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

Vertical Equilibrium, Energetics, and Star Formation Rates in Magnetized Galactic Disks Regulated by Momentum Feedback from Supernovae

Recent hydrodynamic (HD) simulations have shown that galactic disks evolve to reach well-defined statistical equilibrium states. The star formation rate (SFR) self-regulates until energy injection by star formation feedback balances dissipation and cooling in the interstellar medium (ISM), and provides vertical pressure support to balance gravity. In this paper, we extend our previous models to allow for a range of initial magnetic field strengths and configurations, utilizing three-dimensional, magnetohydrodynamic (MHD) simulations. We show that a quasi-steady equilibrium state is established as rapidly for MHD as for HD models unless the initial magnetic field is very strong or very weak, which requires more time to reach saturation. Remarkably, models with initial magnetic energy varying by two orders of magnitude approach the same asymptotic state. In the fully saturated state of the fiducial model, the integrated energy proportions E_kin:E_th:E_mag,t:E_mag,o are 0.35:0.39:0.15:0.11, while the proportions of midplane support P_turb:P_th:\Pi_mag,t:\Pi_mag,o are 0.49:0.18:0.18:0.15. Vertical profiles of total effective pressure satisfy vertical dynamical equilibrium with the total gas weight at all heights. We measure the "feedback yields" \eta_c=P_c/\Sigma_SFR (in suitable units) for each pressure component, finding that \eta_turb~4 and \eta_th~1 are the same for MHD as in previous HD simulations, and \eta_mag,t~1. These yields can be used to predict the equilibrium SFR for a local region in a galaxy based on its observed gas and stellar surface densities and velocity dispersions. As the ISM weight (or dynamical equilibrium pressure) is fixed, an increase in $\eta$ from turbulent magnetic fields reduces the predicted \Sigma_SFR by ~25% relative to the HD case.Comment: To appear in Ap

Momentum Injection by Supernovae in the Interstellar Medium

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).Comment: 51 pages, 16 figures, accepted for publication in Ap

Three Dimensional Hydrodynamic Simulations of Multiphase Galactic Disks with Star Formation Feedback: II. Synthetic HI 21 cm Line Observations

We use three-dimensional numerical hydrodynamic simulations of the turbulent, multiphase atomic interstellar medium (ISM) to construct and analyze synthetic HI 21 cm emission and absorption lines. Our analysis provides detailed tests of 21 cm observables as physical diagnostics of the atomic ISM. In particular, we construct (1) the "observed" spin temperature, $T_{s,obs}(v_{ch})\equiv T_B(v_{ch})/[1-e^{-{\tau}(v_{ch})}]$, and its optical-depth weighted mean T_s,obs; (2) the absorption-corrected "observed" column density, $N_{H,obs}\propto \int dv_{ch} T_B(v_{ch}){\tau}(v_{ch})/[[1-e^{-{\tau}(v_{ch})}]$; and (3) the "observed" fraction of cold neutral medium (CNM), $f_{c,obs}\equiv T_c/T_{s,obs}$ for T_c the CNM temperature; we compare each observed parameter with true values obtained from line-of-sight (LOS) averages in the simulation. Within individual velocity channels, T_s,obs(v_ch) is within a factor 1.5 of the true value up to ${\tau}(v_{ch})\approx10$. As a consequence, N_H,obs and T_s,obs are respectively within 5% and 12% of the true values for 90% and 99% of LOSs. The optically thin approximation significantly underestimates N_H for ${\tau}>1$. Provided that T_c is constrained, an accurate observational estimate of the CNM mass fraction can be obtained down to 20%. We show that T_s,obs cannot be used to distinguish the relative proportions of warm and thermally-unstable atomic gas, although the presence of thermally-unstable gas can be discerned from 21 cm lines with 200K<$T_{s,obs}(v_{ch})$<1000K. Our mock observations successfully reproduce and explain the observed distribution of the brightness temperature, optical depth, and spin temperature in Roy et al. (2013a). The threshold column density for CNM seen in observations is also reproduced by our mock observations. We explain this observed threshold behavior in terms of vertical equilibrium in the local Milky Way's ISM disk.Comment: 34 pages, 12 figures. Accepted for publication in ApJ. For Paper I, see http://arxiv.org/abs/1308.323

Three Dimensional Hydrodynamic Simulations of Multiphase Galactic Disks with Star Formation Feedback: I. Regulation of Star Formation Rates

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 $\Sigma_{SFR}$ 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 $\Sigma_{SFR}$ 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 $\Sigma_{SFR}$ apply. For outer disk regions, this results in $\Sigma_{SFR} \propto \Sigma \sqrt{\rho_{sd}}$, where $\Sigma$ is the total gas surface density and $\rho_{sd}$ is the midplane density of the stellar disk (plus dark matter). This scaling law arises because $\rho_{sd}$ 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.Comment: 20 pages, 17 figures. Accepted for publication in Ap

Numerical Modeling of Multiphase, Turbulent Galactic Disks with Star Formation Feedback

Star formation is self-regulated by its feedback that drives turbulence and heats the gas. In equilibrium, the star formation rate (SFR) should be directly related to the total (thermal plus turbulent) midplane pressure and hence the total weight of the diffuse gas if energy balance and vertical dynamical equilibrium hold simultaneously. To investigate this quantitatively, we utilize numerical hydrodynamic simulations focused on outer-disk regions where diffuse atomic gas dominates. By analyzing gas properties at saturation, we obtain relationships between the turbulence driving and dissipation rates, heating and cooling rates, the total midplane pressure and the total weight of gas, and the SFR and the total midplane pressure. We find a nearly linear relationship between the SFR and the midplane pressure consistent with the theoretical prediction.Comment: 2 pages, 1 figure. To appear in the proceeding of the IAU GA XXVIII, Special Session 12: Modern Views of the Interstellar Mediu

Numerical Simulations of Multiphase Winds and Fountains from Star-Forming Galactic Disks: I. Solar Neighborhood TIGRESS 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 < T < 2x10^4K) fountains. The hot gas at distance d>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.Comment: Accepted for publication in Ap