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

VADER: A Flexible, Robust, Open-Source Code for Simulating Viscous Thin Accretion Disks

The evolution of thin axisymmetric viscous accretion disks is a classic problem in astrophysics. While models based on this simplified geometry provide only approximations to the true processes of instability-driven mass and angular momentum transport, their simplicity makes them invaluable tools for both semi-analytic modeling and simulations of long-term evolution where two- or three-dimensional calculations are too computationally costly. Despite the utility of these models, the only publicly-available frameworks for simulating them are rather specialized and non-general. Here we describe a highly flexible, general numerical method for simulating viscous thin disks with arbitrary rotation curves, viscosities, boundary conditions, grid spacings, equations of state, and rates of gain or loss of mass (e.g., through winds) and energy (e.g., through radiation). Our method is based on a conservative, finite-volume, second-order accurate discretization of the equations, which we solve using an unconditionally-stable implicit scheme. We implement Anderson acceleration to speed convergence of the scheme, and show that this leads to factor of $\sim 5$ speed gains over non-accelerated methods in realistic problems, though the amount of speedup is highly problem-dependent. We have implemented our method in the new code Viscous Accretion Disk Evolution Resource (VADER), which is freely available for download from https://bitbucket.org/krumholz/vader/ under the terms of the GNU General Public License.Comment: 58 pages, 13 figures, accepted to Astronomy & Computing; this version includes more discussion, but no other changes; code is available for download from https://bitbucket.org/krumholz/vader

Numerical Simulations of Radiatively-Driven Dusty Winds

[abridged] Radiation pressure on dust grains may be an important mechanism in driving winds in a wide variety of astrophysical systems. However, the efficiency of the coupling between the radiation field and the dusty gas is poorly understood in environments characterized by high optical depths. We present a series of idealized numerical experiments, performed with the radiation-hydrodynamic code ORION, in which we study the dynamics of such winds and quantify their properties. We find that, after wind acceleration begins, radiation Rayleigh-Taylor instability forces the gas into a configuration that reduces the rate of momentum transfer from the radiation field to the gas by a factor ~ 10 - 100 compared to an estimate based on the optical depth at the base of the atmosphere; instead, the rate of momentum transfer from a driving radiation field of luminosity L to the gas is roughly L/c multiplied by one plus half the optical depth evaluated using the photospheric temperature, which is far smaller than the optical depth one would obtain using the interior temperature. When we apply our results to conditions appropriate to ULIRGs and star clusters, we find that the asymptotic wind momentum flux from such objects should not significantly exceed that carried by the direct radiation field, L/c. This result constrains the expected mass loss rates from systems that exceed the Eddington limit to be of order the so-called "single-scattering" limit, and not significantly higher. We present an approximate fitting formula for the rate of momentum transfer from radiation to dusty gas through which it passes, which is suitable for implementation in sub-grid models of galaxy formation. Finally, we provide a first map of the column density distribution of gas in a radiatively-driven wind as a function of velocity, and velocity dispersion.Comment: 19 pages, 17 figures, MNRAS in press; some additional discussion compared to previous version, no changes in conclusion