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Recent observations with the James Webb Space Telescope (JWST) have uncovered unexpectedly high cosmic star formation activity in the early Universe, mere hundreds of millions of years after the Big Bang. These observations are often understood to reflect an evolutionary shift in star formation efficiency (SFE) caused by changing galactic conditions during these early epochs. We present FIREbox-HR, a high-resolution, cosmological hydrodynamical simulation from the Feedback in Realistic Environments project, which offers insights into the SFE of galaxies during the first billion years of cosmic time. FIREbox-HR re-simulates the cosmic volume (L = 22.1 cMpc) of the original FIREbox run with eight times higher mass resolution (m_b ~ 7800 M_sun), but with identical physics, down to z ~ 6. FIREbox-HR predicts ultraviolet (UV) luminosity functions in good agreement with available observational data. The simulation also successfully reproduces the observed cosmic UV luminosity density at z ~ 6 - 14, demonstrating that relatively high star formation activity in the early Universe is a natural outcome of the baryonic processes encoded in the FIRE-2 model. According to FIREbox-HR, the SFE - halo mass relation for intermediate mass halos (M_halo ~ 10^9 - 10^11 M_sun) does not significantly evolve with redshift and is only weakly mass-dependent. These properties of the SFE - halo mass relation lead to a larger contribution from lower mass halos at higher z, driving the gradual evolution of the observed cosmic UV luminosity density. A theoretical model based on the SFE - halo mass relation inferred from FIREbox-HR allows us to explore implications for galaxy evolution. Future observations of UV faint galaxies at z > 12 will provide an opportunity to further test these predictions and deepen our understanding of star formation during Cosmic Dawn., Comment: 28 pages, 14 figures, 5 tables, revised to match version accepted by MNRAS, Appendix D added, UV LF shown in Fig. 1 provided as txt file

Synchrotron emission is one of few observable tracers of galactic magnetic fields (\textbf{B}) and cosmic rays (CRs). Much of our understanding of \textbf{B} in galaxies comes from utilizing synchrotron observations in conjunction with several simplifying assumptions of equipartition models, however it remains unclear how well these assumptions hold, and what \textbf{B} these estimates physically represent. Using FIRE simulations which self consistently evolve CR proton, electron, and positron spectra from MeV to TeV energies, we present the first synthetic synchrotron emission predictions from simulated L$_{*}$ galaxies with "live" spectrally-resolved CR-MHD. We find that synchrotron emission can be dominated by relatively cool and dense gas, resulting in equipartition estimates of \textbf{B} with fiducial assumptions underestimating the "true" \textbf{B} in the gas that contributes the most emission by factors of 2-3 due to small volume filling factors. Motivated by our results, we present an analytic framework that expands upon equipartition models for estimating \textbf{B} in a multi-phase medium. Comparing our spectrally-resolved synchrotron predictions to simpler spectral assumptions used in galaxy simulations with CRs, we find that spectral evolution can be crucial for accurate synchrotron calculations towards galactic centers, where loss terms are large., Comment: 10 pages, 5 figures (with 3 additional figures in the Appendix). Accepted version (MNRAS December 21, 2023)

We study the kinematics of stars both at their formation and today within 14 Milky Way (MW)-mass galaxies from the FIRE-2 cosmological zoom-in simulations. We quantify the relative importance of cosmological disk settling and post-formation dynamical heating. We identify three eras: a Pre-Disk Era (typically >8 Gyr ago), when stars formed on dispersion-dominated orbits; an Early-Disk Era (~ 8 - 4 Gyr ago), when stars started to form on rotation-dominated orbits but with high velocity dispersion, sigma_form; and a Late-Disk Era (< 4 Gyr ago), when stars formed with low sigma_form. sigma_form increased with time during the Pre-Disk Era, peaking ~ 8 Gyr ago, then decreased throughout the Early-Disk Era as the disk settled and remained low throughout the Late-Disk Era. By contrast, the velocity dispersion measured today, sigma_now, increases monotonically with age because of stronger post-formation heating for Pre-Disk stars. Importantly, most of sigma_now was in place at formation, not added post-formation, for stars younger than ~ 10 Gyr. We compare the evolution of the three velocity components: at all times, sigma_R,form > sigma_phi,form > sigma_Z,form. Post-formation heating primarily increased sigma_R at ages < 4 Gyr but acted nearly isotropically for older stars. The kinematics of young stars in FIRE-2 broadly agree with the range observed across the MW, M31, M33, and PHANGS-MUSE galaxies. The lookback time that the disk began to settle correlates with its dynamical state today: earlier-settling galaxies currently form colder disks. Including stellar cosmic-ray feedback does not significantly change disk rotational support at fixed stellar mass., Comment: 23 pages, accepted for publication in MNRAS

This paper presents a systematic study of the photoionization and thermodynamic properties of the cool circumgalactic medium (CGM) as traced by rest-frame ultraviolet absorption lines around 26 galaxies at redshift $z\lesssim1$. The study utilizes both high-quality far-ultraviolet and optical spectra of background QSOs and deep galaxy redshift surveys to characterize the gas density, temperature, and pressure of individual absorbing components and to resolve their internal non-thermal motions. The derived gas density spans more than three decades, from $\log (n_{\rm H}/{\rm cm^{-3}}) \approx -4$ to $-1$, while the temperature of the gas is confined in a narrow range of $\log (T/{\rm K})\approx 4.3\pm 0.3$. In addition, a weak anti-correlation between gas density and temperature is observed, consistent with the expectation of the gas being in photoionization equilibrium. Furthermore, decomposing the observed line widths into thermal and non-thermal contributions reveals that more than 30% of the components at $z\lesssim 1$ exhibit line widths driven by non-thermal motions, in comparison to $<20$% found at $z\approx 2$-3. Attributing the observed non-thermal line widths to intra-clump turbulence, we find that massive quenched galaxies on average exhibit higher non-thermal broadening/turbulent energy in their CGM compared to star-forming galaxies at $z\lesssim 1$. Finally, strong absorption features from multiple ions covering a wide range of ionization energy (e.g., from Mg II to O IV) can be present simultaneously in a single absorption system with kinematically aligned component structure, but the inferred pressure in different phases may differ by a factor of $\approx 10$., Comment: 16 pages, 4 figures, 1 table, accepted for publication in MNRAS

The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium (ISM) conditions, but the details of this mapping from galactic to cluster scales are poorly understood due to the large dynamic range involved in galaxy and star cluster formation. We introduce a new method for modeling cluster formation in galaxy simulations: mapping giant molecular clouds (GMCs) formed self-consistently in a FIRE-2 MHD galaxy simulation onto a cluster population according to a GMC-scale cluster formation model calibrated to higher-resolution simulations, obtaining detailed properties of the galaxy's star clusters in mass, metallicity, space, and time. We find $\sim 10\%$ of all stars formed in the galaxy originate in gravitationally-bound clusters overall, and this fraction increases in regions with elevated $\Sigma_{\rm gas}$ and $\Sigma_{\rm SFR}$, because such regions host denser GMCs with higher star formation efficiency. These quantities vary systematically over the history of the galaxy, driving variations in cluster formation. The mass function of bound clusters varies -- no single Schechter-like or power-law distribution applies at all times. In the most extreme episodes, clusters as massive as $7\times 10^6 M_\odot$ form in massive, dense clouds with high star formation efficiency. The initial mass-radius relation of young star clusters is consistent with an environmentally-dependent 3D density that increases with $\Sigma_{\rm gas}$ and $\Sigma_{\rm SFR}$. The model does not reproduce the age and metallicity statistics of old ($>11\rm Gyr$) globular clusters found in the Milky Way, possibly because it forms stars more slowly at $z>3$., Comment: Accepted to MNRAS

We analyze the first giant molecular cloud (GMC) simulation to follow the formation of individual stars and their feedback from jets, radiation, winds, and supernovae, using the STARFORGE framework in the GIZMO code. We evolve the GMC for $\sim 9 \rm Myr$, from initial turbulent collapse to dispersal by feedback. Protostellar jets dominate feedback momentum initially, but radiation and winds cause cloud disruption at $\sim 8\%$ star formation efficiency (SFE), and the first supernova at $8.3 \rm Myr$ comes too late to influence star formation significantly. The per-freefall SFE is dynamic, accelerating from 0 to $\sim 18\%$ before dropping quickly to <1%, but the estimate from YSO counts compresses it to a narrower range. The primary cluster forms hierarchically and condenses to a brief ($\sim 1\,\mathrm{Myr}$) compact ($\sim 1 \rm pc$) phase, but does not virialize before the cloud disperses, and the stars end as an unbound expanding association. The initial mass function resembles the Chabrier (2005) form with a high-mass slope $\alpha=-2$ and a maximum mass of $55 M_\odot$. Stellar accretion takes $\sim 400 \rm kyr$ on average, but $\gtrsim 1\rm Myr$ for $>10 M_\odot$ stars, so massive stars finish growing latest. The fraction of stars in multiples increases as a function of primary mass, as observed. Overall, the simulation much more closely resembles reality, compared to variations which neglect different feedback physics entirely. But more detailed comparison with synthetic observations is necessary to constrain the theoretical uncertainties., Comment: Accepted for publication in MNRAS. 17 pages, 10 figures. Comments welcome. Some data products and plotting code available at https://github.com/mikegrudic/StarforgeFullPhysics. Visit http://www.starforge.space to learn more about the STARFORGE Project. Simulation movie available at http://www.starforge.space/M2e4_fullphysics_flyaround.mp4

Cosmic rays (CRs) are an important component in the interstellar medium (ISM), but their effect on the dynamics of the disk-halo interface (< 10 kpc from the disk) is still unclear. We study the influence of CRs on the gas above the disk with high-resolution FIRE-2 cosmological simulations of late-type Lstar galaxies at redshift around zero. We compare runs with and without CR feedback (with constant anisotropic diffusion around 3e29 cm^2/s and streaming). Our simulations capture the relevant disk halo interactions, including outflows, inflows, and galactic fountains. Extra-planar gas in all of the runs satisfies dynamical balance, where total pressure balances the weight of the overlying gas. While the kinetic pressure from non-uniform motion (>1-kpc scale) dominates in the midplane, thermal and bulk pressures (or CR pressure if included) take over at large heights. We find that with CR feedback, (1) the warm (1e4K) gas is slowly accelerated by CRs; (2) the hot (> 5e5K) gas scale height is suppressed; (3) the warm-hot (2e4-5e5K) medium becomes the most volume-filling phase in the disk-halo interface. We develop a novel conceptual model of the near-disk gas dynamics in low-redshift Lstar galaxies: With CRs, the disk-halo interface is filled with CR-driven warm winds and hot super-bubbles that are propagating into the CGM with a small fraction falling back to the disk. Without CRs, most outflows from hot superbubbles are trapped by the existing hot halo and gravity, so typically they form galactic fountains., Comment: 21 pages, 15 figures. Accepted for publication by MNRAS

We present STARFORGE (STAR FORmation in Gaseous Environments): a new numerical framework for 3D radiation MHD simulations of star formation that simultaneously follow the formation, accretion, evolution, and dynamics of individual stars in massive giant molecular clouds (GMCs) while accounting for stellar feedback, including jets, radiative heating and momentum, stellar winds, and supernovae. We use the GIZMO code with the MFM mesh-free Lagrangian MHD method, augmented with new algorithms for gravity, timestepping, sink particle formation and accretion, stellar dynamics, and feedback coupling. We survey a wide range of numerical parameters/prescriptions for sink formation and accretion and find very small variations in star formation history and the IMF (except for intentionally-unphysical variations). Modules for mass-injecting feedback (winds, SNe, and jets) inject new gas elements on-the-fly, eliminating the lack of resolution in diffuse feedback cavities otherwise inherent in Lagrangian methods. The treatment of radiation uses GIZMO's radiative transfer solver to track 5 frequency bands (IR, optical, NUV, FUV, ionizing), coupling direct stellar emission and dust emission with gas heating and radiation pressure terms. We demonstrate accurate solutions for SNe, winds, and radiation in problems with known similarity solutions, and show that our jet module is robust to resolution and numerical details, and agrees well with previous AMR simulations. STARFORGE can scale up to massive ($>10^5 M_\odot $) GMCs on current supercomputers while predicting the stellar ($\gtrsim 0.1 M_\odot$) range of the IMF, permitting simulations of both high- and low-mass cluster formation in a wide range of conditions., Comment: Fix error in Eq. 44 for wind mass loss rate

We present a large suite of MHD simulations of turbulent, star-forming giant molecular clouds(GMCs) with stellar feedback, extending previous work by simulating 10 different random realizations for each point in the parameter space of cloud mass and size. It is found that oncethe clouds disperse due to stellar feedback, both self-gravitating star clusters and unbound stars generally remain, which arise from the same underlying continuum of substructured stellar density, ie. the hierarchical cluster formation scenario. The fraction of stars that are born within gravitationally-bound star clusters is related to the overall cloud star formation efficiency set by stellar feedback, but has significant scatter due to stochastic variations in the small-scale details of the star-forming gas flow. We use our numerical results to calibrate a model for mapping the bulk properties (mass, size, and metallicity) of self-gravitating GMCs onto the star cluster populations they form, expressed statistically in terms of cloud-level distributions. Synthesizing cluster catalogues from an observed GMC catalogue in M83, we find that this model predicts initial star cluster masses and sizes that are in good agreement with observations, using only standard IMF and stellar evolution models as inputs for feedback. Within our model, the ratio of the strength of gravity to stellar feedback is the key parameter setting the masses of star clusters, and of the various feedback channels direct stellar radiation(photon momentum and photoionization) is the most important on GMC scales., Comment: Submitted to MNRAS. 20 pages, 14 figures. Feedback welcome :)

We examine the thermodynamic state and cooling of the low-$z$ Circum-Galactic Medium (CGM) in five FIRE-2 galaxy formation simulations of Milky Way-mass galaxies. We find that the CGM in these simulations is generally multiphase and dynamic, with a wide spectrum of largely nonlinear density perturbations sourced by the accretion of gas from the Inter-Galactic Medium (IGM) and outflows from both the central and satellite galaxies. We investigate the origin of the multiphase structure of the CGM with a particle tracking analysis and find that most of the low entropy gas has cooled from the hot halo as a result of thermal instability triggered by these perturbations. The ratio of cooling to free-fall timescales $t_{\rm cool}/t_{\rm ff}$ in the hot component of the CGM spans a wide range $\sim 1-100$ at a given radius, but exhibits approximately constant median values $\sim 5-20$ at all radii $0.1 R_{\rm vir} < r < R_{\rm vir}$. These are similar to the $\approx 10-20$ value typically adopted as the thermal instability threshold in ``precipitation'' models of the ICM. Consequently, a one-dimensional model based on the assumption of a constant $t_{\rm cool}/t_{\rm ff}$ and hydrostatic equilibrium approximately reproduces the number density and entropy profiles of each simulation, but only if it assumes the metallicity profile and temperature boundary condition taken directly from the simulation. We explicitly show that the $t_{\rm cool}/t_{\rm ff}$ value of a gas parcel in the hot component of the CGM does not predict its probability of subsequently accreting onto the central galaxy. This suggests that the value of $t_{\rm cool}/t_{\rm ff}$ is a poor predictor of thermal stability in gaseous halos in which large-amplitude density perturbations are prevalent., Comment: Updated to match published version. Note: a bug was found in the code used to create Figure 8 - corrected version strengthens conclusions of paper, which remain unchanged

We present new measurements of the spatial distribution and kinematics of neutral hydrogen in the circumgalactic and intergalactic medium surrounding star-forming galaxies at z ~ 2. Using the spectra of ~ 3000 galaxies with redshifts +/- 0.4 from the Keck Baryonic Structure Survey (KBSS), we assemble a sample of more than 200,000 distinct foreground-background pairs with projected angular separations of 3 - 500 arcsec and spectroscopic redshifts, with <$z_{fg}$> = 2.23 and <$z_{bg}$> = 2.57. The ensemble of sightlines and foreground galaxies is used to construct a 2D map of the mean excess Ly$\alpha$ optical depth relative to the intergalactic mean as a function of projected galactocentric distance (20 < $D_{tran}$/pkpc < 4000) and line-of-sight velocity. We provide information on the line-of-sight kinematics of H I gas as a function of projected distance $D_{tran}$. We compare the map with cosmological zoom-in simulation, finding qualitative agreement between them. A simple two-component (accretion, outflow) analytical model generally reproduces the observed line-of-sight kinematics and projected spatial distribution of H I. The best-fitting model suggests that galaxy-scale outflows with initial velocity $v_{out}$ ~ 600 km/s dominate the kinematics of circumgalactic H I out to $D_{tran}$ ~ 50 kpc, while H I at $D_{tran}$ > 100 kpc is dominated by infall with characteristic $v_{in}$ < $v_c$, where $v_c$ is the circular velocity of the host halo ($M_h$ ~ $10^{12} M_\odot$). Over the impact parameter range 80 < $D_{tran}$/pkpc < 200, the H I line-of-sight velocity range reaches a minimum, with a corresponding flattening in the rest-frame Ly$\alpha$ equivalent width. These observations can be naturally explained as the transition between outflow-dominated and accretion-dominated flows. Beyond $D_{tran}$ ~ 300 kpc, the line of sight kinematics are dominated by Hubble expansion., Comment: 27 pages, 24 figures, 3 tables, accepted by MNRAS. Additional data at http://ramekin.caltech.edu/KBSS/

It has been established for decades that rotation curves deviate from the Newtonian gravity expectation given baryons alone below a characteristic acceleration scale $g_{\dagger}\sim 10^{-8}\,\rm{cm\,s^{-2}}$, a scale promoted to a new fundamental constant in MOND. In recent years, theoretical and observational studies have shown that the star formation efficiency (SFE) of dense gas scales with surface density, SFE $\sim \Sigma/\Sigma_{\rm crit}$ with $\Sigma_{\rm crit} \sim \langle\dot{p}/m_{\ast}\rangle/(\pi\,G)\sim 1000\,\rm{M_{\odot}\,pc^{-2}}$ (where $\langle \dot{p}/m_{\ast}\rangle$ is the momentum flux output by stellar feedback per unit stellar mass in a young stellar population). We argue that the SFE, more generally, should scale with the local gravitational acceleration, i.e. that SFE $\sim g_{\rm tot}g_\mathrm{crit} \equiv (G\,M_{\rm tot}/R^{2}) / \langle\dot{p}/m_{\ast}\rangle$, where $M_{\rm tot}$ is the total gravitating mass and $g_\mathrm{crit}=\langle\dot{p}/m_{\ast}\rangle = \pi\,G\,\Sigma_{\rm crit} \approx 10^{-8}\,\rm{cm\,s^{-2}} \approx g_{\dagger}$. Hence the observed $g_\dagger$ may correspond to the characteristic acceleration scale above which stellar feedback cannot prevent efficient star formation, and baryons will eventually come to dominate. We further show how this may give rise to the observed acceleration scaling $g_{\rm obs}\sim(g_{\rm baryon}\,g_{\dagger})^{1/2}$ (where $g_{\rm baryon}$ is the acceleration due to baryons alone) and flat rotation curves. The derived characteristic acceleration $g_{\dagger}$ can be expressed in terms of fundamental constants (gravitational constant, proton mass, and Thomson cross section): $g_{\dagger}\sim 0.1\,G\,m_{p}/\sigma_{\rm T}$., Comment: corrected MNRAS version

Measurements of the star formation efficiency (SFE) of giant molecular clouds (GMCs) in the Milky Way generally show a large scatter, which could be intrinsic or observational. We use magnetohydrodynamic simulations of GMCs (including feedback) to forward-model the relationship between the true GMC SFE and observational proxies. We show that individual GMCs trace broad ranges of observed SFE throughout collapse, star formation, and disruption. Low measured SFEs (<<1%) are "real" but correspond to early stages, the true "per-freefall" SFE where most stars actually form can be much larger. Very high (>>10%) values are often artificially enhanced by rapid gas dispersal. Simulations including stellar feedback reproduce observed GMC-scale SFEs, but simulations without feedback produce 20x larger SFEs. Radiative feedback dominates among mechanisms simulated. An anticorrelation of SFE with cloud mass is shown to be an observational artifact. We also explore individual dense "clumps" within GMCs and show that (with feedback) their bulk properties agree well with observations. Predicted SFEs within the dense clumps are ~2x larger than observed, possibly indicating physics other than feedback from massive (main sequence) stars is needed to regulate their collapse., Comment: Fixed typo in the arXiv abstract

We present a suite of 3D multi-physics MHD simulations following star formation in isolated turbulent molecular gas disks 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 GMCs ($\sim 10^2 M_\odot\,pc^{-2}}$) and extreme ULIRG environments ($\sim 10^2 M_\odot\,pc^{-2}}$) 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 ($\epsilon_{ff}$) and integrated ($\epsilon_{int}$) star formation efficiencies. In all simulations, the gas disks 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 $\epsilon_{int}$, as suggested by analytic force balance arguments from previous works. SFE eventually saturates to $\sim 1$ at high surface density. We also find a proportional relationship between $\epsilon_{ff}$ and $\epsilon_{int}$, 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 disks, the nature and fate of nuclear starbursts, and the formation of bound star clusters. The scaling of $\epsilon_{ff}$ with surface density is not consistent with the notion that $\epsilon_{ff}$ is always $\sim 1\%$ on the scale of GMCs, but our predictions recover the $\sim 1\%$ value for GMC parameters similar to those found in sprial galaxies, including our own., Comment: 21 pages, 7 figures. Accepted to MNRAS

We use cosmological simulations from the FIRE (Feedback In Realistic Environments) project to study the baryon cycle and galaxy mass assembly for central galaxies in the halo mass range $M_{\rm halo} \sim 10^{10} - 10^{13} M_{\odot}$. By tracing cosmic inflows, galactic outflows, gas recycling, and merger histories, we quantify the contribution of physically distinct sources of material to galaxy growth. We show that in situ star formation fueled by fresh accretion dominates the early growth of galaxies of all masses, while the re-accretion of gas previously ejected in galactic winds often dominates the gas supply for a large portion of every galaxy's evolution. Externally processed material contributes increasingly to the growth of central galaxies at lower redshifts. This includes stars formed ex situ and gas delivered by mergers, as well as smooth intergalactic transfer of gas from other galaxies, an important but previously under-appreciated growth mode. By $z=0$, wind transfer, i.e. the exchange of gas between galaxies via winds, can dominate gas accretion onto $\sim L^{*}$ galaxies over fresh accretion and standard wind recycling. Galaxies of all masses re-accrete >50% of the gas ejected in winds and recurrent recycling is common. The total mass deposited in the intergalactic medium per unit stellar mass formed increases in lower mass galaxies. Re-accretion of wind ejecta occurs over a broad range of timescales, with median recycling times ($\sim 100-350$ Myr) shorter than previously found. Wind recycling typically occurs at the scale radius of the halo, independent of halo mass and redshift, suggesting a characteristic recycling zone around galaxies that scales with the size of the inner halo and the galaxy's stellar component., Comment: 22 pages, 17 figures, Submitted to MNRAS

The morphology of massive star-forming galaxies at high redshift is often dominated by giant clumps of mass ~10^8-10^9 Msun and size ~100-1000 pc. Previous studies have proposed that giant clumps might have an important role in the evolution of their host galaxy, particularly in building the central bulge. However, this depends on whether clumps live long enough to migrate from their original location in the disc or whether they get disrupted by their own stellar feedback before reaching the centre of the galaxy. We use cosmological hydrodynamical simulations from the FIRE (Feedback in Realistic Environments) project that implement explicit treatments of stellar feedback and ISM physics to study the properties of these clumps. We follow the evolution of giant clumps in a massive (stellar mass ~10^10.8 Msun at z=1), discy, gas-rich galaxy from redshift z>2 to z=1. Even though the clumpy phase of this galaxy lasts over a gigayear, individual gas clumps are short-lived, with mean lifetime of massive clumps of ~20 Myr. During that time, they turn between 0.1% and 20% of their gas into stars before being disrupted, similar to local GMCs. Clumps with M>10^7 Msun account for ~20% of the total star formation in the galaxy during the clumpy phase, producing ~10^10 Msun of stars. We do not find evidence for net inward migration of clumps within the galaxy. The number of giant clumps and their mass decrease at lower redshifts, following the decrease in the overall gas fraction and star-formation rate., Comment: 20 pages, 19 figures; revised version, accepted for publication in MNRAS