The SILCC (SImulating the LifeCycle of molecular Clouds) project – I. Chemical evolution of the supernova-driven ISM

“However, Springel (2005) shows that the worst-case errors, resulting from situations when the target cell is inside the contributing node, can be avoided by introducing an additional criterion that does not allow the target cell lie within a volume of the node increased by a certain factor, ηSB.”

“During the tree walk, the gravitational potential is calculated by the modified Ewald method (Ewald 1921; Klessen 1997).”

“These are (i) the Kennicutt– Schmidt (KS) relation (Kennicutt 1998) with SFR ∝ 1.4H2+H I , as well as (ii) newer results which relate the SFR surface density to the MNRAS 454, 238–268 (2015) molecular gas surface density, H2 , in a galaxy in a linear fashion 3 (Bigiel et al. 2008; Tacconi et al.…”

“It is a Barnes-Hut type octal-spatial tree (Barnes & Hut 1986) described in detail in Wünsch et al., in preparation.”

“2 N U M E R I C A L M E T H O D We use the fully three-dimensional, AMR code FLASH 4 (Fryxell et al. 2000; Dubey et al. 2009, 2012) to simulate representative pieces of galactic discs with dimensions 500 pc × 500 pc × ±5 kpc. FLASH is parallelized via domain decomposition under the Message Passing…”

“…rate is determined self-consistently at all temperatures, allowing us to properly model the non-equilibrium effects that can strongly affect the cooling rate at temperatures close to 104 K (see e.g. Kafatos 1973; Sutherland & Dopita 1993; Micic et al. 2013; Richings, Schaye & Oppenheimer 2014).”

“Following McKee & Ostriker (1977) and Tielens (2005), we can estimate the VFF of the hot phase that we expect for a given SN rate and mean gas density.”

“…are (i) the Kennicutt– Schmidt (KS) relation (Kennicutt 1998) with SFR ∝ 1.4H2+H I , as well as (ii) newer results which relate the SFR surface density to the MNRAS 454, 238–268 (2015) molecular gas surface density, H2 , in a galaxy in a linear fashion 3 (Bigiel et al. 2008; Tacconi et al. 2013).”

“…spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor & Springel 2014; Übler et al. 2014; Murante et al. 2015).”

“In the runs that we perform with our standard SN rate of 15 Myr−1, we use the estimate of Draine (1978) for the strength of the UV radiation field, and set G0 = 1.7.”

“Following McKee & Ostriker (1977) and Tielens (2005), we can estimate the VFF of the hot phase that we expect for a given SN rate and mean gas density.”

“Phys., 230, 3331 Walch S., Naab T., 2015, MNRAS, 451, 2757 Walch S., Wünsch R., Burkert A., Glover S., Whitworth A., 2011, ApJ, 733, 47 Walch S. K., Whitworth A. P., Bisbas T., Wünsch R., Hubber D., 2012, MNRAS, 427, 625 Walch S., Whitworth A. P., Bisbas T. G., Wünsch R., Hubber D. A., 2013, MNRAS, 435, 917 Wetzste…”

“…and the regulation of star formation on galactic scales (see e.g. Stinson et al. 2010; Hopkins, Quataert & Murray 2011, Agertz et al. 2013, and Genel et al. 2014 for a few recent examples), but much of this work considers only large scales and fails to resolve the small-scale processes…”

“…used in the work of Kim, Kim & Ostriker (2011), Shetty & Ostriker (2012), and Kim, Ostriker & Kim (2013), carried out with the ATHENA MHD code (Stone et al. 2008), is different since they correlate SN explosions with dynamically forming, local density maxima, and include shearing box boundary…”

“To account for X-ray heating and ionization, we use the prescription given in appendix A of Wolfire et al. (1995), assuming a fixed absorbing column of hydrogen NH = 1020 cm−2.”

“H2 is assumed to form only on the surface of dust grains, following the prescription given in Hollenbach & McKee (1989), as this dominates over gas-phase formation via the H− or H+2 ions at metallicities close to solar (Glover 2003).”

“This temperature is well above the local minimum in the cooling curve at high temperatures at a few × 105 K (see e.g. Dalgarno & McCray 1972).”

“…& Tielens 1994; Bergin et al. 2004) pe = 1.3 × 10−24 Geffn erg s−1 cm−3, (22) where Geff = G0exp (−2.5AV), and where the photoelectric heating efficiency is given by (Bakes & Tielens 1994; Wolfire et al. 2003) = 0.049 1 + (ψ/963)0.73 + 0.037(T /10 000)0.7 1 + (ψ/2500) , (23) with ψ = GeffT 1/2 ne .”

“To determine fshield,H2 for a particular line of sight, we use the following self-shielding function from Draine & Bertoldi (1996): fshield,H2 = 0.965 (1 + x/b5)2 + 0.035√ 1 + x × exp ( −8.5 × 10−4√1 + x ) , (19) where x = NH2/ ( 5 × 1014 cm−2), b5 = b/(105 cm s−1), and b is the Doppler broadening…”

“For the dust absorption term fdust,CO, we use the expression (van Dishoeck & Black 1988) fdust,CO = exp (−2.5AV) (21) using the same relationship as before between the visual extinction AV and the total hydrogen column density NH,tot.”

“…we do not include at the moment – is potentially important, in particular for gas-rich disc models (Shetty & Ostriker 2012), which resemble the conditions within the Galactic Center or in high-redshift, star-forming galaxies (Förster Schreiber et al. 2011; Genzel et al. 2011; Fisher et al. 2013).”

“…are (i) the Kennicutt– Schmidt (KS) relation (Kennicutt 1998) with SFR ∝ 1.4H2+H I , as well as (ii) newer results which relate the SFR surface density to the MNRAS 454, 238–268 (2015) molecular gas surface density, H2 , in a galaxy in a linear fashion 3 (Bigiel et al. 2008; Tacconi et al. 2013).”

“…forming molecular clouds, i.e. at the peaks in the density distribution; (3) half of the SNe explode randomly, and half of them explode within dense clouds (mixed driving); or (4) the SNe explode in clusters and are therefore correlated in space and time (e.g. Mac Low & McCray 1988; Matzner 2002).”

“…of galactic winds, which play an important role for regulating spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor &…”

“…study of stellar feedback and the regulation of star formation on galactic scales (see e.g. Stinson et al. 2010; Hopkins, Quataert & Murray 2011, Agertz et al. 2013, and Genel et al. 2014 for a few recent examples), but much of this work considers only large scales and fails to resolve the…”

“For comparison, we also show the midplane pressure as estimated by Blitz & Rosolowsky (2006): PBR06/kB = GASv √ 2 Gρ /kB = 9965 [K cm−3], (35) where v is the vertical velocity dispersion of the gas, which we set to v = 8 km s−1, following Koyama & Ostriker (2009, green dashed horizontal line).”

“Schruba et al. (2011) use the IRAM HERACLES survey (Leroy et al. 2009) to determine the molecular to atomic gas mass fractions as a function of radius for 33 spiral galaxies.”

“The heating rate per unit volume due to cosmic ray ionization is then given by cr = 20 ζ Hn eV s−1 cm−3 = 3.2 × 10−11ζ Hn erg s−1 cm−3 (Goldsmith & Langer 1978).”

“…spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor & Springel 2014; Übler et al. 2014; Murante et al. 2015).”

“Schruba et al. (2011) use the IRAM HERACLES survey (Leroy et al. 2009) to determine the molecular to atomic gas mass fractions as a function of radius for 33 spiral galaxies.”

“Previous studies of stratified discs (e.g. Joung & Mac Low 2006; Gent et al. 2013b; Kim & Ostriker 2015), have not employed a chemical network to distinguish between molecular and atomic or ionized gas, and have therefore used temperature cuts to estimate the amount of molecular hydrogen that forms…”

“We use an isothermal sheet, originally proposed by Spitzer (1942), in which the distribution function of stars is Maxwellian.”

“We typically use Minj = 800 M for single SNe, which roughly corresponds to a star formation efficiency of ∼8 per cent for a Chabrier initial stellar mass function (IMF; Chabrier 2001).”

“Runaway OB stars contribute to this ‘random’ SN component (Kimm & Cen 2014).”

“…distribution of H2 is consistent with a broad lognormal shape plus a high-density power-law tail, which is expected to develop due to local gravitational collapse (Klessen, Heitsch & Mac Low 2000; Slyz et al. 2005; Kainulainen et al. 2009; Schneider et al. 2011; Girichidis et al. 2014a).”

“If the mean density becomes too high, i.e. the mean density is n̄ 103 cm−3, then the SN remnants quickly become radiative (Blondin et al. 1998; Gatto et al. 2015; Li et al. MNRAS 454, 238–268 (2015) 2015) and the leftover momentum input (∼3 × 105 M km s−1) is not strong enough to disperse the…”

“…forming molecular clouds, i.e. at the peaks in the density distribution; (3) half of the SNe explode randomly, and half of them explode within dense clouds (mixed driving); or (4) the SNe explode in clusters and are therefore correlated in space and time (e.g. Mac Low & McCray 1988; Matzner 2002).”

“…we do not include at the moment – is potentially important, in particular for gas-rich disc models (Shetty & Ostriker 2012), which resemble the conditions within the Galactic Center or in high-redshift, star-forming galaxies (Förster Schreiber et al. 2011; Genzel et al. 2011; Fisher et al. 2013).”

“A similar basic approach was used in the ZEUSMP MHD code by Glover et al. (2010) and in an earlier version of the FLASH code by Walch et al. (2011) and Micic et al. (2012, 2013).”

“…play an important role for regulating spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor & Springel 2014; Übler et…”

“As the bubble(s) expand and collide (similar to a typical colliding flow scenario, e.g. Banerjee et al. 2009; Heitsch, Naab & Walch 2011) the H2 distribution in case of peak driving is dispersed and becomes very filamentary.”

“…many of these clouds and exert strong feedback on the surrounding gas, in the form of UV radiation (Dale et al. 2005; Dale, Ercolano & Bonnell 2012; Walch et al. 2012, 2013), stellar winds (Toalá & Arthur 2011; Rogers & Pittard 2013), and supernova (SN) explosions (Hill et al. 2012; Gatto et al.…”

“Controlling the code accuracy by setting ap is not as safe as criteria introduced by Salmon & Warren (1994) that allow control of the total error in gravitational acceleration, resulting from contributions of all nodes.”

“The chemical network used in our simulations is based on the network for hydrogen chemistry presented in Glover & Mac Low (2007a,b), supplemented with the simplified model for CO formation introduced by Nelson & Langer (1997).”

“(33) In a high-density environment (n 100 cm−3; see e.g. Walch & Naab 2015) the condition that Rinj ≥ 4 x can typically not be met with Minj = 800 M .”

“Finally, we model the effects of photoelectric heating using a heating rate given by (Bakes & Tielens 1994; Bergin et al. 2004) pe = 1.3 × 10−24 Geffn erg s−1 cm−3, (22) where Geff = G0exp (−2.5AV), and where the photoelectric heating efficiency is given by (Bakes & Tielens 1994; Wolfire et al.…”

“…gas, in the form of UV radiation (Dale et al. 2005; Dale, Ercolano & Bonnell 2012; Walch et al. 2012, 2013), stellar winds (Toalá & Arthur 2011; Rogers & Pittard 2013), and supernova (SN) explosions (Hill et al. 2012; Gatto et al. 2015; Kim & Ostriker 2015; Martizzi, Faucher-Giguère &…”

“…(2015) chemistry of H2 within galactic-scale simulations of the ISM (see e.g. Dobbs et al. 2008; Gnedin, Tassis & Kravtsov 2009; Dobbs, Burkert & Pringle 2011; Christensen et al. 2012), and more recently a couple of studies have also treated CO formation (Pettitt et al. 2014; Smith et al. 2014).”

“Dynamically significant magnetic fields help to guide the gas flows that form and disperse the clouds (e.g. de Avillez & Breitschwerdt 2004, 2005; Banerjee et al. 2009; Heitsch, Stone & Hartmann 2009), and cosmic rays can also play an important role, as they represent a significant fraction of the…”

“Dynamically significant magnetic fields help to guide the gas flows that form and disperse the clouds (e.g. de Avillez & Breitschwerdt 2004, 2005; Banerjee et al. 2009; Heitsch, Stone & Hartmann 2009), and cosmic rays can also play an important role, as they represent a significant fraction of the…”

“Stars E-mail: walch@ph1.uni-koeln.de form in many of these clouds and exert strong feedback on the surrounding gas, in the form of UV radiation (Dale et al. 2005; Dale, Ercolano & Bonnell 2012; Walch et al. 2012, 2013), stellar winds (Toalá & Arthur 2011; Rogers & Pittard 2013), and supernova (SN)…”

“We take the total gas-phase carbon, oxygen and silicon abundances to be xC,tot = 1.41 × 10−4, xO,tot = 3.16 × 10−4 and xSi,tot = 1.5 × 10−5 (Sembach et al. 2000).”

“Other clouds are destroyed by largescale dynamical processes in the disc, such as the strong shear flows around spiral arms (see e.g. Dobbs & Pringle 2013).”

“…(2015) chemistry of H2 within galactic-scale simulations of the ISM (see e.g. Dobbs et al. 2008; Gnedin, Tassis & Kravtsov 2009; Dobbs, Burkert & Pringle 2011; Christensen et al. 2012), and more recently a couple of studies have also treated CO formation (Pettitt et al. 2014; Smith et al. 2014).”

“…et al. 2009; Heitsch, Stone & Hartmann 2009), and cosmic rays can also play an important role, as they represent a significant fraction of the local energy density in the interstellar medium (ISM; e.g. Breitschwerdt 2008; Dorfi & Breitschwerdt 2012; Hanasz et al. 2013; Girichidis et al. 2014b).”

“If the mean density becomes too high, i.e. the mean density is n̄ 103 cm−3, then the SN remnants quickly become radiative (Blondin et al. 1998; Gatto et al. 2015; Li et al. MNRAS 454, 238–268 (2015) 2015) and the leftover momentum input (∼3 × 105 M km s−1) is not strong enough to disperse the…”

“In addition, we have improved and optimized the algorithm of Clark et al. (2012) significantly, leading to a speedup of more than a factor of 10 with respect to the original implementation.”

“Substantial effort has already been devoted to the study of stellar feedback and the regulation of star formation on galactic scales (see e.g. Stinson et al. 2010; Hopkins, Quataert & Murray 2011, Agertz et al. 2013, and Genel et al. 2014 for a few recent examples), but much of this work considers…”

“Full details of our treatment of these processes can be found in Glover & Mac Low (2007a,b) and Glover & Clark (2012b).”

“…distribution of H2 is consistent with a broad lognormal shape plus a high-density power-law tail, which is expected to develop due to local gravitational collapse (Klessen, Heitsch & Mac Low 2000; Slyz et al. 2005; Kainulainen et al. 2009; Schneider et al. 2011; Girichidis et al. 2014a).”

“…spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor & Springel 2014; Übler et al. 2014; Murante et al. 2015).”

“Each cluster has a pre-defined position and a constant lifetime of 40 Myr (Oey & Clarke 1997), and the total number of SNe per cluster, NSNe,clus, are drawn from a truncated power-law distribution f (NSNe,clus) = N−2SNe,clus (Clarke & Oey 2002) with a lower limit of NSNe,clus = 7 and an upper limit…”

“…distribution of H2 is consistent with a broad lognormal shape plus a high-density power-law tail, which is expected to develop due to local gravitational collapse (Klessen, Heitsch & Mac Low 2000; Slyz et al. 2005; Kainulainen et al. 2009; Schneider et al. 2011; Girichidis et al. 2014a).”

“…Dobbs & Smith 2013) even describe shear as one of the main drivers of ISM turbulence (e.g. Piontek & Ostriker 2005; Kevlahan & Pudritz 2009; and see Agertz et al. 2009 for a discussion), although the main role of the spiral arm structure to form and cause collisions between molecular clouds is…”

“…et al. 2009; Heitsch, Stone & Hartmann 2009), and cosmic rays can also play an important role, as they represent a significant fraction of the local energy density in the interstellar medium (ISM; e.g. Breitschwerdt 2008; Dorfi & Breitschwerdt 2012; Hanasz et al. 2013; Girichidis et al. 2014b).”

“Recently, Hennebelle & Iffrig (2014) computed models of low surface density discs with GAS ∼ 3 M pc−2 and galactic SN rates with RAMSES (Teyssier 2002).”

“…scheme that is based on the 5-wave Bouchut MHD solver HLL5R (Bouchut, Klingenberg & Waagan 2007; Klingenberg, Schmidt & Waagan 2007; Waagan 2009; Bouchut, Klingenberg & Waagan 2010; Waagan, Federrath & Klingenberg 2011), which is stable and preserves positivity for high Mach number…”

“In particular, Joung & Mac Low (2006), Hill et al. (2012), Gent et al. (2013a), Gent et al. (2013b), and Creasey, Theuns & Bower (2013) have carried out simulations of stratified discs with the FLASH code (although older releases of it), employing mostly randomly placed or clustered SNe.”

“The role of shear – which we do not include at the moment – is potentially important, in particular for gas-rich disc models (Shetty & Ostriker 2012), which resemble the conditions within the Galactic Center or in high-redshift, star-forming galaxies (Förster Schreiber et al. 2011; Genzel et al.…”

“…pre-defined position and a constant lifetime of 40 Myr (Oey & Clarke 1997), and the total number of SNe per cluster, NSNe,clus, are drawn from a truncated power-law distribution f (NSNe,clus) = N−2SNe,clus (Clarke & Oey 2002) with a lower limit of NSNe,clus = 7 and an upper limit of NSNe,clus = 40.”

“…have been made to account for the non-equilibrium MNRAS 454, 238–268 (2015) chemistry of H2 within galactic-scale simulations of the ISM (see e.g. Dobbs et al. 2008; Gnedin, Tassis & Kravtsov 2009; Dobbs, Burkert & Pringle 2011; Christensen et al. 2012), and more recently a couple of studies…”

“…galactic discs (Dobbs, Pringle & Burkert 2012; Bonnell, Dobbs & Smith 2013) even describe shear as one of the main drivers of ISM turbulence (e.g. Piontek & Ostriker 2005; Kevlahan & Pudritz 2009; and see Agertz et al. 2009 for a discussion), although the main role of the spiral arm structure to…”

“Instead, we assume that at T > 104 K, the helium and the metals are in collisional ionization equilibrium, and determine their contribution to the cooling rate using the ion-by-ion cooling rates given in Gnat & Ferland (2012).”

“…on the surrounding gas, in the form of UV radiation (Dale et al. 2005; Dale, Ercolano & Bonnell 2012; Walch et al. 2012, 2013), stellar winds (Toalá & Arthur 2011; Rogers & Pittard 2013), and supernova (SN) explosions (Hill et al. 2012; Gatto et al. 2015; Kim & Ostriker 2015; Martizzi,…”

“…(temperaturedensity or pressure-density) distributions of the gas are broad due to turbulent heating in dissipative shocks on the one hand, and cooling by expansion on the other hand (Vazquez-Semadeni 2009; Seifried, Schmidt & Niemeyer 2011; Walch et al. 2011; Micic et al. 2013; Saury et al. 2014).”

“…many of these clouds and exert strong feedback on the surrounding gas, in the form of UV radiation (Dale et al. 2005; Dale, Ercolano & Bonnell 2012; Walch et al. 2012, 2013), stellar winds (Toalá & Arthur 2011; Rogers & Pittard 2013), and supernova (SN) explosions (Hill et al. 2012; Gatto et al.…”

“In particular, Joung & Mac Low (2006), Hill et al. (2012), Gent et al. (2013a), Gent et al. (2013b), and Creasey, Theuns & Bower (2013) have carried out simulations of stratified discs with the FLASH code (although older releases of it), employing mostly randomly placed or clustered SNe.”

“…role for regulating spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor & Springel 2014; Übler et al. 2014; Murante…”

“…et al. 2009; Heitsch, Stone & Hartmann 2009), and cosmic rays can also play an important role, as they represent a significant fraction of the local energy density in the interstellar medium (ISM; e.g. Breitschwerdt 2008; Dorfi & Breitschwerdt 2012; Hanasz et al. 2013; Girichidis et al. 2014b).”

“…rate is determined self-consistently at all temperatures, allowing us to properly model the non-equilibrium effects that can strongly affect the cooling rate at temperatures close to 104 K (see e.g. Kafatos 1973; Sutherland & Dopita 1993; Micic et al. 2013; Richings, Schaye & Oppenheimer 2014).”

“…spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor & Springel 2014; Übler et al. 2014; Murante et al. 2015).”

“However, the oct-tree with monopole moments can be constructed in an extremely memory efficient way and consequently, computational costs are spared due to efficient cache usage and faster network communication (Springel 2005; Wetzstein et al. 2009).”

“…(2015) chemistry of H2 within galactic-scale simulations of the ISM (see e.g. Dobbs et al. 2008; Gnedin, Tassis & Kravtsov 2009; Dobbs, Burkert & Pringle 2011; Christensen et al. 2012), and more recently a couple of studies have also treated CO formation (Pettitt et al. 2014; Smith et al. 2014).”

“…spiral galaxy evolution on larger spatial and temporal scales at all cosmic epochs (Oppenheimer et al. 2010; Aumer et al. 2013; Hirschmann et al. 2013; Stinson et al. 2013; Brook et al. 2014; Hopkins et al. 2014; Marinacci, Pakmor & Springel 2014; Übler et al. 2014; Murante et al. 2015).”

“During the tree walk, the gravitational potential is calculated by the modified Ewald method (Ewald 1921; Klessen 1997).”

“A similar basic approach was used in the ZEUSMP MHD code by Glover et al. (2010) and in an earlier version of the FLASH code by Walch et al. (2011) and Micic et al. (2012, 2013).”

“In dense clouds, grain coagulation leads to a slightly different relationship between AV and NH,tot (see e.g. Foster et al. 2013), but we neglect this complication here.”

“A similar basic approach was used in the ZEUSMP MHD code by Glover et al. (2010) and in an earlier version of the FLASH code by Walch et al. (2011) and Micic et al. (2012, 2013).”

“…Pringle & Burkert 2012; Bonnell, Dobbs & Smith 2013) even describe shear as one of the main drivers of ISM turbulence (e.g. Piontek & Ostriker 2005; Kevlahan & Pudritz 2009; and see Agertz et al. 2009 for a discussion), although the main role of the spiral arm structure to form and cause…”

“2 N U M E R I C A L M E T H O D We use the fully three-dimensional, AMR code FLASH 4 (Fryxell et al. 2000; Dubey et al. 2009, 2012) to simulate representative pieces of galactic discs with dimensions 500 pc × 500 pc × ±5 kpc. FLASH is parallelized via domain decomposition under the Message Passing…”

“A similar basic approach was used in the ZEUSMP MHD code by Glover et al. (2010) and in an earlier version of the FLASH code by Walch et al. (2011) and Micic et al. (2012, 2013).”

“…we do not include at the moment – is potentially important, in particular for gas-rich disc models (Shetty & Ostriker 2012), which resemble the conditions within the Galactic Center or in high-redshift, star-forming galaxies (Förster Schreiber et al. 2011; Genzel et al. 2011; Fisher et al. 2013).”

“…et al. 2009; Heitsch, Stone & Hartmann 2009), and cosmic rays can also play an important role, as they represent a significant fraction of the local energy density in the interstellar medium (ISM; e.g. Breitschwerdt 2008; Dorfi & Breitschwerdt 2012; Hanasz et al. 2013; Girichidis et al. 2014b).”

“This is in contradiction to simulations by de Avillez & Breitschwerdt (2004), Joung & Mac Low (2006) and Hill et al. (2012), who find that most of the volume is filled with a pervasive, warm medium (VFF ∼50 per cent) while the VFF of the hot gas component is smaller and where the hot gas is mostly…”

“By creating the hot, X-ray emitting, phase they impact the large-scale multi-phase structure of the ISM (Li et al. 2015, McKee & Ostriker 1977, Walch et al. 2015) and might be important for driving galactic outflows, fountain flows, and galactic winds through hot, low density, chimneys (Chevalier &…”

“…in driving turbulence and shaping the multiphase ISM in galactic disks have been extensively investigated (e.g., Korpi et al. 1999; de Avillez 2000; de Avillez & Breitschwerdt 2004; Joung & Mac Low 2006; Hill et al. 2012; Gent et al. 2013; Walch et al. 2015; Girichidis et al. 2016; Li et al. 2017).”

“Within the SILCC project (SImulating the Life-Cycle of molecular Clouds1), starting with Walch et al. (2015), we aim to advance our understanding of the physical processes in the ISM by investigating the impact of differently placed SNe as individual explosions as well as clustered explosions.”

“…equation adopts uniform photoelectric heating as in Wolfire et al. (1995), with efficiency = 0.05 and the FUV radiation field of Habing (1968) with coefficient G0 = 0.6, chosen to obtain temperature distributions consistent with those from the comprehensive simulations by Walch et al. (2015).”

“Recent numerical simulations of the galactic interstellar medium (ISM;Girichidis et al. 2015; Walch et al. 2015) have shown that the properties of SN-driven outflows are tightly connected to details of the ISM structure and the environmental densities of SNe as one of the main driving mechanisms.”

“…can create a hot ionized medium (Cox & Smith 1974; McKee & Ostriker 1977) with high volume-filling factors (Ferrière 2001; Kalberla & Dedes 2008; Walch et al. 2015), which may launch powerful outflows from galactic discs (e.g. Oppenheimer et al. 2010; Creasey, Theuns & Bower 2013; Hopkins et…”

“…SN feedback (e.g., Korpi et al. 1999; de Avillez 2000; de Avillez & Breitschwerdt 2004; Joung & Mac Low 2006; Hill et al. 2012; Gent et al. 2013; Walch et al. 2015; Girichidis et al. 2016b; Li et al. 2017), albeit with SN rates and locations imposed rather responding self-consistently to star…”

“Based on results from direct numerical simulations, an increasingly detailed understanding of the overall three-phase ISM disk is developing (e.g., de Avillez & Breitschwerdt 2004; Joung & Mac Low 2006; Hill et al. 2012; Hennebelle & Iffrig 2014; Li et al. 2015; Walch et al. 2015).”

“A more detailed description can be found in Walch et al. (2015).”

“…typical timescale of order 107 yr (e.g., Kawamura et al. 2009; Meidt et al. 2015; Schinnerer et al. 2019) and molecular gas is expected to form out of atomic gas on a similar timescale (depending on metallicity, e.g., Fukui et al. 2009; Glover & Mac Low 2011; Clark et al. 2012; Walch et al. 2015).”

“We note that our former studies (Walch et al. 2015; Girichidis et al. 2016a) did not find molecular gas if selfgravity is not included.”

“Stellar feedback plays a critical role in galaxy- and star-formation through its regulation of the interstellar medium (ISM) (Joung et al. 2009; Walch et al. 2015; Martizzi et al. 2016; Girichidis et al. 2016b) and the powering of galactic winds (Hopkins et al. 2014; Marinacci et al. 2014;…”

“It is commonly assumed that dust abundance is scaled with metallicity and the scaling factor, grain size distribution and chemical composition have the average characteristics of dust in the local Galaxy (e.g. Walch et al. 2015, and references therein).”

“In conjunction with the recent major progress in numerical simulations of cloud-scale star formation and feedback (e.g. Dale, 2015; Walch et al., 2015; Grudić et al., 2018; Haid et al., 2018; Kim and Ostriker, 2018; Kim et al., 2018; Semenov et al., 2018), a consistent picture of the GMC lifecycle is now emerging.”

“…modelling (e.g. Pawlik & Schaye 2008; Altay et al. 2011; Christensen et al. 2012; Rahmati et al. 2013a; Richings, Schaye & Oppenheimer 2014a,b; Walch et al. 2015), the computational expense of dynamically coupling these techniques to the simulation and e.g. calculate SFRs directly from the H2…”

“10 in Walch et al. 2015).”

“…SN feedback (e.g., Korpi et al. 1999; de Avillez 2000; Joung & Mac Low 2006; Gressel et al. 2008; Joung et al. 2009; Hill et al. 2012; Gent et al. 2013a, 2013b; Hennebelle & Iffrig 2014; Walch et al. 2015; Iffrig & Hennebelle 2017; Peters et al. 2017; Colling et al. 2018; Girichidis et al. 2018b).”

“…resolution, and the trade-off one often has to make is to focus only on a single gas cloud or a small patch of a galaxy (see e.g. Joung & Mac Low 2006; Dale & Bonnell 2011; Kim, Kim & Ostriker 2011; Walch et al. 2012; Hill et al. 2012; Walch et al. 2015; Simpson et al. 2016; Naab & Ostriker 2016).”

“…of highly nonlinear feedback loops that impact ISM dynamics across a wide range of physical scales (e.g., Hopkins et al. 2014; Lopez et al. 2014; Walch et al. 2015; Gnedin 2016; Rahner et al. 2017; Olivier et al. 2021), thereby determining the chemical and thermal state of the ISM and affecting…”

“Walch et al. (2015) do not include the DM halo potential, so they have a smaller g; at z = 5 kpc, their g-field is about 1/3 of our value.”

“In recent years, efforts have therefore been increasing to incorporate time-dependent chemistry within both local (Walch et al. 2015; Girichidis et al. 2016) and global (Richings & Schaye 2016a, 2016b) galactic hydrodynamic and magnetohydrodynamic numerical simulations of the ISM.”

“In addition, the properties of star clusters have also been studied in stratified disk models (e.g. Walch et al. 2015; Peters et al. 2017; Kim & Ostriker 2018), in spiral galaxies and their mergers (e.g. Bekki et al. 2002; Li et al. 2004, 2005; Bournaud et al. 2008) and in dwarf galaxies (e.g.…”

“Within clumps and filaments of dense gas, strong magnetic fields are proposed to inhibit movement of material across field lines (while the motion parallel to the field lines does not face any resistance), possibly delaying the onset of SF (Inutsuka et al. 2015; Walch et al. 2015).”

“…adopted in the literature (see e.g. Kim, Ostriker & Kim 2013; Hopkins et al. 2014; Gatto et al. 2015; Martizzi, Faucher-Giguère & Quataert 2015; Simpson et al. 2015; Kimm et al. 2015; Walch et al. 2015; Rosdahl et al. 2017; Hopkins et al. 2017; Kim & Ostriker 2018) when the SNe are unresolved.”

“More information on the initial conditions and the setup of the simulations can be found in Walch et al. (2015) and Girichidis et al. (2016).”

“2. analysis of simulations of MHD turbulence (Soler et al. 2013; Walch et al. 2015; Chen et al. 2016).”

“We include a simple chemical network, which is explained in detail in Walch et al. (2015).”

“Finally, we note that including lower temperature cooling and heating processes will change the phase structure of the ISM for some galaxy models, and potentially how SNe vent into the corona to drive a wind (see, e.g., Walch et al. 2015; Girichidis et al. 2016).”

“…by Seifried et al. (2017, 2018) have been used to study at high resolution the behaviour of several molecular clouds selected from the SILCC simulations of Walch et al. (2015), and have shown that supernova explosions are inefficient at driving turbulence within preexisting dense molecular clouds.”

“…model (Bertoldi 1989; Lefloch & Lazareff 1994; Mellema et al. 1998; Kessel-Deynet & Burkert 2003; Mackey & Lim 2011; Bisbas et al. 2011; Mackey & Lim 2011; Haworth & Harries 2012), or of more generalized fractal substructure (Colella & Woodward 1984; LeVeque 2002; Walch et al. 2012, 2013, 2015).”

“…of SF may be important for the efficiency of feedback, i.e. it may matter whether the distribution of SF, and hence SN explosions, is scattered smoothly in space and time, or happens in short localized bursts (e.g. Federrath & Klessen 2013; Hopkins, Narayanan & Murray 2013; Walch et al. 2015).”

“…this project involves the carrying out of “zoom-in” simulations that follow the formation and growth of a small set of clouds formed in the large-scale simulations of the Galactic plane performed as part of the SILCC project3 (see e.g. Walch et al. 2015, Girichidis et al. 2016 for more details).”

“…to the ISM, providing the energy to support the midplane from collapsing, and establishing the disk scale height (Ostriker et al. 2010; Shetty & Ostriker 2012; Hill et al. 2012; Kim et al. 2013; Walch et al. 2015; Girichidis et al. 2016a,b), as well as forming dense clouds in converging flows.”

“However, two factors should be taken into account: (i) the ISM might be dominated by gas which is out of equilibrium (e.g., Walch et al. 2015), and (ii) the temperatures are effective temperatures with small-scale turbulence included, whereas the ionization relies on the absolute temperature.”

“Starting from similar local galactic disk models with solar neighborhood-like parameters (Walch et al. 2015), Seifried et al. (2017, 2020) performed zoomin simulations of giant molecular clouds (GMCs) with time-dependent chemistry using the Nelson & Langer (1997) network, and achieved a resolution…”

“A fraction of the gas can be pushed out of the galactic disc to form a fountain flow or even escape from the galaxy as a wind (e.g. Hill et al. 2012; Walch et al. 2015; Girichidis et al. 2016).”

“Details about the chemical network, e.g. the considered reactions and the employed rate coefficients in the current implementation can be found in Glover et al. (2010) and Walch et al. (2015).”

“1 in Seifried et al. 2019), thus covering the typical range for Galactic MCs (e.g. Larson 1981; Solomon et al. 1987; Elmegreen & Falgarone 1996; Heyer et al. 2001; RomanDuval et al. 2010; Miville-Deschenes et al. 2017).”

“…(e.g. Tasker & Bryan 2006; Agertz et al. 2009; Dobbs, Burkert & Pringle 2011; Hopkins, Quataert & Murray 2012; Renaud et al. 2013; Marasco et al. 2015), as well as individual patches of the ISM (Joung & Mac Low 2006; Gatto et al. 2015; Martizzi, Faucher-Giguere & Quataert 2015; Walch et al. 2015).”

“Multi-physics simulations (including gravity, chemistry, photoelectric heating, molecular physics and supernovae feedback) of ISM have been done by many authors (e.g., Gatto et al. 2015; Martizzi et al. 2015; Walch & Naab 2015; Walch et al. 2015).”

“Apart from the highest resolution, the general features are similar to the ones of the lower resolution runs presented in Hennebelle & Iffrig (2014) and also seen in other works (e.g. Kim et al. 2011; Walch et al. 2015; Kim & Ostriker 2015a,b).”

“Supernovae (SN) play a fundamental role in setting the properties of the multi-phase interstellar medium (ISM) (e.g. Salpeter 1955; de Avillez & Breitschwerdt 2004; Joung & Mac Low 2006; Kim et al. 2013; Walch et al. 2015).”

“We apply the clustered SN driving from Walch et al. (2015) and Girichidis et al. (2016), which we summarize briefly.”

“…estimation of the radial distance dependency from OB stars (e.g. Wolfire et al. 2003; Tasker 2011), self-shielding and shielding of radiation field (Walch et al. 2015; Hu et al. 2016), as well as detailed model of dust physical properties such as grain sizes, compositions and charge state (Bakes &…”

“…SNe is essential to provide vertical support against gravity in the ISM (deAvillez & Breitschwerdt 2005; Joung et al. 2009b; Hill et al. 2012; Kim et al. 2013; Walch et al. 2015), possibly explaining the development of the internal turbulent structure inside molecular clouds (Padoan et al. 2016).”

“We set z0 within 0 - 500 pc, which is the net extent of the neutral phase seen in most SN-driven ISM simulations (Hill et al. 2012; Gent et al. 2013; Walch et al. 2015; Kim & Ostriker 2015).”

“The SILCC framework first introduced by Walch et al. (2015) focuses on solar neighborhood ISM modeling, with particular emphasis on hydrodynamical evolution with a hydrogen and carbon chemistry network (Glover & Mac Low 2007a,b; Glover & Clark 2012, collectively called SGChem).”

“Such a picture is seen in the high-resolution, stratified-disc simulations from the SILCC project (Walch et al. 2015), which have a spatial cell resolution of < 10 pc and initial gas surface density of Σgas = 10 M /pc2.”

“…R) = (-190, 65, -84, 78) hydrodynamical (Fielding et al. 2017, 2018), and 3D magneto-hydrodynamical (Tomisaka 1998; Korpi et al. 1999; de Avillez & Breitschwerdt 2005; Walch et al. 2015; Girichidis et al. 2016) simulations, spanning a wide range of initial disk conditions, box sizes, and run times.”

“In z-direction, the positioning of the random SNe is weighted with a Gaussian distribution with a scale height of 50 pc for (see Walch et al. 2015 and Girichidis et al. 2016 for more details).”

“…assume a constant flux of 1.7G0 and estimate the local visual extinction ( )l~A n N , 18v J H H where NH=1.87×10 21 cm2, and we take the length scale to be the local Jeans length (Jeans 1902) [ ( )] ( )l p r= c G , 19J s2 1 2 following the methods of Seifried et al. (2011) and Walch et al. (2015).”

“In the limit of sub-parsec resolution, we know from dedicated ISM studies (Kimm & Cen 2014; Walch et al. 2015; Iffrig & Hennebelle 2017) that a crucial ingredient is the inclusion of walk-away and run-away massive stars.”

“…to apply this detailed modelling to simulations of an entire galaxy (see e.g. Smith et al. 2014; Bournaud et al. 2015; Iffrig & Hennebelle 2015; Walch et al. 2015; Geen et al. 2016; Girichidis et al. 2016; Hu et al. 2017; Kim & Ostriker 2017; Peters et al. 2017; Seifried et al. 2017;…”

“…has been considered in hydrodynamical models coupled with chemical networks by Nelson & Langer (1997); Glover et al. (2010); Grassi et al. (2014); Walch et al. (2015); Seifried & Walch (2016); Girichidis et al. (2016); Seifried et al. (2017); Franeck et al. (2018); Inoue et al. (2020) and in…”

“However, recent experience has revealed that for flow configurations containing very strong shocks or high Mach numbers (like those found in astrophysics [1, 17, 28, 29]) a dissipation term that is not carefully designed is insufficient to guarantee robustness.”

“This is not the case for H2, which is present in more diffuse regions where the temperature range can be higher (see also Walch et al. 2015 and Glover & Smith 2016 who find similar results in larger-scale simulations of the ISM).”

“One approach has been to simulate isolated regions (e.g. ≤ 1 kpc3 boxes) of the ISM (for example Audit & Hennebelle 2010; Walch et al. 2015; Ibáñez-Mejı́a et al. 2016; Padoan et al. 2016; Iffrig & Hennebelle 2017, to name a few).”

“…et al. 2015; Scannapieco & Brüggen 2015; Brüggen & Scannapieco 2016; Schneider & Robertson 2017), and simulations of patches of a galaxy’s interstellar medium (ISM) and regions above the disk (e.g., Joung & Mac Low 2006; Kim et al. 2013; Walch et al. 2015; Martizzi et al. 2016; Li et al. 2017).”

“…ISM patches have been carried out to understand their evolution in detail (e.g. Ostriker & McKee 1988; Blondin et al. 1998; Thornton et al. 1998; Draine 2011; Kim & Ostriker 2015; Walch et al. 2015; Gatto et al. 2015; Martizzi et al. 2015; Badjin et al. 2016; Haid et al. 2016; Ohlin et al. 2019).”

“Local, higher-resolution studies such as the TIGRESS simulations (Kim & Ostriker 2017, 2018) and the SILCC simulations (Walch et al. 2015), demonstrate the relevance of magnetic fields, binary stars, cosmic rays, resolved SN bubbles and the selfconsistent injection of momentum from stellar winds…”

“…models with observations, and comparing the results with extragalactic studies (e.g., Hennebelle et al. 2007; Glover et al. 2010; Glover & Mac Low 2011; Shetty et al. 2011; Walter et al. 2008; Leroy et al. 2008; Smith et al. 2014; Walch et al. 2015; Girichidis et al. 2016; Bertram et al. 2016).”

“…that there is less c© 0000 RAS, MNRAS 000, 000–000 mixing of material between the cold and warm phases, and hence less gas at intermediate temperatures than found in simulations that include supernova feedback (c.f. Hill et al. 2012; Gent et al. 2013; Walch et al. 2015; Hennebelle & Iffrig 2014).”

“This is also hinted in the results of Walch et al. (2015), who, when simulating a galaxy with different star formation and feedback recipes, observe a delay in the formation of molecular gas in the presence of a magnetic field.”

“We note that we here apply the SN driving for a longer time than for MC1 and MC2 since the magnetic field delays the formation of overdense structures, which subsequently form MCs (Walch et al. 2015; Girichidis et al. 2016, Girichidis et al., submitted).”