The interstellar medium and star formation of galactic disks. I. Interstellar medium and giant molecular cloud properties with diffuse far-ultraviolet and cosmic-ray backgrounds
Qi Li, Jonathan C Tan, Duncan Christie, Thomas G Bisbas, Benjamin Wu, The interstellar medium and star formation of galactic disks. I. Interstellar medium and giant molecular cloud properties with diffuse far-ultraviolet and cosmic-ray backgrounds, Publications of the Astronomical Society of Japan, Volume 70, Issue SP2, May 2018, S56, https://doi.org/10.1093/pasj/psx136
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Abstract
We present a series of adaptive mesh refinement hydrodynamic simulations of flat rotation curve galactic gas disks, with a detailed treatment of the interstellar medium (ISM) physics of the atomic to molecular phase transition under the influence of diffuse far-ultraviolet (FUV) radiation fields and cosmic-ray backgrounds. We explore the effects of different FUV intensities, including a model with a radial gradient designed to mimic the Milky Way. The effects of cosmic rays, including radial gradients in their heating and ionization rates, are also explored. The final simulations in this series achieve 4 pc resolution across the ∼20 kpc global disk diameter, with heating and cooling followed down to temperatures of ∼10 K. The disks are evolved for 300 Myr, which is enough time for the ISM to achieve a quasi-statistical equilibrium. In particular, the mass fraction of molecular gas is stabilized by ∼200 Myr. Additional global ISM properties are analyzed. Giant molecular clouds (GMCs) are also identified and the statistical properties of their populations are examined. GMCs are tracked as the disks evolve. GMC collisions, which may be a means of triggering star cluster formation, are counted and their rates are compared with analytic models. Relatively frequent GMC collision rates are seen in these simulations, and their implications for understanding GMC properties, including the driving of internal turbulence, are discussed.
Most stars form in galactic disk systems, from “normal” disk galaxies to circumnuclear starburst disks (see, e.g., Kennicutt & Evans 2012; König et al. 2017). These disks can share a number of common properties, such as having approximately flat rotation curves (i.e., they are shearing disks) and being marginally gravitationally unstable [i.e., with a Toomre ( 1964) parameter Q ∼ 1]. Observational evidence has accumulated to connect star formation rates (SFRs) to the global disk environments (e.g., Kennicutt 1998; Bigiel et al. 2008; Genzel et al. 2010; Tan 2010; Suwannajak et al. 2014). It is thus important to understand the processes controlling interstellar medium (ISM) dynamics and star formation activity in such systems.
There have been many previous numerical simulation studies of galactic disks. The most comparable sets of simulations to our current work are those of Tasker and Tan ( 2009, hereafter TT09), Tasker ( 2011), and Tasker, Wadsley, and Pudritz ( 2015). TT09 presented a simulation of a galactic disk with a total gas mass surface density ranging from about Σg ≃ 60 M⊙ pc −2 at galactocentric radius r = 2 kpc to ≃10 M⊙ pc −2 at 10 kpc, with a maximum resolution of 8 pc that could undergo cooling to 300 K with a multiphase ISM. The cooling floor of 300 K (i.e., a minimum sound speed of cs = 1.6 km s −1 ) was an approximate method of modeling sub-grid turbulent support. For this reason, the detailed physics of the atomic to molecular transition was not followed in these simulations. The TT09 disk fragmented into a population of self-gravitating giant molecular clouds (GMCs), defined simply as connected, locally peaked structures above a threshold density of nH = 100 cm −3 , which were tracked and had their collision rates measured. However, this simulation did not include far-ultraviolet (FUV) heating or any other feedback processes. It thus had a GMC mass fraction that was moderately too high, ∼2/3, compared to, e.g., the Milky Way disk inside the solar orbit, which has a molecular mass fraction |$f_equiv Sigma _>/(Sigma _>+Sigma _>)simeq 0.75$| at r = 2 kpc falling to ≃0.6 at 5 kpc and ≃0.2 by 8 kpc (Koda et al. 2016). Also, GMCs in the TT09 simulation had a typical mass surface density, ΣGMC ∼ 300 M⊙ pc −2 , i.e., about a factor of two to three times higher than observed Milky Way GMCs.
Tasker ( 2011) presented a simulation of the same disk setup, but now including a constant diffuse FUV background with intensity of G0 = 4, normalized according to Habing ( 1968) (i.e., 4 Habings, which is about 2.4 times the local value in the solar vicinity of G0 = 1.7; Draine 1978), which leads to photoelectric heating via dust grains. A model of star formation, i.e., star particle creation, above a fixed density threshold of nH,* = 100 cm −3 at constant efficiency per local free-fall time (Krumholz & Tan 2007), but no feedback from young stars. One of the caveats of this simulation is that identified GMC properties were affected by the presence of clusters of star particles that could dominate the mass of the identified gaseous “GMC” structure. GMC dynamical properties and collision rates were thus affected by the presence of these star clusters. Tasker, Wadsley, and Pudritz ( 2015) included localized supernovae (SNe) feedback, in addition to the diffuse photoelectric heating. Their result suggests that weak localized thermal feedback may play a relatively minor role in shaping the galactic structure compared to gravitational interactions and disk shear. In both studies, very approximate heating/cooling physics only down to 300 K was adopted, and the atomic to molecular transition was not modeled. Fujimoto et al. ( 2014, 2016), utilizing the same simulation code and cooling function as TT09, investigated the GMC evolution in an M 83-type barred spiral galaxy with 1.5 pc resolution. Frequent cloud–cloud and tidal interactions in the bar region help to build up massive GMCs and unbound, transient clouds.
With a “two-fluid” (isothermal warm and cold gas) model without thermal processes, Dobbs ( 2008) carried out isolated, magnetized disk simulations with an SPMHD code and studied GMC formation and evolution via agglomeration and self gravity in spiral galaxies with different surface densities. Dobbs, Burkert, and Pringle ( 2011) adopted diffuse FUV heating, radiative and collisional cooling, and a simple prescription of stellar energy feedback. It was found that the spiral arms do not significantly trigger star formation but help to gather gas and to increase collision rates to produce more massive and denser GMCs. The GMC mass function was approximately reproduced and similar populations of retrograde and prograde clouds (relative to the galaxy rotation) are found due to enhanced collisions in the spiral arm regions (although TT09 saw a similar result without the need for large-scale spiral arms). Dobbs et al. ( 2017) extended these models to study populations of star clusters formed in the disks and compared them with observed systems.
Other galactic disk simulations have been conducted to investigate the physical processes that influence disk evolution. The role of stellar feedback has been emphasized by, e.g., Hopkins, Quataert, and Murray ( 2011, 2012), Agertz et al. ( 2013), Hopkins et al. ( 2014), and Agertz and Kravtsov ( 2015). Hopkins, Quataert, and Murray ( 2011, 2012) developed a set of numerical models to follow stellar feedback on scales from sub-GMC star-forming regions through entire galaxies, including the energy, momentum, mass, and metal fluxes from stellar radiation pressure, H ii photoionization and photoelectric heating, Types I and II SNe, and stellar winds (O-star and AGB). Based on the models, Hopkins, Quataert, and Murray ( 2012) and Hopkins et al. ( 2013) conducted pc-resolution smoothed-particle hydrodynamics (SPH) simulations of three types of isolated galaxies, i.e., SMC, Milky Way, and Sbc, and produce a quasi-steady ISM in which GMCs form and they disperse rapidly, with phase structure, turbulence, and disk and GMC properties concluded to be in good agreement with observations. Mayer et al. ( 2016) studied disk fragmentation and formation of giant clumps regulated by turbulence via superbubble or blastwave supernovae feedback, using the GASOLINE2 SPH code and the Lagrangian mesh-less code GIZMO. The difference in clump properties between the two sources of turbulence are found as a potential test of feedback mechanisms.
Goldbaum, Krumholz, and Forbes ( 2015, 2016) investigated the driving of turbulence by gravitational instabilities and star formation feedback, including stochastic stellar population synthesis, H ii region feedback, SNe, and stellar winds via 20 pc-resolution adaptive mesh refinement (AMR) hydrodynamics simulations. They argue from their results that gravitational instability is likely to be the dominant source of turbulence and transport in galactic disks, and that it is responsible for fueling star formation in the inner parts of galactic disks over cosmological times. The cascade of turbulence to smaller scales may be one process that regulates the local star formation rate within GMCs (Padoan & Nordlund 2002; Krumholz & McKee 2005), which is known to occur at a low efficiency per local free-fall time (Zuckerman & Evans 1974; Krumholz & Tan 2007).
In this work, our overall goal is to understand how the interstellar medium, including GMCs, and star formation activity in galactic disk systems are regulated, ultimately modeling all important physical processes and determining their relative importance, including in different galactic environments. In this first paper we introduce our fiducial “normal” disk model and our methods of treating the microphysics of ISM heating and cooling processes. We start with the simplifying assumption of only considering FUV and cosmic-ray (CR) heating, which can both be approximated as diffuse components. The first main goal is to understand ISM structure, including GMC structural and dynamical properties, in this limiting case, before complexities of magnetic fields, star formation, and localized feedback are introduced (deferred until future papers in this series). Compared to the simulations of TT09, the main improvements are the following: (1) we follow heating and cooling down to ∼10 K; (2) we use much-improved heating and cooling functions that we develop in this paper based on photodissociation region (PDR) calculations (for up to four-dimensional grids of density, temperature, FUV intensity, and CR ionization rate, adopting an empirical extinction versus density relation to allow local evaluation); (3) a variable mean particle mass across the atomic to molecular transition is allowed for in the hydrodynamic equations; (4) we study models, step by step, that investigate the effects of a variety of different assumptions for the FUV radiation field, including a model with a radial gradient within the disk; (5) we reach higher resolutions of 4 pc.
In section 2 we explain our simulation setup and methods. We present our results on global ISM properties in section 3. We examine GMC properties in section 4, and discuss GMC collisions in section 5. We conclude in section 6.
2 Methods
2.1 Numerical code and simulation suite
The simulations presented in this paper were run using the numerical code Enzo , an AMR hydrodynamics code (Bryan et al. 2014). This code solves the hydrodynamics equations using the 3D Zeus hydrodynamics solver (Stone & Norman 1992), which uses an artificial viscosity term to handle shocks. The quadratic artificial viscosity parameter (von Neumann & Richtmyer 1950) was set to 2.0 (the default value) for all simulations.
For most simulations (Runs I–V) we use a root grid (32.768 kpc on each side) of 256 3 and 4 additional AMR levels, giving a minimum spatial resolution of 8 pc. Cells are refined when the local Jeans length becomes smaller than four cell-widths, which is the condition typically used to avoid artificial fragmentation (Truelove et al. 1997). In comparison with the results of TT09, in Runs I, II, and III we first study disks that have a temperature floor of 300 K, which corresponds to the upper range of temperatures of the atomic cold neutral medium (CNM: Wolfire et al. 2003). We then adopt a 10 K temperature floor (Runs IV, V, and VI) to more accurately follow the atomic to molecular transition and thus the properties of GMCs. In Run VI we also introduce an extra level of AMR refinement, i.e., five levels in total, achieving 4 pc resolution to better resolve cloud structures. Note, however, that with temperatures now followed to 10 K, the Jeans length may not be well resolved above densities of ∼400 cm −3 . Artificial fragmentation may be occurring above these densities, which should be kept in mind when interpreting some of the results.
In this paper, we aim to examine the formation and evolution of GMCs in a flat rotation curve galactic disk without consideration of star formation, magnetic fields, and localized feedback mechanisms. We mainly study the effects of diffuse FUV feedback and the influence of diffuse CR ionization/heating. To investigate the influence of diffuse FUV feedback, we present simulation runs with different static FUV background radiation fields. In Runs I and II we set up a constant diffuse FUV radiation field with G0 = 1.0 and 4.0, respectively, where G0 = 1 is the FUV intensity normalized to the Habing ( 1968) estimate and a value of G0 = 1.7 corresponds to the local FUV radiation field in the Milky Way disk (Draine 1978). In Run III, the FUV field is set following the profile from Wolfire et al. ( 2003), where we take a local value of G0(R0) = 1.7 (Draine 1978). In Runs I–III, the CR ionization rate is set to a constant value ζ = 1 × 10 −16 s −1 (e.g., Dalgarno 2006). G0 and ζ are two input parameters of the PDR models. The configuration of each run is summarized in table 1.
Table 1.
Configurations of simulations.
| Run . | Resolution (pc) . | Tfloor (K) . | G0 . | ζ (s −1 ) . |
|---|---|---|---|---|
| I | 8 | 300 | 4 | 10 −16 |
| II | 8 | 300 | 1 | 10 −16 |
| III | 8 | 300 | Wolfire* | 10 −16 |
| IV | 8 | 10 | Wolfire | 10 −16 |
| V | 8 | 10 | Wolfire | ζ(r) † |
| VI | 4 | 10 | Wolfire | 10 −16 |
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