The THESAN-ZOOM project: Star formation efficiency from giant molecular clouds to galactic scale in high-redshift starbursts

TL;DR

This study uses the THESAN-ZOOM cosmological zoom-in simulations to connect galaxy-scale and cloud-scale star formation efficiencies (SFEs) in high-redshift starbursts. It finds that the galaxy-scale SFE scales as $\langle \epsilon^{\rm gal}_{\rm ff} \rangle \propto M_{\rm h}^{1/3}(1+z)^{1/2} \sim V_{\rm vir}$, consistent with feedback-regulated models, while GMCs exhibit universal properties (mass function, size, turbulence, surface density) across environments, with a nearly constant GMC gas surface density $\Sigma_{\rm GMC} \approx 70\ M_{\odot}\,{\rm pc}^{-2}$. The cloud-scale SFE is modest ($\sim$2–3%) in fiducial runs and rises when early feedback is removed, and the global Kennicutt–Schmidt relation is largely determined by the GMC mass fraction in the ISM. A key link between scales is that the global depletion time $t_{\rm dep}$ can be written as $t_{\rm dep} = \langle t^{\rm GMC}_{\rm ff} \rangle / (\langle \epsilon^{\rm GMC}_{\rm ff} \rangle f_{\rm GMC})$, showing that GMC abundance dominates global star formation efficiency, with DM-dominated GMCs potentially arising at very high redshift ($z\gtrsim 8$) though not consistently suppressing feedback. Overall, the results highlight a quasi-universal cloud-scale star formation efficiency and reveal how GMC properties mediate the connection to galaxy-scale regulation, while pointing to the nuanced role of dark matter in extreme early epochs.

Abstract

Star formation in galaxies is inherently complex, involving the interplay of physical processes over a hierarchy of spatial scales. In this work, we investigate the connection between global (galaxy-scale) and local (cloud-scale) star formation efficiencies (SFEs) at high redshifts ($z\gtrsim 3$), using the state-of-the-art cosmological zoom-in simulation suite THESAN-ZOOM. We find that the galaxy-scale average SFE, $\langle ε^{\rm gal}_{\rm ff} \rangle$, scales with $M_{\rm halo}^{1/3}\,(1+z)^{1/2} \sim V_{\rm vir}$, consistent with expectations from feedback-regulated models. On cloud scales, we identify giant molecular clouds (GMCs) in a broad sample of high-redshift starbursts spanning a wide range of halo masses and redshifts. Star formation in these systems is predominantly hosted by filamentary GMCs embedded in a dense and highly turbulent interstellar medium (ISM). GMCs exhibit remarkably universal properties, including mass function, size, turbulence, and surface density, regardless of the environment in which they are identified. The global gas depletion time (and the Kennicutt-Schmidt relation) is determined by the GMC mass fraction in the ISM, while the cloud-scale SFE shows little variation. In particular, we find a nearly constant gas surface density of $Σ_{\rm GMC} \approx 70\,{\rm M}_{\odot}\,{\rm pc}^{-2}$ across different host galaxies. Nevertheless, we identify two regimes where phases with high SFE can arise. First, stars may form efficiently in the shock fronts generated by feedback from a preceding starburst. Second, the increasing background dark matter surface density with redshift may contribute to the gravitational potential of clouds at $z \gtrsim 8$ and confine them in high-SFE phases over extended periods.

Figures (22)

• Figure 1: Examples of selected starbursts from the main target galaxies in thesan-zoom. Their dynamical evolution is shown with lines, and the starburst phases are marked by discrete data points. Starburst segments are defined as periods exhibiting a local peak in SFR within a duration of one dynamical time, $t_{\rm dyn}$. The marker shape indicates the highest resolution available for each target (circles for 4x, squares for 8x, and stars for 16x). Due to the limited dynamical range of the thesan-zoom simulations, no starbursts in our sample fully satisfy the conditions for the FFB regime (blue dashed lines). In the inset panel, we show the normalized SFHs, $\mathrm{SFR}(t/t_{\rm dyn})/\mathrm{SFR}(t/t_{\rm dyn}=-0.5)$, for starbursts in three different regimes to illustrate the selection criteria. The dashed lines represent the median normalized SFH in each bin, while the shaded regions indicate the $1\sigma$ galaxy-to-galaxy scatter.
• Figure 2: A visualization of a thesan-zoom galaxy ("m11.1") at $z \simeq 6$ across multiple spatial scales. The left panel shows the surface density of neutral and molecular gas across the entire galaxy within a field of view of $0.5\,R_{\mathrm{vir}}$, corresponding to the spatial scale at which the global SFE is measured. The orange square marks the central kpc-scale region, which is further examined in the top right panels, where the KS relation is expected to hold. There, we show the neutral gas surface density hosting the GMCs (indicated by dashed circles) and the stellar UV emission tracing young stellar objects (YSOs). The radius of each circle corresponds to the effective radius of the GMC, as defined in Eq. \ref{['eq:gmc_r']}. The bottom panel provides a zoomed-in view of a representative GMC with $\alpha \simeq 3$, showing the relative velocity field of the surrounding gas and its mean temperature. CloudPhinder successfully identifies cold, dense ISM structures consistent with GMCs.
• Figure 3: Top panels: Multi-scale SFE manifested in the SFE versus the critical number density of thesan-zoom galaxies from selected redshift and halo mass bins. For each bin, we combine snapshots within $t_{\rm dyn}$ around the starburst peak and integrate all cool gas cells ($T<10^5 \,{\rm K}$) to measure the SFE of gas above a certain number density. The dashed lines represent the mass-weighted average multi-scale SFE within each bin, while the triangles mark the point where 50% of gas mass is enclosed. The shaded contours illustrate the snapshot-to-snapshot variation, enclosing the $10^{\rm th}$–$90^{\rm th}$ percentile range of the multi-scale SFE values during the corresponding starburst periods. The gray shaded region on the right corresponds to densities above the median density of star-forming gas. Since the cell-level SFE for these star-forming gas is hardcoded to unity, this regime serves as a reference for the unresolved limit. Results from all bins trace a similar pattern where the SFE remains steady due to self-regulation, then gradually increases as self-regulation begins to fail, until it reaches a numerical limit and approaches unity as only star-forming gas cells are included. Lower panels: Average ISM density distribution of galaxies in each bin. The mean density for each bin is indicated by a vertical line at the bottom, color-coded consistently with the corresponding distribution. Each follows a log-normal profile. The median density rises with increasing redshift and exhibits a modest upward trend with halo mass.
• Figure 4: Left panel: Distribution of starburst samples in the redshift–halo mass plane, color-coded by the galaxy-scale average SFE. For each starburst, we compute the median SFE within $t_{\rm dyn}$ and use it as the representative value. The color of each square denotes the median SFE within that bin, while the square size reflects the number of starbursts in the bin. Dashed lines indicate analytical predictions derived from the right panel for four reference values of virial velocity. Right panel: Galaxy-scale average SFE as a function of virial velocity. The blue dashed line shows the median relation, with the shaded region indicating the $1\sigma$ scatter. The red dotted line marks the scaling relation, $\epsilon_{\rm ff} \propto V_{\rm vir}$. Both panels illustrate that galaxy-scale SFE increases with redshift and halo mass, roughly scaling with virial velocity.
• Figure 5: GMC mass functions across different redshifts and halo masses. The solid line is the median value across all starbursts with more than 50 clouds in this bin, while the shaded areas enclose the $10^{\rm th}$-$90^{\rm th}$ range. The red star indicates the median mass of the entire GMC sample, which is approximately $1 \times 10^5\,{\,\rm M_\odot}$. The gray dashed lines mark our resolution limit (30 gas elements). Compared with observations of GMCs in the Milky Way Rice2016, high-mass GMCs at high redshift in thesan-zoom are noticeably less abundant, and the mass function exhibits a steeper slope. Note that the minimum mass covered by observational constraints coincides with the simulation resolution limit.