We review progress over the past decade in observations of large-scale star formation, with a focus on the interface between extragalactic and Galactic studies. Methods of measuring gas contents and star-formation rates are discussed, and updated prescriptions for calculating star-formation rates are provided. We review relations between star formation and gas on scales ranging from entire galaxies to individual molecular clouds.

Star Formation in the Milky Way and Nearby Galaxies

We review current understanding of star formation, outlining an overall theoretical framework and the observations that motivate it. A conception of star formation has emerged in which turbulence plays a dual role, both creating overdensities to initiate gravitational contraction or collapse, and countering the effects of gravity in these overdense regions. The key dynamical processes involved in star formation—turbulence, magnetic fields, and self-gravity— are highly nonlinear and multidimensional. Physical arguments are used to identify and explain the features and scalings involved in star formation, and results from numerical simulations are used to quantify these effects. We divide star formation into large-scale and small-scale regimes and review each in turn. Large scales range from galaxies to giant molecular clouds (GMCs) and their substructures. Important problems include how GMCs form and evolve, what determines the star formation rate (SFR), and what determines the initial mass function (IMF). Small scales range from dense cores to the protostellar systems they beget. We discuss formation of both low- and high-mass stars, including ongoing accretion. The development of winds and outflows is increasingly well understood, as are the mechanisms governing angular momentum transport in disks. Although outstanding questions remain, the framework is now in place to build a comprehensive theory of star formation that will be tested by the next generation of telescopes.

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Theory of Star Formation

A reexamination is conducted of the formation of dwarf, diffuse, metal-poor galaxies due to supernova-driven winds, in view of data on the systematic properties of dwarfs in the Local Group and Virgo Cluster. The critical condition for global gas loss as a result of the first burst of star formation is that the virial velocity lie below an approximately 100 km/sec critical value. This leads, as observed, to two distinct classes of galaxies, encompassing the diffuse dwarfs, which primarily originate from typical density perturbations, and the normal, brighter galaxies, including compact dwarfs, which can originate only from the highest density peaks. This furnishes a statistical biasing mechanism for the preferential formation of bright galaxies in denser regions, enhancing high surface brightness galaxies' clustering relative to the diffusive dwarfs.

Dwarf galaxies, cold dark matter, and biased galaxy formation

Exploring and identifying structure is even more important for multivariate data than univariate data, given the difficulties in graphically presenting multivariate data and the comparative lack of parametric models to represent it. Unfortunately, such exploration is also inherently more difficult.

Multivariate Density Estimation

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.

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FIRE-2 simulations: physics versus numerics in galaxy formation

Supernova (SN) explosions deposit prodigious energy and momentum in their environments, with the former regulating multiphase thermal structure and the latter regulating turbulence and star formation rates in the interstellar medium (ISM). However, systematic studies quantifying the impact of SNe in realistic inhomogeneous ISM conditions have been lacking. Using three-dimensional hydrodynamic simulations, we investigate the dependence of radial momentum injection on both physical conditions (considering a range of mean density n=0.1-100) and numerical parameters. Our inhomogeneous simulations adopt two-phase background states that result from thermal instability in atomic gas. Although the SNR morphology becomes highly complex for inhomogeneous backgrounds, the radial momentum injection is remarkably insensitive to environmental details. For our two-phase simulations, the final momentum produced by a single SN is given by 2.8*10^5 M_sun*km/s n^{-0.17}. This is only 5% less than the momentum injection for a homogeneous environment with the same mean density, and only 30% greater than the momentum at the time of shell formation. The maximum mass in hot gas is quite insensitive to environmental inhomogeneity. Strong magnetic fields alter the hot gas mass at very late times, but the momentum injection remains the same. Initial experiments with multiple spatially-correlated SNe show a momentum per event nearly as large as single-SN cases. We also present a full numerical parameter study to assess convergence requirements. For convergence in the momentum and other quantities, we find that the numerical resolution dx and the initial size of the SNR r_init must satisfy dx, r_init<r_sf/3, where the shell formation radius is given by r_sf = 30 pc n^{-0.46} for two-phase models (or 30% smaller for a homogeneous medium).

https://iopscience.iop.org/article/10.1088/0004-637X/802/2/99/pdf

Momentum injection by supernovae in the interstellar medium

The energy and momentum feedback from young stars has a profound impact on the interstellar medium (ISM), including heating and driving turbulence in the neutral gas that fuels future star formation. Recent theory has argued that this leads to a quasi-equilibrium self-regulated state, and for outer atomic-dominated disks results in the surface density of star formation ?SFR varying approximately linearly with the weight of the ISM (or midplane turbulent + thermal pressure). We use three-dimensional numerical hydrodynamic simulations to test the theoretical predictions for thermal, turbulent, and vertical dynamical equilibrium, and the implied functional dependence of ?SFR on local disk properties. Our models demonstrate that all equilibria are established rapidly, and that the expected proportionalities between mean thermal and turbulent pressures and ?SFR apply. For outer disk regions, this results in , where ? is the total gas surface density and ?sd is the midplane density of the stellar disk (plus dark matter). This scaling law arises because ?sd sets the vertical dynamical time in our models (and outer disk regions generally). The coefficient in the star formation law varies inversely with the specific energy and momentum yield from massive stars. We find proportions of warm and cold atomic gas, turbulent-to-thermal pressure, and mean velocity dispersions that are consistent with solar-neighborhood and other outer disk observations. This study confirms the conclusions of a previous set of simulations, which incorporated the same physics treatment but was restricted to radial-vertical slices through the ISM.

http://iopscience.iop.org/article/10.1088/0004-637X/776/1/1/pdf

Three-dimensional hydrodynamic simulations of multiphase galactic disks with star formation feedback. i. regulation of star formation rates

We use vertically resolved numerical hydrodynamic simulations to study star formation and the interstellar medium (ISM) in galactic disks. We focus on outer-disk regions where diffuse H I dominates, with gas surface densities Σ = 3-20 M ☉ pc–2 and star-plus-dark matter volume densities ρsd = 0.003-0.5 M ☉ pc–3. Star formation occurs in very dense, self-gravitating clouds that form by mergers of smaller cold cloudlets. Turbulence, driven by momentum feedback from supernova events, destroys bound clouds and puffs up the disk vertically. Time-dependent radiative heating (FUV from recent star formation) offsets gas cooling. We use our simulations to test a new theory for self-regulated star formation. Consistent with this theory, the disks evolve to a state of vertical dynamical equilibrium and thermal equilibrium with both warm and cold phases. The range of star formation surface densities and midplane thermal pressures is ΣSFR ~ 10–4 to 10–2 M ☉ kpc–2 yr–1 and P th/k B ~ 102 to 104 cm–3 K. In agreement with observations, turbulent velocity dispersions are ~7 km s–1 and the ratio of the total (effective) to thermal pressure is P tot/P th ~ 4-5, across this whole range (provided shielding is similar to the solar neighborhood). We show that ΣSFR is not well correlated with Σ alone, but rather with , because the vertical gravity from stars and dark matter dominates in outer disks. We also find that ΣSFR has a strong, nearly linear correlation with P tot, which itself is within ~13% of the dynamical equilibrium estimate P tot, DE. The quantitative relationships we find between ΣSFR and the turbulent and thermal pressures show that star formation is highly efficient for energy and momentum production, in contrast to the low efficiency of mass consumption. Star formation rates adjust until the ISM's energy and momentum losses are replenished by feedback within a dynamical time.

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Regulation of Star Formation Rates in Multiphase Galactic Disks: Numerical Tests of the Thermal/Dynamical Equilibrium Model

Gas blown away from galactic disks by supernova (SN) feedback plays a key role in galaxy evolution. We investigate outflows utilizing the solar neighborhood model of our high-resolution, local galactic disk simulation suite, TIGRESS. In our numerical implementation, star formation and SN feedback are self-consistently treated and well resolved in the multiphase, turbulent, magnetized interstellar medium. Bursts of star formation produce spatially and temporally correlated SNe that drive strong outflows, consisting of hot (T>5x10^5K) winds and warm (5050K 1kpc from the midplane has mass and energy fluxes nearly constant with d. The hot flow escapes our local Cartesian box barely affected by gravity and is expected to accelerate up to the terminal velocity of v_wind~350-500km/s. The mean mass and energy loading factors of the hot wind are 0.1 and 0.02, respectively. For warm gas, the mean outward mass flux through d=1kpc is comparable to the mean star formation rate, but only a small fraction of this gas is at velocity >50km/s. Thus, the warm outflows eventually fall back as inflows. The warm fountain flows are created by expanding hot superbubbles at d< 1kpc; at larger d neither ram pressure acceleration nor cooling transfers significant momentum or energy flux from the hot wind to the warm outflow. The velocity distribution at launching near d~1kpc better represents warm outflows than a single mass loading factor, potentially enabling development of subgrid models for warm galactic winds in arbitrary large-scale galactic potentials.

https://iopscience.iop.org/article/10.3847/1538-4357/aaa5ff/pdf

Numerical Simulations of Multiphase Winds and Fountains from Star-forming Galactic Disks. I. Solar Neighborhood TIGRESS Model

We use numerical simulations to analyze the evolution and properties of superbubbles (SBs), driven by multiple supernovae (SNe), that propagate into the two-phase (warm/cold), cloudy interstellar medium (ISM). We consider a range of mean background densities n_avg=0.1-10 cm^{-3} and intervals between SNe dt_sn=0.01-1 Myr, and follow each SB until the radius reaches (1-2)H, where H is the characteristic ISM disk thickness. Except for embedded dense clouds, each SB is hot until a time t_sf,m when the shocked warm gas at the outer front cools and forms an overdense shell. Subsequently, diffuse gas in the SB interior remains at T_h 10^6-10^7K with expansion velocity v_h~10^2-10^3km/s (both highest for low dt_sn). At late times, the warm shell gas velocities are several 10's to ~100km/s. While shell velocities are too low to escape from a massive galaxy, they are high enough to remove substantial mass from dwarfs. Dense clouds are also accelerated, reaching a few to 10's of km/s. We measure the mass in hot gas per SN, M_h/N_SN, and the total radial momentum of the bubble per SN, p_b/N_SN. After t_sf,m, M_h/N_SN 10-100M_sun (highest for low n_avg), while p_b/N_SN 0.7-3x10^5M_sun km/s (highest for high dt_sn). If galactic winds in massive galaxies are loaded by the hot gas in SBs, we conclude that the mass-loss rates would generally be lower than star formation rates. Only if the SN cadence is much higher than typical in galactic disks, as may occur for nuclear starbursts, SBs can break out while hot and expel up to 10 times the mass locked up in stars. The momentum injection values, p_b/N_SN, are consistent with requirements to control star formation rates in galaxies at observed levels.

Chang-Goo Kim

Papers

Momentum injection by supernovae in the interstellar medium

Three-dimensional hydrodynamic simulations of multiphase galactic disks with star formation feedback. i. regulation of star formation rates

Regulation of Star Formation Rates in Multiphase Galactic Disks: Numerical Tests of the Thermal/Dynamical Equilibrium Model

Numerical Simulations of Multiphase Winds and Fountains from Star-forming Galactic Disks. I. Solar Neighborhood TIGRESS Model

Superbubbles in the multiphase ism and the loading of galactic winds