Xiangcheng Ma

The Origin and Evolution of the Galaxy Mass-Metallicity Relation

We use high-resolution cosmological zoom-in simulations from the Feedback in Realistic Environment (FIRE) project to study the galaxy mass–metallicity relations (MZR) from z=0–6. These simulations include explicit models of the multi-phase ISM, star formation, and stellar feedback. The simulations cover halo masses M_(halo) = 10^9–10^(13) M_☉ and stellar masses M_* = 10^4–10^(11) M_☉ at z = 0 and have been shown to produce many observed galaxy properties nfrom z = 0–6. For the first time, our simulations agree reasonably well with the observed mass–metallicity relations at z = 0–3 for a broad range of galaxy masses. We predict the evolution of the MZR from z = 0–6, as log(Z_(gas)/Z_☉) = 12+log(O/H)-9.0 = 0.35 [log(M_*/M_☉) - 10] + 0.93exp(-0.43z) - 1.05 and log(Z_*/Z_☉) = [Fe=H] + 0.2 = 0.40 [log(M_*/M_☉)-10]+0.67exp(-0.50z)-1.04, for gas-phase and stellar metallicity, respectively. nOur simulations suggest that the evolution of MZR is associated with the evolution of stellar/gas mass fractions at different redshifts, indicating the existence of a universal metallicity relation between stellar mass, gas mass, and metallicities. In our simulations, galaxies nabove M_* = 10^6 M_☉ are able to retain a large fraction of their metals inside the halo, because metal-rich winds fail to escape completely and are recycled into the galaxy. This resolves a long-standing discrepancy between “sub-grid” wind models (and semi-analytic models) and nobservations, where common sub-grid models cannot simultaneously reproduce the MZR and the stellar mass functions.

The difficulty of getting high escape fractions of ionizing photons from high-redshift galaxies: A view from the FIRE cosmological simulations

We present a series of high-resolution (20–2000 M⊙, 0.1–4 pc) cosmological zoom-in simulations at z ≳ 6 from the Feedback In Realistic Environment (FIRE) project. These simulations cover halo masses 10^9–10^(11)u2009M⊙ and rest-frame ultraviolet magnitude M_(UV) = −9 to −19. These simulations include explicit models of the multi-phase ISM, star formation, and stellar feedback, which produce reasonable galaxy properties at z = 0–6. We post-process the snapshots with a radiative transfer code to evaluate the escape fraction (f_(esc)) of hydrogen ionizing photons. We find that the instantaneous f_(esc) has large time variability (0.01–20u2009peru2009cent), while the time-averaged f_(esc) over long time-scales generally remains ≲ 5u2009peru2009cent, considerably lower than the estimate in many reionization models. We find no strong dependence of f_(esc) on galaxy mass or redshift. In our simulations, the intrinsic ionizing photon budgets are dominated by stellar populations younger than 3 Myr, which tend to be buried in dense birth clouds. The escaping photons mostly come from populations between 3 and 10 Myr, whose birth clouds have been largely cleared by stellar feedback. However, these populations only contribute a small fraction of intrinsic ionizing photon budgets according to standard stellar population models. We show that f_(esc) can be boosted to high values, if stellar populations older than 3 Myr produce more ionizing photons than standard stellar population models (as motivated by, e.g. models including binaries). By contrast, runaway stars with velocities suggested by observations can enhance f_(esc) by only a small fraction. We show that ‘sub-grid’ star formation models, which do not explicitly resolve star formation in dense clouds with n ≫ 1u2009cm^(−3), will dramatically overpredict f_(esc).

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.

The structure and dynamical evolution of the stellar disc of a simulated Milky Way-mass galaxy

We study the structure, age and metallicity gradients, and dynamical evolution using a cosmological zoom-in simulation of a Milky Way-mass galaxy from the Feedback in Realistic Environments project. In the simulation, stars older than 6 Gyr were formed in a chaotic, bursty mode and have the largest vertical scaleheights (1.5–2.5 kpc) by z = 0, while stars younger than 6 Gyr were formed in a relatively calm, stable disc. The vertical scaleheight increases with stellar age at all radii, because (1) stars that formed earlier were thicker ‘at birth’, and (2) stars were kinematically heated to an even thicker distribution after formation. Stars of the same age are thicker in the outer disc than in the inner disc (flaring). These lead to positive vertical age gradients and negative radial age gradients. The radial metallicity gradient is negative at the mid-plane, flattens at larger disc height |Z|, and turns positive above |Z| ∼ 1.5u2009kpc. The vertical metallicity gradient is negative at all radii, but is steeper at smaller radii. These trends broadly agree with observations in the Milky Way and can be naturally understood from the age gradients. The vertical stellar density profile can be well described by two components, with scaleheights 200–500 pc and 1–1.5 kpc, respectively. The thick component is a mix of stars older than 4 Gyr, which formed through a combination of several mechanisms. Our results also demonstrate that it is possible to form a thin disc in cosmological simulations even with a strong stellar feedback.

Metal flows of the circumgalactic medium, and the metal budget in galactic haloes

We present an analysis of the flow of metals through the circumgalactic medium (CGM) in the Feedback in Realistic Environments (FIRE) simulations of galaxy formation, ranging from isolated dwarfs to L* galaxies. We find that nearly all metals produced in high-redshift galaxies are carried out in winds that reach 0.25R_(vir). When measured at 0.25R_(vir) the metallicity of outflows is slightly higher than the interstellar medium (ISM) metallicity. Many metals thus reside in the CGM. Cooling and recycling from this reservoir determine the metal budget in the ISM. The outflowing metal flux decreases by a factor of ∼2–5 between 0.25R_(vir) and R_(vir). Furthermore, outflow metallicity is typically lower at R_(vir) owing to dilution of the remaining outflow by metal-poor material swept up from the CGM. The inflow metallicity at R_(vir) is generally low, but outflow and inflow metallicities are similar in the inner halo. At low redshift, massive galaxies no longer generate outflows that reach the CGM, causing a divergence in CGM and ISM metallicity. Dwarf galaxies continue to generate outflows, although they preferentially retain metal ejecta. In all but the least massive galaxy considered, a majority of the metals are within the halo at z = 0. We measure the fraction of metals in CGM, ISM and stars, and quantify the thermal state of CGM metals in each halo. The total amount of metals in the low-redshift CGM of two simulated L* galaxies is consistent with estimates from the Cosmic Origin Spectrograph haloes survey, while for the other two it appears to be lower.

Binary Stars Can Provide the “Missing Photons” Needed for Reionization

Empirical constraints on reionization require galactic ionizing photon escape fractions f_(esc) ≳ 20u2009peru2009cent, but recent high-resolution radiation-hydrodynamic calculations have consistently found much lower values ∼1–5u2009peru2009cent. While these models include strong stellar feedback and additional processes such as runaway stars, they almost exclusively consider stellar evolution models based on single (isolated) stars, despite the fact that most massive stars are in binaries. We re-visit these calculations, combining radiative transfer and high-resolution cosmological simulations with detailed models for stellar feedback from the Feedback in Realistic Environments project. For the first time, we use a stellar evolution model that includes a physically and observationally motivated treatment of binaries (the Binary Population and Spectral Synthesis model). Binary mass transfer and mergers enhance the population of massive stars at late times (≳3u2009Myr) after star formation, which in turn strongly enhances the late-time ionizing photon production (especially at low metallicities). These photons are produced after feedback from massive stars has carved escape channels in the interstellar medium, and so efficiently leak out of galaxies. As a result, the time-averaged ‘effective’ escape fraction (ratio of escaped ionizing photons to observed 1500u2009A photons) increases by factors ∼4–10, sufficient to explain reionization. While important uncertainties remain, we conclude that binary evolution may be critical for understanding the ionization of the Universe.

Feedback first: the surprisingly weak effects of magnetic fields, viscosity, conduction and metal diffusion on sub-L* galaxy formation

Using high-resolution simulations with explicit treatment of stellar feedback physics based on the FIRE (Feedback In Realistic Environments) project, we study how galaxy formation and the interstellar medium (ISM) are affected by magnetic fields, anisotropic Spitzer–Braginskii conduction and viscosity, and sub-grid metal diffusion from unresolved turbulence. We consider controlled simulations of isolated (non-cosmological) galaxies but also a limited set of cosmological ‘zoom-in’ simulations. Although simulations have shown significant effects from these physics with weak or absent stellar feedback, the effects are much weaker than those of stellar feedback when the latter is modelled explicitly. The additional physics have no systematic effect on galactic star formation rates (SFRs). In contrast, removing stellar feedback leads to SFRs being overpredicted by factors of ∼10–100. Without feedback, neither galactic winds nor volume-filling hot-phase gas exist, and discs tend to runaway collapse to ultra-thin scaleheights with unphysically dense clumps congregating at the galactic centre. With stellar feedback, a multi-phase, turbulent medium with galactic fountains and winds is established. At currently achievable resolutions and for the investigated halo mass range 10^(10)–10^(13)u2009M⊙, the additional physics investigated here (magnetohydrodynamic, conduction, viscosity, metal diffusion) have only weak (∼10u2009peru2009cent-level) effects on regulating SFR and altering the balance of phases, outflows or the energy in ISM turbulence, consistent with simple equipartition arguments. We conclude that galactic star formation and the ISM are primarily governed by a combination of turbulence, gravitational instabilities and feedback. We add the caveat that active galactic nucleus feedback is not included in the present work.

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)u2009M⊙ 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)≲ 3u2009Myr, 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 ∼420u2009Myr 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.

Simulating galaxies in the reionization era with FIRE-2: galaxy scaling relations, stellar mass functions, and luminosity functions

We present a suite of cosmological zoom-in simulations at z>5 from the Feedback In Realistic Environments project, spanning a halo mass range M_halo~10^8-10^12 M_sun at z=5. We predict the stellar mass-halo mass relation, stellar mass function, and luminosity function in several bands from z=5-12. The median stellar mass-halo mass relation does not evolve strongly at z=5-12. The faint-end slope of the luminosity function steepens with increasing redshift, as inherited from the halo mass function at these redshifts. Below z~6, the stellar mass function and ultraviolet (UV) luminosity function slightly flatten below M_star~10^4.5 M_sun (fainter than M_1500~-12), owing to the fact that star formation in low-mass halos is suppressed by the ionizing background by the end of reionization. Such flattening does not appear at higher redshifts. We provide redshift-dependent fitting functions for the SFR-M_halo, SFR-M_star, and broad-band magnitude-stellar mass relations. We derive the star formation rate density and stellar mass density at z=5-12 and show that the contribution from very faint galaxies becomes more important at z>8. Furthermore, we find that the decline in the z~6 UV luminosity function brighter than M_1500~-20 is largely due to dust attenuation. Approximately 37% (54%) of the UV luminosity from galaxies brighter than M_1500=-13 (-17) is obscured by dust at z~6. Our results broadly agree with current data and can be tested by future observations.

The origin of the diverse morphologies and kinematics of Milky Way-mass galaxies in the FIRE-2 simulations

We use hydrodynamic cosmological zoom-in simulations from the Feedback in Realistic Environments project to explore the morphologies and kinematics of 15 Milky Way (MW)-mass galaxies. Our sample ranges from compact, bulge-dominated systems with 90 per cent of their stellar mass within 2.5 kpc to well-ordered discs that reach ≳15 kpc. The gas in our galaxies always forms a thin, rotation-supported disc at z = 0, with sizes primarily determined by the gas mass. For stars, we quantify kinematics and morphology both via the fraction of stars on disc-like orbits and with the radial extent of the stellar disc. In this mass range, stellar morphology and kinematics are poorly correlated with the properties of the halo available from dark matter-only simulations (halo merger history, spin, or formation time). They more strongly correlate with the gaseous histories of the galaxies: those that maintain a high gas mass in the disc after z ~ 1 develop well-ordered stellar discs. The best predictor of morphology we identify is the spin of the gas in the halo at the time the galaxy formed 1/2 of its stars (i.e. the gas that builds the galaxy). High-z mergers, before a hot halo emerges, produce some of the most massive bulges in the sample (from compact discs in gas-rich mergers), while later-forming bulges typically originate from internal processes, as satellites are stripped of gas before the galaxies merge. Moreover, most stars in z = 0 MW-mass galaxies (even z = 0 bulge stars) form in a disc: ≳60-90 per cent of stars begin their lives rotationally supported.