Implementation of Sink Particles in the Athena Code

We describe implementation and tests of sink particle algorithms in the Eulerian grid-based code Athena. Introduction of sink particles enables long-term evolution of systems in which localized collapse occurs, and it is impractical (or unnecessary) to resolve the accretion shocks at the centers of collapsing regions. We discuss similarities and differences of our methods compared to other implementations of sink particles. Our criteria for sink creation are motivated by the properties of the Larson-Penston collapse solution. We use standard particle-mesh methods to compute particle and gas gravity together. Accretion of mass and momenta onto sinks is computed using fluxes returned by the Riemann solver. A series of tests based on previous analytic and numerical collapse solutions is used to validate our method and implementation. We demonstrate use of our code for applications with a simulation of planar converging supersonic turbulent flow, in which multiple cores form and collapse to create sinks; these sinks continue to interact and accrete from their surroundings over several Myr.Comment: 39 pages, 14 figures, Accepted to ApJ

Prestellar Core Formation, Evolution, and Accretion from Gravitational Fragmentation in Turbulent Converging Flows

We investigate prestellar core formation and accretion based on three-dimensional hydrodynamic simulations. Our simulations represent local $\sim 1$pc regions within giant molecular clouds where a supersonic turbulent flow converges, triggering star formation in the post-shock layer. We include turbulence and self-gravity, applying sink particle techniques, and explore a range of inflow Mach number ${\cal M}=2-16$. Two sets of cores are identified and compared: $t_1$-cores are identified of a time snapshot in each simulation, representing dense structures in a single cloud map; $t_\mathrm{coll}$-cores are identified at their individual time of collapse, representing the initial mass reservoir for accretion. We find that cores and filaments form and evolve at the same time. At the stage of core collapse, there is a well-defined, converged characteristic mass for isothermal fragmentation that is comparable to the critical Bonner-Ebert mass at the post-shock pressure. The core mass functions (CMFs) of $t_\mathrm{coll}$-cores show a deficit of high-mass cores ($\gtrsim 7M_\odot$) compared to the observed stellar initial mass function (IMF). However, the CMFs of $t_1$-cores are similar to the observed CMFs and include many low-mass cores that are gravitationally stable. The difference between $t_1$-cores and $t_\mathrm{coll}$-cores suggests that the full sample from observed CMFs may not evolve into protostars. Individual sink particles accrete at a roughly constant rate throughout the simulations, gaining one $t_\mathrm{coll}$-core mass per free-fall time even after the initial mass reservoir is accreted. High-mass sinks gain proportionally more mass at late times than low-mass sinks. There are outbursts in accretion rates, resulting from clumpy density structures falling into the sinks

Maximally Star-Forming Galactic Disks I. Starburst Regulation Via Feedback-Driven Turbulence

Star formation rates in the centers of disk galaxies often vastly exceed those at larger radii. We investigate the idea that these central starbursts are self-regulated, with the momentum flux injected to the ISM by star formation balancing the gravitational force confining the gas. For most starbursts, supernovae are the largest contributor to the momentum flux, and turbulence provides the main pressure support for the predominantly-molecular ISM. If the momentum feedback per stellar mass formed is p_*/m_* ~ 3000 km/s, the predicted star formation rate is Sigma_SFR=2 pi G Sigma^2 m_*/p_* ~0.1(Sigma/100Msun/pc^2)^2 Msun/kpc^2/yr in regions where gas dominates the vertical gravity. We compare this prediction with numerical simulations of vertically-resolved disks that model star formation including feedback, finding good agreement for gas surface densities Sigma ~ 10^2-10^3 Msun/pc^2. We also compare to a compilation of star formation rates and gas contents from local and high-redshift galaxies (both mergers and normal galaxies), finding good agreement provided that X_CO decreases weakly as Sigma and Sigma_SFR increase. Star formation rates in dense, turbulent gas are also expected to depend on the gravitational free-fall time; if the efficiency per free-fall time is epsilon_ff ~ 0.01, the turbulent velocity dispersion driven by feedback is expected to be v_z = 0.4 epsilon_ff p_*/m_* ~ 10 km/s, relatively independent of Sigma or Sigma_SFR. Turbulence-regulated starbursts (controlled by kinetic momentum feedback) are part of the larger scheme of self-regulation; primarily-atomic low-Sigma outer disks may have star formation regulated by UV heating feedback, whereas regions at extremely high Sigma may be regulated by feedback of radiation that is reprocessed into trapped IR.Comment: 35 pages, 5 figures; accepted by the Ap

Can Nonlinear Hydromagnetic Waves Support a Self-Gravitating Cloud?

Using self-consistent magnetohydrodynamic (MHD) simulations, we explore the hypothesis that nonlinear MHD waves dominate the internal dynamics of galactic molecular clouds. We employ an isothermal equation of state and allow for self-gravity. We adopt ``slab-symmetry,'' which permits motions $\bf v_\perp$ and fields $\bf B_\perp$ perpendicular to the mean field, but permits gradients only parallel to the mean field. The Alfv\'en speed $v_A$ exceeds the sound speed $c_s$ by a factor $3-30$. We simulate the free decay of a spectrum of Alfv\'en waves, with and without self-gravity. We also perform simulations with and without self-gravity that include small-scale stochastic forcing. Our major results are as follows: (1) We confirm that fluctuating transverse fields inhibit the mean-field collapse of clouds when the energy in Alfv\'en- like disturbances remains comparable to the cloud's gravitational binding energy. (2) We characterize the turbulent energy spectrum and density structure in magnetically-dominated clouds. The spectra evolve to approximately $v_{\perp,\,k}^2\approx B_{\perp,\,k}^2/4\pi\rho\propto k^{-s}$ with $s\sim 2$, i.e. approximately consistent with a ``linewidth-size'' relation $\sigma_v(R) \propto R^{1/2}$. The simulations show large density contrasts, with high density regions confined in part by the fluctuating magnetic fields. (3) We evaluate the input power required to offset dissipation through shocks, as a function of $c_s/v_A$, the velocity dispersion $\sigma_v$, and the scale $\lambda$ of the forcing. In equilibrium, the volume dissipation rate is $5.5(c_s/v_a)^{1/2} (\lambda/L)^{-1/2}\times \rho \sigma_v^3/L$, for a cloud of linear size $L$ and density $\rho$. (4) Somewhat speculatively, we apply our results to a ``typical'' molecular cloud. The mechanical power input requiredComment: Accepted for publication in Ap.J. 47 pages, 13 postscript figures. Report also available at http://cfa-www.harvard.edu/~gammie/MHD.p

Numerical Simulations of Turbulent Molecular Clouds Regulated by Reprocessed Radiation Feedback from Nascent Super Star Clusters

Radiation feedback from young star clusters embedded in giant molecular clouds (GMCs) is believed to be important to the control of star formation. For the most massive and dense clouds, including those in which super star clusters (SSCs) are born, pressure from reprocessed radiation exerted on dust grains may disperse a significant portion of the cloud mass back into the interstellar medium (ISM). Using our radiaton hydrodynamics (RHD) code, Hyperion, we conduct a series of numerical simulations to test this idea. Our models follow the evolution of self-gravitating, strongly turbulent clouds in which collapsing regions are replaced by radiating sink particles representing stellar clusters. We evaluate the dependence of the star formation efficiency (SFE) on the size and mass of the cloud and $\kappa$, the opacity of the gas to infrared (IR) radiation. We find that the single most important parameter determining the evolutionary outcome is $\kappa$, with $\kappa \gtrsim 15 \text{ cm}^2 \text{ g}^{-1}$ needed to disrupt clouds. For $\kappa = 20-40 \text{ cm}^2 \text{ g}^{-1}$, the resulting SFE=50-70% is similar to empirical estimates for some SSC-forming clouds. The opacities required for GMC disruption likely apply only in dust-enriched environments. We find that the subgrid model approach of boosting the direct radiation force $L/c$ by a "trapping factor" equal to a cloud's mean IR optical depth can overestimate the true radiation force by factors of $\sim 4-5$. We conclude that feedback from reprocessed IR radiation alone is unlikely to significantly reduce star formation within GMCs unless their dust abundances or cluster light-to-mass ratios are enhanced.Comment: 19 pages, 18 figures, accepted for publication in Ap

A Two-moment Radiation Hydrodynamics Module in Athena Using a Time-explicit Godunov Method

We describe a module for the Athena code that solves the gray equations of radiation hydrodynamics (RHD), based on the first two moments of the radiative transfer equation. We use a combination of explicit Godunov methods to advance the gas and radiation variables including the non-stiff source terms, and a local implicit method to integrate the stiff source terms. We adopt the M1 closure relation and include all leading source terms. We employ the reduced speed of light approximation (RSLA) with subcycling of the radiation variables in order to reduce computational costs. Our code is dimensionally unsplit in one, two, and three space dimensions and is parallelized using MPI. The streaming and diffusion limits are well-described by the M1 closure model, and our implementation shows excellent behavior for a problem with a concentrated radiation source containing both regimes simultaneously. Our operator-split method is ideally suited for problems with a slowly varying radiation field and dynamical gas flows, in which the effect of the RSLA is minimal. We present an analysis of the dispersion relation of RHD linear waves highlighting the conditions of applicability for the RSLA. To demonstrate the accuracy of our method, we utilize a suite of radiation and RHD tests covering a broad range of regimes, including RHD waves, shocks, and equilibria, which show second-order convergence in most cases. As an application, we investigate radiation-driven ejection of a dusty, optically thick shell in the interstellar medium (ISM). Finally, we compare the timing of our method with other well-known iterative schemes for the RHD equations. Our code implementation, Hyperion, is suitable for a wide variety of astrophysical applications and will be made freely available on the Web.Comment: 30 pages, 29 figures, accepted for publication in ApJ

Feedback Regulated Turbulence, Magnetic Fields, and Star Formation Rates in Galactic Disks

We use three-dimensional magnetohydrodynamic (MHD) simulations to investigate the quasi-equilibrium states of galactic disks regulated by star formation feedback. We incorporate effects from massive-star feedback via time-varying heating rates and supernova (SN) explosions. We find that the disks in our simulations rapidly approach a quasi-steady state that satisfies vertical dynamical equilibrium. The star formation rate (SFR) surface density self-adjusts to provide the total momentum flux (pressure) in the vertical direction that matches the weight of the gas. We quantify feedback efficiency by measuring feedback yields, \eta_c\equiv P_c/\Sigma_SFR (in suitable units), for each pressure component. The turbulent and thermal feedback yields are the same for HD and MHD simulations, \eta_th~1 and \eta_ turb~4, consistent with the theoretical expectations. In MHD simulations, turbulent magnetic fields are rapidly generated by turbulence, and saturate at a level corresponding to \eta_mag,t~1. The presence of magnetic fields enhances the total feedback yield and therefore reduces the SFR, since the same vertical support can be supplied at a smaller SFR. We suggest further numerical calibrations and observational tests in terms of the feedback yields.Comment: To appear in Proceedings of IAU Symposium 315, From interstellar clouds to star-forming galaxies: universal processes?, P. Jablonka, P. Andre, and F.. van der Tak, ed