The Atomic-to-Molecular Transition in Galaxies. III. A New Method for Determining the Molecular Content of Primordial and Dusty Clouds

Understanding the molecular content of galaxies is a critical problem in star formation and galactic evolution. Here we present a new method, based on a Stromgren-type analysis, to calculate the amount of HI that surrounds a molecular cloud irradiated by an isotropic radiation field. We consider both planar and spherical clouds, and H_2 formation either in the gas phase or catalyzed by dust grains. Under the assumption that the transition from atomic to molecular gas is sharp, our method gives the solution without any reference to the photodissociation cross section. We test our results for the planar case against those of a PDR code, and find typical accuracies of about 10%. Our results are also consistent with the scaling relations found in Paper I of this series, but they apply to a wider range of physical conditions. We present simple, accurate analytic fits to our results that are suitable for comparison to observations and to implementation in numerical and semi-analytic models.Comment: 14 pages, 5 figures, accepted to Ap

Radiation-Hydrodynamic Simulations of the Formation of Orion-Like Star Clusters I. Implications for the Origin of the Initial Mass Function

One model for the origin of typical galactic star clusters such as the Orion Nebula Cluster (ONC) is that they form via the rapid, efficient collapse of a bound gas clump within a larger, gravitationally-unbound giant molecular cloud. However, simulations in support of this scenario have thus far have not included the radiation feedback produced by the stars; radiative simulations have been limited to significantly smaller or lower density regions. Here we use the ORION adaptive mesh refinement code to conduct the first ever radiation-hydrodynamic simulations of the global collapse scenario for the formation of an ONC-like cluster. We show that radiative feedback has a dramatic effect on the evolution: once the first ~10-20% of the gas mass is incorporated into stars, their radiative feedback raises the gas temperature high enough to suppress any further fragmentation. However, gas continues to accrete onto existing stars, and, as a result, the stellar mass distribution becomes increasingly top-heavy, eventually rendering it incompatible with the observed IMF. Systematic variation in the location of the IMF peak as star formation proceeds is incompatible with the observed invariance of the IMF between star clusters, unless some unknown mechanism synchronizes the IMFs in different clusters by ensuring that star formation is always truncated when the IMF peak reaches a particular value. We therefore conclude that the global collapse scenario, at least in its simplest form, is not compatible with the observed stellar IMF. We speculate that processes that slow down star formation, and thus reduce the accretion luminosity, may be able to resolve the problem.Comment: 17 pages, 13 figures, emulateapj format, ApJ in press; simulation movies available at http://www.ucolick.org/~krumholz/publications.htm

Resolution Requirements and Resolution Problems in Simulations of Radiative Feedback in Dusty Gas

In recent years a number of authors have introduced methods to model the effects of radiation pressure feedback on flows of interstellar and intergalactic gas, and have posited that the forces exerted by stars' radiation output represents an important feedback mechanism capable of halting accretion and thereby regulating star formation. However, numerical simulations have reached widely varying conclusions about the effectiveness of this feedback. In this paper I show that much of the divergence in the literature is a result of failure to obey an important resolution criterion: whether radiation feedback is able to reverse an accretion flow is determined on scales comparable to the dust destruction radius, which is $\lesssim 1000$ AU even for the most luminous stellar sources. Simulations that fail to resolve this scale can produce unphysical results, in many cases leading to a dramatic overestimate of the effectiveness of radiation feedback. Most published simulations of radiation feedback on molecular cloud and galactic scales fail to satisfy this condition. I show how the problem can be circumvented by introducing a new subgrid model that explicitly accounts for momentum balance on unresolved scales, making it possible to simulate dusty accretion flows safely even at low resolution.Comment: 15 pages, 5 figures, MNRAS in press; this version has some added discussion, but no changes to figures or conclusion

The Star Formation Law in Molecule-Poor Galaxies

In this paper, I investigate the processes that regulate the rate of star formation in regions of galaxies where the neutral interstellar medium is predominantly composed of non-star-forming HI. In such regions, found today predominantly in low-metallicity dwarf galaxies and in the outer parts of large spirals, the star formation rate per unit area and per unit mass is much smaller than in more molecule-rich regions. While in molecule-rich regions the ultraviolet radiation field produced by efficient star formation forces the density of the cold neutral medium to a value set by two-phase equilibrium, I show that the low rates of star formation found in molecule-poor regions preclude this condition. Instead, the density of the cold neutral gas is set by the requirements of hydrostatic balance. Using this result, I extend the Krumholz, McKee, & Tumlinson model for star formation and the atomic to molecular transition to the molecule-poor regime. This "KMT+" model matches a wide range of observations of the star formation rate and the balance between the atomic and molecular phases in dwarfs and in the outer parts of spirals, and is well-suited to implementation as a subgrid recipe for star formation in cosmological simulations and semi-analytic models. I discuss the implications of this model for star formation over cosmological times.Comment: 18 pages, 9 figures, accepted for publication in MNRA

A Test of Star Formation Laws in Disk Galaxies

We use observations of the radial profiles of the mass surface density of total, Sigma_g, and molecular, Sigma_H2, gas, rotation velocity and star formation rate surface density, Sigma_sfr, of the molecular dominated regions of 12 disk galaxies from Leroy et al. to test several star formation laws: a "Kennicutt-Schmidt power law", Sigma_sfr=A_g Sigma_{g,2}^{1.5}$; a "Constant molecular law", Sigma_sfr = A_H2 Sigma_{H2,2}; the "Turbulence-regulated laws" of Krumholz & McKee (KM) and Krumholz, McKee & Tumlinson (KMT), a "Gas-Omega law", Sigma_sfr = B_Omega Sigma_g Omega; and a shear-driven "GMC collisions law", Sigma_sfr = B_CC Sigma_g Omega (1 - 0.7beta), where beta is d ln v_circ / d ln r. We find the constant molecular law, KMT turbulence law and GMC collision law are the most accurate, with an rms error of a factor of 1.5 if the normalization constants are allowed to vary between galaxies. Of these three laws, the GMC collision law does not require a change in physics to account for the full range of star formation activity seen from normal galaxies to circumnuclear starbursts. A single global GMC collision law with B_CC=8.0x10^{-3}, i.e. a gas consumption time of 20 orbital times for beta=0, yields an rms error of a factor of 1.8.Comment: 6 pages, including 2 figures, matches version published in ApJ

Analytical star formation rate from gravoturbulent fragmentation

We present an analytical determination of the star formation rate (SFR) in molecular clouds, based on a time-dependent extension of our analytical theory of the stellar initial mass function (IMF). The theory yields SFR's in good agreement with observations, suggesting that turbulence {\it is} the dominant, initial process responsible for star formation. In contrast to previous SFR theories, the present one does not invoke an ad-hoc density threshold for star formation; instead, the SFR {\it continuously} increases with gas density, naturally yielding two different characteristic regimes, thus two different slopes in the SFR vs gas density relationship, in agreement with observational determinations. Besides the complete SFR derivation, we also provide a simplified expression, which reproduces reasonably well the complete calculations and can easily be used for quick determinations of SFR's in cloud environments. A key property at the heart of both our complete and simplified theory is that the SFR involves a {\it density-dependent dynamical time}, characteristic of each collapsing (prestellar) overdense region in the cloud, instead of one single mean or critical freefall timescale. Unfortunately, the SFR also depends on some ill determined parameters, such as the core-to-star mass conversion efficiency and the crossing timescale. Although we provide estimates for these parameters, their uncertainty hampers a precise quantitative determination of the SFR, within less than a factor of a few.Comment: accepted for publication in ApJ

A Comparison of Methods for Determining the Molecular Content of Model Galaxies

Recent observations indicate that star formation occurs only in the molecular phase of a galaxy's interstellar medium. A realistic treatment of star formation in simulations and analytic models of galaxies therefore requires that one determine where the transition from the atomic to molecular gas occurs. In this paper we compare two methods for making this determination in cosmological simulations where the internal structures of molecular clouds are unresolved: a complex time-dependent chemistry network coupled to a radiative transfer calculation of the dissociating ultraviolet (UV) radiation field, and a simple time-independent analytic approximation. We show that these two methods produce excellent agreement at all metallicities >~10^-2 of the Milky Way value across a very wide range of UV fields. At lower metallicities the agreement is worse, likely because time-dependent effects become important; however, there are no observational calibrations of molecular gas content at such low metallicities, so it is unclear if either method is accurate. The comparison suggests that, in many but not all applications, the analytic approximation provides a viable and nearly cost-free alternative to full time-dependent chemistry and radiative transfer.Comment: 8 pages, 7 figures, accepted to ApJ, emulateapj format. This version contains typo corrections and changes to figure presentation, but is otherwise the same as the previous versio

On the Origin of Stellar Masses

It has been a longstanding problem to determine, as far as possible, the characteristic masses of stars in terms of fundamental constants; the almost complete invariance of this mass as a function of the star-forming environment suggests that this should be possible. Here I provide such a calculation. The typical stellar mass is set by the characteristic fragment mass in a star-forming cloud, which depends on the cloud's density and temperature structure. Except in the very early universe, the latter is determined mainly by the radiation released as matter falls onto seed protostars. The energy yield from this process is ultimately set by the properties of deuterium burning in protostellar cores, which determines the stars' radii. I show that it is possible to combine these considerations to compute a characteristic stellar mass almost entirely in terms of fundamental constants, with an extremely weak residual dependence on the interstellar pressure and metallicity. This result not only explains the invariance of stellar masses, it resolves a second mystery: why fragmentation of a cold, low-density interstellar cloud, a process with no obvious dependence on the properties of nuclear reactions, happens to select a stellar mass scale such that stellar cores can ignite hydrogen. Finally, the weak residual dependence on the interstellar pressure and metallicity may explain recent observational hints of a smaller characteristic mass in the high pressure, high metallicity cores of giant elliptical galaxies.Comment: 7 pages, 5 figures, emulateapj format. Accepted to Ap