Star Formation on Galactic Scales: Empirical Laws (original) (raw)

EAS Publications Series, 2011 STAR FORMATION ON GALACTIC SCALES: EMPIRICAL

2016

Empirical star formation laws from the last 20 years are reviewed with a comparison to simulations. The current form in main galaxy disks has a linear relationship between the star formation rate per unit area and the molecular cloud mass per unit area with a timescale for molecular gas conversion of about 2 Gyr. The local ratio of molecular mass to atomic mass scales nearly linearly with pressure, as determined from the weight of the gas layer in the galaxy. In the outer parts of galaxies and in dwarf irregular galaxies, the disk can be dominated by atomic hydrogen and the star formation rate per unit area becomes directly proportional to the total gas mass per unit area, with a consumption time of about 100 Gyr. The importance of a threshold for gravitational instabilities is not clear. Observations suggest such a threshold is not always important, while simulations generally show that it is. The threshold is difficult to evaluate because it is sensitive to magnetic and viscous forces, the presence of spiral waves and other local effects, and the equation of state.

Star Formation from Galaxies to Globules

The Astrophysical Journal, 2002

The origin of the empirical laws of galactic-scale star formation are considered in view of the self-similar nature of interstellar gas and the observation that most local clusters are triggered by specific high-pressure events. The empirical laws suggest that galactic-scale gravity is involved in the first stages of star formation, but they do not identify the actual triggering mechanisms for clusters in the final stages. Many triggering processes satisfy the empirical laws, including turbulence compression and expanding shell collapse. The self-similar nature of the gas and associated young stars suggests that turbulence is more directly involved, but the energy source for this turbulence is not clear and the small scale morphology of gas around most embedded clusters does not look like a random turbulent flow. Most clusters look triggered by other nearby stars. Such a prominent local influence makes it difficult to understand the universality of the Kennicutt and Schmidt laws on galactic scales. A unified view of multi-scale star formation avoids most of these problems. The Toomre and Kennicutt surface density thresholds, along with the large-scale gas and star formation morphology, imply that ambient self-gravity produces spiral arms and giant cloud complexes and at the same time drives much of the turbulence that leads to self-similar structures. Localized energy input from existing clusters and field supernova drives turbulence and cloud formation too, while triggering clusters directly in pre-existing clouds. The hierarchical structure in the gas made by turbulence ensures that the triggering time scales with size, thereby giving the Schmidt law over a wide range of scales and the size-duration correlation for young star fields. Reanalysis of the Schmidt law from a local point of view suggests that the efficiency of star formation is determined by the fraction of the gas above a critical density of around 10 5 m(H 2) cm −3. Such high densities probably result from turbulence compression in a self-gravitating gas, in which case their mass fraction can be estimated from the density distribution function that results from turbulence. For Wada & Norman's log-normal function that arises in whole-galaxy

On the impact of empirical and theoretical star formation laws on galaxy formation

Monthly Notices of the Royal Astronomical Society, 2011

We investigate the consequences of applying different star formation laws in the galaxy formation model GALFORM. Three broad star formation laws are implemented: the empirical relations of Kennicutt and Schmidt and Blitz & Rosolowsky and the theoretical model of Krumholz, McKee & Tumlinson. These laws have no free parameters once calibrated against observations of the star formation rate (SFR) and gas surface density in nearby galaxies. We start from published models, and investigate which observables are sensitive to a change in the star formation law, without altering any other model parameters. We show that changing the star formation law (i) does not significantly affect either the star formation history of the universe or the galaxy luminosity functions in the optical and near-IR, due to an effective balance between the quiescent and burst star formation modes; (ii) greatly affects the cold gas contents of galaxies; (iii) changes the location of galaxies in the SFR versus stellar mass plane, so that a second sequence of "passive" galaxies arises, in addition to the known "active" sequence. We show that this plane can be used to discriminate between the star formation laws.

Star Formation Laws and Efficiencies across 80 Nearby Galaxies

The Astrophysical Journal Letters

We measure empirical relationships between the local star formation rate (SFR) and properties of the star-forming molecular gas on 1.5 kpc scales across 80 nearby galaxies. These relationships, commonly referred to as “star formation laws,” aim at predicting the local SFR surface density from various combinations of molecular gas surface density, galactic orbital time, molecular cloud free fall time, and the interstellar medium dynamical equilibrium pressure. Leveraging a multiwavelength database built for the Physics at High Angular Resolution in Nearby Galaxies (PHANGS) survey, we measure these quantities consistently across all galaxies and quantify systematic uncertainties stemming from choices of SFR calibrations and the CO-to-H2 conversion factors. The star formation laws we examine show 0.3–0.4 dex of intrinsic scatter, among which the molecular Kennicutt–Schmidt relation shows a ∼10% larger scatter than the other three. The slope of this relation ranges β ≈ 0.9–1.2, implying...

The star formation rate in disc galaxies: thresholds and dependence on gas amount

Monthly Notices of the Royal Astronomical Society, 2003

We reassess the applicability of the Toomre criterion in galactic discs and we study the local star formation law in 16 disc galaxies for which abundance gradients are published. The data we use consist of stellar light profiles, atomic and molecular gas (deduced from CO with a metallicity-dependent conversion factor), star formation rates (from Hα emissivities), metallicities, dispersion velocities and rotation curves. We show that the Toomre criterion applies successfully to the case of the Milky Way disc, but it has limited success with the data of our sample; depending on whether or not the stellar component is included in the stability analysis, we find average values for the threshold ratio of the gas surface density to the critical surface density in the range 0.5-0.7. We also test various star formation laws proposed in the literature, i.e. either the simple Schmidt law or modifications of it, that take into account dynamical factors. We find only small differences among them as far as the overall fit to our data is concerned; in particular, we find that all three star formation laws (with parameters derived from the fits to our data) match observations in the Milky Way disc particularly well. In all cases we find that the exponent n of our best-fitting star formation rate has slightly higher values than in other recent works and we suggest several reasons that may cause that discrepancy.

On the Star Formation Law for Spiral and Irregular Galaxies

The Astrophysical Journal, 2015

A dynamical model for star formation on a galactic scale is proposed in which the interstellar medium is constantly condensing to star-forming clouds on the dynamical time of the average midplane density, and the clouds are constantly being disrupted on the dynamical timescale appropriate for their higher density. In this model, the areal star formation rate scales with the 1.5 power of the total gas column density throughout the main regions of spiral galaxies, and with a steeper power, 2, in the far outer regions and in dwarf irregular galaxies because of the flaring disks. At the same time, there is a molecular star formation law that is linear in the main and outer parts of disks and in dIrrs because the duration of individual structures in the molecular phase is also the dynamical timescale, canceling the additional 0.5 power of surface density. The total gas consumption time scales directly with the midplane dynamical time, quenching star formation in the inner regions if there is no accretion, and sustaining star formation for ∼100 Gyr or more in the outer regions with no qualitative change in gas stability or molecular cloud properties. The ULIRG track follows from high densities in galaxy collisions.

On the Appearance of Thresholds in the Dynamical Model of Star Formation

The Astrophysical Journal, 2018

The Kennicutt-Schmidt (KS) relationship between the surface density of the star formation rate (SFR) and the gas surface density has three distinct power laws that may result from one model in which gas collapses at a fixed fraction of the dynamical rate. The power law slope is 1 when the observed gas has a characteristic density for detection, 1.5 for total gas when the thickness is about constant as in the main disks of galaxies, and 2 for total gas when the thickness is regulated by self-gravity and the velocity dispersion is about constant, as in the outer parts of spirals, dwarf irregulars, and giant molecular clouds. The observed scaling of the star formation efficiency (SFR per unit CO) with the dense gas fraction (HCN/CO) is derived from the KS relationship when one tracer (HCN) is on the linear part and the other (CO) is on the 1.5 part. Observations of a threshold density or column density with a constant SFR per unit gas mass above the threshold are proposed to be selection effects, as are observations of star formation in only the dense parts of clouds. The model allows a derivation of all three KS relations using the probability distribution function of density with no thresholds for star formation. Failed galaxies and systems with sub-KS SFRs are predicted to have gas that is dominated by an equilibrium warm phase where the thermal Jeans length exceeds the Toomre length. A squared relation is predicted for molecular gas-dominated young galaxies.

A Star Formation Law for Dwarf Irregular Galaxies

The Astrophysical Journal, 2015

The radial profiles of gas, stars, and far ultraviolet radiation in 20 dwarf Irregular galaxies are converted to stability parameters and scale heights for a test of the importance of two-dimensional (2D) instabilities in promoting star formation. A detailed model of this instability involving gaseous and stellar fluids with self-consistent thicknesses and energy dissipation on a perturbation crossing time give the unstable growth rates. We find that all locations are effectively stable to 2D perturbations, mostly because the disks are thick. We then consider the average volume densities in the midplanes, evaluated from the observed HI surface densities and calculated scale heights. The radial profiles of the star formation rates are equal to about 1% of the HI surface densities divided by the free fall times at the average midplane densities. This 1% resembles the efficiency per unit free fall time commonly found in other cases. There is a further variation of this efficiency with radius in all of our galaxies, following the exponential disk with a scale length equal to about twice the stellar mass scale length. This additional variation is modeled by the molecular fraction in a diffuse medium using radiative transfer solutions for galaxies with the observed dimensions and properties of our sample. We conclude that star formation is activated by a combination of threedimensional gaseous gravitational processes and molecule formation. Implications for outer disk structure and formation are discussed.

On the cosmic evolution of the specific star formation rate

Astronomy & Astrophysics, 2015

The apparent correlation between the specific star formation rate (sSFR) and total stellar mass (M) of galaxies is a fundamental relationship indicating how they formed their stellar populations. To attempt to understand this relation, we hypothesize that the relation and its evolution is regulated by the increase in the stellar and gas mass surface density in galaxies with redshift, which is itself governed by the angular momentum of the accreted gas, the amount of available gas, and by self-regulation of star formation. With our model, we can reproduce the specific SFR− M relations at z ∼ 1-2 by assuming gas fractions and gas mass surface densities similar to those observed for z = 1-2 galaxies. We further argue that it is the increasing angular momentum with cosmic time that causes a decrease in the surface density of accreted gas. The gas mass surface densities in galaxies are controlled by the centrifugal support (i.e., angular momentum), and the sSFR is predicted to increase as, sSFR(z) = (1 + z) 3 /t H0 , as observed (where t H0 is the Hubble time and no free parameters are necessary). In addition, the simple evolution for the star-formation intensity we propose is in agreement with observations of Milky Way-like galaxies selected through abundance matching. At z > ∼ 2, we argue that star formation is self-regulated by high pressures generated by the intense star formation itself. The star formation intensity must be high enough to either balance the hydrostatic pressure (a rather extreme assumption) or to generate high turbulent pressure in the molecular medium which maintains galaxies near the line of instability (i.e. Toomre Q ∼ 1). We provide simple prescriptions for understanding these self-regulation mechanisms based on solid relationships verified through extensive study. In all cases, the most important factor is the increase in stellar and gas mass surface density with redshift, which allows distant galaxies to maintain high levels of sSFR. Without a strong feedback from massive stars, such galaxies would likely reach very high sSFR levels, have high star formation efficiencies, and because strong feedback drives outflows, ultimately have an excess of stellar baryons.

Star Formation During Galaxy Formation

EAS Publications Series, 2011

Young galaxies are clumpy, gas-rich, and highly turbulent. Star formation appears to occur by gravitational instabilities in galactic disks. The high dispersion makes the clumps massive and the disks thick. The star formation rate should be comparable to the gas accretion rate of the whole galaxy, because star formation is usually rapid and the gas would be depleted quickly otherwise. The empirical laws for star formation found locally hold at redshifts around 2, although the molecular gas consumption time appears to be smaller, and mergers appear to form stars with a slightly higher efficiency than the majority of disk galaxies.