM and CGM. The gas motions are characterized by a combination of dispersion and bulk flows, with dynamically subdominant rotation and thermal pressure near the center (see also Fig. \ref{['fig:comp_energetics']}). For reference, contours for the mass surface density of young stars (formed in the past 10 Myr) $\Sigma_{\star, \rm young}=10^4\,M_{\odot}\,\mathrm{kpc}^{-2}$ are overlaid to show the correspondence between cold, dense gas and recent star formation. The black dashed (solid) circles indicate the virial radius (half virial radius) of the galaxy host halos. Most of the star formation occurs in the inner half of the halo (as quantified in Figure \ref{['fig:subhalo_frac']}) owing to the higher average gas densities, but there is no well-defined boundary and some star formation takes place outside this radius.
• Figure 4: Comparison of the thermal energy ($E_\mathrm{therm}$), the total kinetic energy ($E_\mathrm{kin}$) and its three spherical components ($E_{R}$, $E_{z}$, and $E_{\phi}$), and the turbulent energy based on velocity dispersions ($E_\mathrm{turb}$, defined as in Equation (\ref{['eq:Eturb']})) for the halo gas in the simulation $\texttt{z5m11h}$ as a function of halo radius. The average and $1\sigma$ dispersion measured from snapshots over $5<z<6$ are represented by the curves and shaded bands, respectively. Left: gas kinetic energy (the majority of which comes from turbulent motions) dominates over thermal energy across the halo. Right: the gas shows no sign of significant rotational support, i.e., the polar and azimuthal components, $E_{\theta}$ and $E_{\phi}$, never dominates. The three components of kinetic energy are comparable (quasi-isotropic) at small radii, whereas $E_R$ becomes increasingly significant at larger radii, likely as a consequence of turbulence driven by inflows/outflows.
• Figure 5: A comparison of the mass-weighted PDFs of the density contrast $y=\ln{(\rho/\langle \rho \rangle)}$ for gas in different temperature ranges (cold: $T_\mathrm{gas}<10^3\,$K; warm: $10^3<T_\mathrm{gas}<10^5\,$K; hot: $T_\mathrm{gas}>10^5\,$K) at two different halo radii. The PDFs are evaluated using the combination of gas particle data in the corresponding radial bin taken from the 16 snapshots of the simulation z5m11h over $5<z<6$, normalized according to the mass fraction of each temperature range with respect to the total gas mass. Although the PDFs vary across different gas temperatures, the total $P_{M}(y)$ in black can be described as a broad, uni-modal PDF that roughly resembles a log-normal distribution characteristic of supersonic turbulence.