MNRAS 000,1{12 (2015) Preprint 29 August 2018 Compiled using MNRAS LATEX style file v3.0 Dynamical cooling of galactic discs by molecular cloud collisions { Origin of giant clumps in gas-rich galaxy discs Guang-Xing Li1? 1University Observatory Munich, Scheinerstrasse 1, D-81679 Munchen,¨ Germany Accepted XXX. Received YYY; in original form ZZZ ABSTRACT Different from Milky-Way-like galaxies, discs of gas-rich galaxies are clumpy. It is believed that the clumps form because of gravitational instability. However, a nec- essary condition for gravitational instability to develop is that the disc must dissi- pate its kinetic energy effectively, this energy dissipation (also called cooling) is not well-understood. We propose that collisions (coagulation) between molecular clouds dissipate the kinetic energy of the discs, which leads to a dynamical cooling. The effec- tiveness of this dynamical cooling is quantifiedp by the dissipation parameter D, which is the ratio between the free-fall time tff ≈ 1= Gρdisc and the cooling time determined by the cloud collision process tcool. This ratio is related to the ratio between the mean surface density of the disc Σdisc and the mean surface density of molecular clouds in the disc Σcloud. When D < 1=3 (which roughly corresponds to Σdisc < 1=3Σcloud), cloud collision cooling is inefficient, and fragmentation is suppressed. When D > 1=3 (which roughly corresponds to Σdisc > 1=3Σcloud), cloud-cloud collisions lead to a rapid cool- ing through which clumps form. On smaller scales, cloud-cloud collisions can drive molecular cloud turbulence. This dynamical cooling process can be taken into account in numerical simulations as a subgrid model to simulate the global evolution of disc galaxies. Key words: Galaxy: disc { Galaxy: evolution {ISM: clouds {ISM: kinematics and dynamics { instabilities 1 INTRODUCTION One promising clump formation path is the gravita- tional instability, where the growth of perturbations on the Star formation occurs in the cold phase of the galactic inter- disc scale leads to structure formation. In fact, the sizes of stellar medium (ISM), which exhibits diverse morphologies the observed clumps are often comparable to the Toomre in different galaxies. The Milky Way is an example where length (Fisher et al. 2017a), suggesting that gravitational molecular gas is mostly distributed in molecular clouds instability is at work. The short-time evolution of the grav- whose sizes are much smaller than the disc scaleheight. In itational instability is determined by the Toomre Q param- contrast to this, in high-redshift, gas-rich galaxies, molec- eter, where Q = σ Ω =πGΣ , σ is the velocity ular gas seems to concentrate in giant (kpc-size), massive disc v;disc disc disc v;disc dispersion, Σdisc is the disc surface density, and Ωdisc is disc arXiv:1703.10613v3 [astro-ph.GA] 29 Aug 2017 clumps, and majority of the star formation occurs in the angular frequency. In Toomre's formalism, fragmentation is clumps (Abraham et al. 1996; Noguchi 1998; Elmegreen driven by gravity (which is characterized by Σ ), which is & Elmegreen 2005; Genzel et al. 2008; Guo et al. 2015; disc balanced by a combination of supported caused by local mo- Elmegreen et al. 2009;F ¨orster Schreiber et al. 2009) 1. Un- tions σ and shear (Ω , which is roughly the epicyclic like molecular clouds, the clumps have sizes that are often v;disc disc frequency). Discs with Q < 1 are unstable against non- comparable to the disc scaleheight. How do they form? disc axisymmetric instabilities and should fragment. It has been believed that the clump formation is largely controlled by the Toomre parameter (Kereˇs et al. 2005; ? E-mail: [email protected] (USM) Dekel et al. 2009a,b; Inoue et al. 2016) or a Toomre-like 1 Sometimes the giant clumps appear in chains, and these galax- ies are called \chain galaxies" (Cowie et al. 1995; van den Bergh formalism, e.g. Romeo et al.(2010). However, the Toomre et al. 1996; Elmegreen et al. 2004b,a; Conselice et al. 2005), and formalism seems to provide a still incomplete description to Dalcanton & Shectman(1996) suggested that the chain-like mor- the clump formation process: observationally, the connec- phology is due the projected view of an edge-on galaxy. tion between a smaller Toomre Q parameter and a clumpy c 2015 The Authors 2 Guang-Xing Li disc has not been established. On the contrary, observations the disc-scale cooling should be able to reduce this velocity indicate that galactic discs tend to have Qdisc ≈ 1 with an dispersion. When the disc is supported by thermal pressure, observed uncertainty of a factor of two, and this is almost σv;disc is related to the temperature of the gas; when the disc 2 independent on whether a disc is clumpy or not (Hitschfeld is supported by some random motions, σv;disc is the velocity et al. 2009; Puech 2010; Cacciato et al. 2012; Fisher et al. dispersion of these random motions. Previously, the domi- 2014; Romeo & Falstad 2013; Romeo & Mogotsi 2017) 3. nate cooling mechanism of these discs is not well-identified: This cannot be explained within the Toomre formalism, but Dekel et al.(2009b); Mayer et al.(2016) identified the ra- is believed to the the result of a self-regulated disc evolution. diative cooling time of the atomic ISM as the cooling time Since the discs are already self-regulating systems, a better relevant for disc fragmentation, and Wada et al.(2002); theory of clump formation should take this into account. Elmegreen & Burkert(2010); Klessen & Hennebelle(2010); Apart from this, more recent theoretical studies also Elmegreen(2011); Forbes et al.(2014) 4 assumed galactic suggested that the efficiency of disc cooling plays a more disc turbulence model, and identified the turbulence dissipa- fundamental role in clump formation. Gammie(2001); John- tion time as the disc cooling time. We argue that neither are son & Gammie(2003) carried out a set of local, shearing box adequate. This is because in a real galactic disc (we will be simulations of disc evolution, and found that (a) the balance focusing on gas-rich discs where more than half of the gas is between heating and cooling processes tends to regulate the molecular, see e.g. Tacconi et al.(2010)), the local dynamical disc to a state where Qdisc ≈ 1 . They also found that (b) it is support comes from the quasi-random motions of the molec- the cooling time that determines the long-time evolution of ular gas. To cool down a disc one must reduce this random such discs: if cooling is inefficient (cooling time is long com- motion. Dekel et al.(2009b) mistakenly believed that rele- pared to the dynamical time), the disc should evolve into a vant cooling time is the radiative cooling time of the atomic gravo-turbulent state where turbulence maintained by accre- gas. However, they overlooked the critical fact that even if tion can effectively suppress the overly-rapid fragmentation, one has successfully converted the atomic gas into the molec- and the disc is dominated by fluffy, filamentary structures ular gas through the radiative cooling, the disc can still be that are constantly smeared apart by rotation; when cooling supported by motions of the molecular ISM. The kinetic en- is efficient (cooling time is short compared to the dynamical ergy contained in these motions cannot be reduced with the time), gas in the disc rapidly dissipates kinetic energy and radiative cooling, and additional dynamical cooling channels fragments into a few giant clumps. are needed. Another set of models are based on the picture The theory of Gammie(2001) seems to provide a good of galactic disc turbulence (Wada et al. 2002; Elmegreen & description the evolution of disc galaxies. First, both simu- Burkert 2010; Klessen & Hennebelle 2010; Elmegreen 2011; lations (e.g. Hopkins et al. 2012; Lehnert et al. 2013; Gold- Forbes et al. 2014). These models correctly identified that to baum et al. 2016) and observations (Hitschfeld et al. 2009; cool down the disc, one must reduce the velocity dispersion Puech 2010; Cacciato et al. 2012; Fisher et al. 2014) seem of the ISM. However, they made the assumption that the to indicate that discs tend to have Qdisc ≈ 1 , consistent dynamics of the multi-phase ISM can be described by the with self-regulation. Secondly, we do observe a similar di- turbulence model { an assumption that is widely accepted chotomy in the morphology of the observed galaxies: in yet not justified: the standard theory of turbulence has only Gammie(2001), a disc can be either filamentary or clumpy, been shown to be valid for non-self-gravitating gas with well- and this seems to correspond to the fact that in galaxies gas defined equation of states. In a real galactic disc, gas is sepa- either organises into smaller clouds that can be aligned on a rated into different phases where molecular gas has a density larger scale (e.g. the Milky Way where they form larger fila- that is two orders of magnitudes larger than the density of ments) or into giant clumps (e.g. the gas-rich clumpy galax- the ambient ISM (See also Sec. 2.1). This density contrast ies). This resemblance poses the question: can we explain makes many assumptions of the galactic disc turbulence the morphological difference of galaxies using the theory of model invalid. For example, in the standard picture of galac- Gammie(2001)? What is the major cooling mechanism in tic disc turbulence, ideally, one requires energy to cascade these discs? from the larger scales continuously down to the Kolmogorov The cooling of a galactic disc remains an open issue. We microscales where it dissipates into heat.