A semi-analytic model of the turbulent multi-phase interstellar medium

Abstract

We present a semi-analytic model for the interstellar medium that considers local processes and structures of turbulent star-forming gas. A volume element of the interstellar medium is described as a multiphase system, comprising a cold and a warm gas phase in effective (thermal plus turbulent) pressure equilibrium, and a stellar component. Since turbulence has a critical impact on the shape of the gaseous phases, on the production of molecular hydrogen and on the formation of stars, the consistent treatment of turbulence energy -- the kinetic energy of unresolved motions -- is an important new feature of our model. Besides turbulence production by supernovae and by the cooling instability, we also take into account the forcing by large scale motions. We formulate a set of ordinary differential equations, which statistically describes star formation and the exchange between the different budgets of mass and energy in a region of the interstellar medium with given mean density, size, metallicity and external turbulence forcing. By exploring the behaviour of the solutions, we find equilibrium states, in which the star formation efficiencies are consistent with observations. Kennicutt-Schmidt-like relations naturally arise from the equilibrium solutions, while conventional star formation models in numerical simulations impose such relations with observed efficiency parameters as phenomenological calibrations. Beyond the semi-analytic approach, a potential application is a complete subgrid scale model of the unresolved multi-phase structure, star formation and turbulence in simulations of galaxies or in cosmological simulations. The formulation presented in this article combines various models focusing on particular processes and yet can be adopted to specific applications, depending on the range of resolved length scales.Comment: 25 pages, 22 figures, 1 table, accepted for publication by MNRA

Large-Scale Structure Formation: From the First Non-linear Objects to Massive Galaxy Clusters

“…Given the current limitations, stellar feedback is usually incorporated in cluster simulations via phenomenological prescriptions of star formation and SN heating (e.g. Braun & Schmidt 2012) at moderately low resolutions.…”

Galaxy evolution: modelling the role of non-thermal pressure in the interstellar medium

“…We demonstrate that non-thermal pressure components can be instrumental in solving the depletion time discrepancy in two respects: they reduce the quasi-steady state density and the corresponding star formation rates and cooling times, and they stabilize the gas by adding longer relaxation times in cases where star formation flickers on and off. The regulating effect has been shown previously for cosmic rays (Salem & Bryan 2014;Booth et al 2013;Hanasz et al 2013) and turbulence (Ostriker et al 2001;Braun & Schmidt 2012) but the two were not considered together and in any case were not yet formulated in a way which is applicable to large scale cosmological simulations.…”

“…Below this threshold, the steady-state non-thermal pressure is expected to vanish. However, in reality, a non-star forming region can still maintain a steady state non-thermal pressure due to diffusion processes from neighboring regions (Joung et al 2009;Scannapieco et al 2012), or to various other sources (Braun & Schmidt 2012;Dekel et al 2009). We partly account for that within our "single-cell" framework by setting a finite decay rate for non-star-forming regions.…”

“…Specifically, this suggests that the coupling is not instantaneous, but has a finite response time as energy convects with the gas or diffuses through it. Alternatively, there may be additional sources for turbulence, magnetic fields and CR which are dominant at ≈ 1kpc altitudes above the disc (see, for example, Dekel et al (2009) for extra-galactic driving of turbulence and Braun & Schmidt (2012) for internal ISM instability-driven turbulence).…”

“…An equation of state for subgrid turbulence has been proposed in Maier et al (2009). Joung et al (2009) proposed an effective EoS directly related to star formation rates, and Braun & Schmidt (2012) incorporated turbulent pressure as a sub-grid model of the various phases motivated by McKee & Ostriker (1977). Scannapieco & Brüggen (2010) showed that sub-grid models for supersonic turbulence can have a large affect on dwarf galaxies.…”