ALBERT

Description: The SILCC (SImulating the Life-Cycle of molecular Clouds) project aims to self-consistently understand the small-scale structure of the interstellar medium (ISM) and its link to galaxy evolution. We simulate the evolution of the multiphase ISM in a (500 pc) 2   x  ±5 kpc region of a galactic disc, with a gas surface density of $\Sigma _{_{\rm GAS}} = 10 \;{\rm M}_{\odot }\,{\rm pc}^{-2}$ . The flash 4 simulations include an external potential, self-gravity, magnetic fields, heating and radiative cooling, time-dependent chemistry of H 2 and CO considering (self-) shielding, and supernova (SN) feedback but omit shear due to galactic rotation. We explore SN explosions at different rates in high-density regions ( peak ), in random locations with a Gaussian distribution in the vertical direction ( random ), in a combination of both ( mixed ), or clustered in space and time ( clus / clus2 ). Only models with self-gravity and a significant fraction of SNe that explode in low-density gas are in agreement with observations. Without self-gravity and in models with peak driving the formation of H 2 is strongly suppressed. For decreasing SN rates, the H 2 mass fraction increases significantly from 〈10 per cent for high SN rates, i.e. 0.5 dex above Kennicutt–Schmidt, to 70–85 per cent for low SN rates, i.e. 0.5 dex below KS. For an intermediate SN rate, clustered driving results in slightly more H 2 than random driving due to the more coherent compression of the gas in larger bubbles. Magnetic fields have little impact on the final disc structure but affect the dense gas ( n   10 cm –3 ) and delay H 2 formation. Most of the volume is filled with hot gas (~80 per cent within ±150 pc). For all but peak driving a vertically expanding warm component of atomic hydrogen indicates a fountain flow. We highlight that individual chemical species populate different ISM phases and cannot be accurately modelled with temperature-/density-based phase cut-offs.

Description: We investigate the early impact of single and binary supernova (SN) explosions on dense gas clouds with three-dimensional, high-resolution, hydrodynamic simulations. The effect of cloud structure, radiative cooling and ionizing radiation from the progenitor stars on the net input of kinetic energy, f kin  =  E kin / E SN , thermal energy, f therm  =  E therm / E SN , and gas momentum, f P  =  P / P SN , to the interstellar medium (ISM) is tested. For clouds with $\bar{n} = 100\;{\rm cm}^{-3}$ , the momentum generating Sedov and pressure-driven snowplough phases are terminated early (0.01 Myr) and radiative cooling limits the coupling to f therm  ~ 0.01, f kin  ~ 0.05, and f P  ~ 9, significantly lower than for the case without cooling. For pre-ionized clouds, these numbers are only increased by ~50 per cent, independent of the cloud structure. This only suffices to accelerate ~5 per cent of the cloud to radial velocities 30 km s –1 . A second SN might enhance the coupling efficiencies if delayed past the Sedov phase of the first explosion. Such very low coupling efficiencies cast doubts on many subresolution models for SN feedback, which are, in general, validated a posteriori. Ionizing radiation appears not to significantly enhance the coupling of SNe to the surrounding gas as it drives the ISM into inert dense shells and cold clumps, a process which is unresolved in galaxy-scale simulations. Our results indicate that the momentum input of SNe in ionized, structured clouds is larger (more than a factor of 10) than the corresponding momentum yield of the progenitor's stellar winds.

Description: starbench is a project focused on benchmarking and validating different star formation and stellar feedback codes. In this first starbench paper we perform a comparison study of the D-type expansion of an H ii region. The aim of this work is to understand the differences observed between the 12 participating numerical codes against the various analytical expressions examining the D-type phase of H ii region expansion. To do this, we propose two well-defined tests which are tackled by 1D and 3D grid- and smoothed particle hydrodynamics-based codes. The first test examines the ‘early phase’ D-type scenario during which the mechanical pressure driving the expansion is significantly larger than the thermal pressure of the neutral medium. The second test examines the ‘late phase’ D-type scenario during which the system relaxes to pressure equilibrium with the external medium. Although they are mutually in excellent agreement, all 12 participating codes follow a modified expansion law that deviates significantly from the classical Spitzer solution in both scenarios. We present a semi-empirical formula combining the two different solutions appropriate to both early and late phases that agrees with high-resolution simulations to  2 per cent. This formula provides a much better benchmark solution for code validation than the Spitzer solution. The present comparison has validated the participating codes and through this project we provide a data set for calibrating the treatment of ionizing radiation hydrodynamics codes.

Description: Supernova (SN) blast waves inject energy and momentum into the interstellar medium (ISM), control its turbulent multiphase structure and the launching of galactic outflows. Accurate modelling of the blast wave evolution is therefore essential for ISM and galaxy formation simulations. We present an efficient method to compute the input of momentum, thermal energy, and the velocity distribution of the shock-accelerated gas for ambient media (densities of 0.1 ≥ n 0 [cm – 3 ] ≥ 100) with uniform (and with stellar wind blown bubbles), power-law, and turbulent (Mach numbers $\mathcal {M}$ from 1to100) density distributions. Assuming solar metallicity cooling, the blast wave evolution is followed to the beginning of the momentum conserving snowplough phase. The model recovers previous results for uniform ambient media. The momentum injection in wind-blown bubbles depend on the swept-up mass and the efficiency of cooling, when the blast wave hits the wind shell. For power-law density distributions with n ( r ) ~  r –2 (for n ( r ) 〉  n floor ) the amount of momentum injection is solely regulated by the background density n floor and compares to n uni = n floor . However, in turbulent ambient media with lognormal density distributions the momentum input can increase by a factor of 2 (compared to the homogeneous case) for high Mach numbers. The average momentum boost can be approximated as $p_{{\rm turb}}/{p_{{0}}}\ =23.07\, \left(\frac{n_{{0,\rm turb}}}{1\,{\rm cm}^{-3}}\right)^{-0.12} + 0.82 (\ln (1+b^{2}\mathcal {M}^{2}))^{1.49}\left(\frac{n_{{0,\rm turb}}}{1\,{\rm cm}^{-3}}\right)^{-1.6}$ . The velocity distributions are broad as gas can be accelerated to high velocities in low-density channels. The model values agree with results from recent, computationally expensive, three-dimensional simulations of SN explosions in turbulent media.

Description: The SILCC (SImulating the Life-Cycle of molecular Clouds) project aims to self-consistently understand the small-scale structure of the interstellar medium (ISM) and its link to galaxy evolution. We simulate the evolution of the multiphase ISM in a (500 pc) 2   x  ±5 kpc region of a galactic disc, with a gas surface density of $\Sigma _{_{\rm GAS}} = 10 \;{\rm M}_{\odot }\,{\rm pc}^{-2}$ . The flash 4 simulations include an external potential, self-gravity, magnetic fields, heating and radiative cooling, time-dependent chemistry of H 2 and CO considering (self-) shielding, and supernova (SN) feedback but omit shear due to galactic rotation. We explore SN explosions at different rates in high-density regions ( peak ), in random locations with a Gaussian distribution in the vertical direction ( random ), in a combination of both ( mixed ), or clustered in space and time ( clus / clus2 ). Only models with self-gravity and a significant fraction of SNe that explode in low-density gas are in agreement with observations. Without self-gravity and in models with peak driving the formation of H 2 is strongly suppressed. For decreasing SN rates, the H 2 mass fraction increases significantly from 〈10 per cent for high SN rates, i.e. 0.5 dex above Kennicutt–Schmidt, to 70–85 per cent for low SN rates, i.e. 0.5 dex below KS. For an intermediate SN rate, clustered driving results in slightly more H 2 than random driving due to the more coherent compression of the gas in larger bubbles. Magnetic fields have little impact on the final disc structure but affect the dense gas ( n   10 cm –3 ) and delay H 2 formation. Most of the volume is filled with hot gas (~80 per cent within ±150 pc). For all but peak driving a vertically expanding warm component of atomic hydrogen indicates a fountain flow. We highlight that individual chemical species populate different ISM phases and cannot be accurately modelled with temperature-/density-based phase cut-offs.

Description: The SILCC project (SImulating the Life-Cycle of molecular Clouds) aims at a more self-consistent understanding of the interstellar medium (ISM) on small scales and its link to galaxy evolution. We present three-dimensional (magneto)hydrodynamic simulations of the ISM in a vertically stratified box including self-gravity, an external potential due to the stellar component of the galactic disc, and stellar feedback in the form of an interstellar radiation field and supernovae (SNe). The cooling of the gas is based on a chemical network that follows the abundances of H + , H, H 2 , C + , and CO and takes shielding into account consistently. We vary the SN feedback by comparing different SN rates, clustering and different positioning, in particular SNe in density peaks and at random positions, which has a major impact on the dynamics. Only for random SN positions the energy is injected in sufficiently low-density environments to reduce energy losses and enhance the effective kinetic coupling of the SNe with the gas. This leads to more realistic velocity dispersions ( $\sigma _\mathrm{H\,{\small {I}}}\approx 0.8\sigma _{300\rm{-}8000\,\mathrm{K}}\sim 10\hbox{-}20\,\mathrm{km}\,\mathrm{s}^{-1}$ , $\sigma _\mathrm{H\,\alpha }\approx 0.6\sigma _{8000-3\times 10^5\,\mathrm{K}}\sim 20\hbox{-}30\,\mathrm{km}\,\mathrm{s}^{-1}$ ), and strong outflows with mass loading factors (ratio of outflow to star formation rate) of up to 10 even for solar neighbourhood conditions. Clustered SNe abet the onset of outflows compared to individual SNe but do not influence the net outflow rate. The outflows do not contain any molecular gas and are mainly composed of atomic hydrogen. The bulk of the outflowing mass is dense ( ~ 10 –25 –10 –24 g cm –3 ) and slow ( v ~ 20–40 km s –1 ) but there is a high-velocity tail of up to v ~ 500 km s –1 with ~ 10 –28 –10 –27 g cm –3 .

Description: We use hydrodynamical simulations in a (256 pc) 3 periodic box to model the impact of supernova (SN) explosions on the multiphase interstellar medium (ISM) for initial densities n  = 0.5–30 cm –3 and SN rates 1–720 Myr –1 . We include radiative cooling, diffuse heating, and the formation of molecular gas using a chemical network. The SNe explode either at random positions, at density peaks, or both. We further present a model combining thermal energy for resolved and momentum input for unresolved SNe. Random driving at high SN rates results in hot gas ( T   10 6  K) filling 〉90 per cent of the volume. This gas reaches high pressures (10 4  〈  P / k B  〈 10 7  K cm –3 ) due to the combination of SN explosions in the hot, low-density medium and confinement in the periodic box. These pressures move the gas from a two-phase equilibrium to the single-phase, cold branch of the cooling curve. The molecular hydrogen dominates the mass (〉50 per cent), residing in small, dense clumps. Such a model might resemble the dense ISM in high-redshift galaxies. Peak driving results in huge radiative losses, producing a filamentary ISM with virtually no hot gas, and a small molecular hydrogen mass fraction (〈〈1 per cent). Varying the ratio of peak to random SNe yields ISM properties in between the two extremes, with a sharp transition for equal contributions. The velocity dispersion in H i remains 10 km s –1 in all cases. For peak driving, the velocity dispersion in Hα can be as high as 70 km s –1 due to the contribution from young, embedded SN remnants.

Description: Lomax et al. have constructed an ensemble of 60 pre-stellar cores having masses, sizes, projected shapes, temperatures, and non-thermal radial velocity dispersions that match, statistically, the cores in Ophiuchus, and have simulated the evolution of these cores using smoothed particle hydrodynamics. Each core has been evolved once with no radiative feedback from stars, once with continuous radiative feedback, and once with episodic radiative feedback. Here we analyse the multiplicity statistics from these simulations. With episodic radiative feedback, (i) the multiplicity frequency is ~60 per cent higher than in the field; (ii) the multiplicity frequency and the mean semimajor axis both increase with primary mass; (iii) one-third of multiple systems are hierarchical systems with more than two components; (iv) in these hierarchical systems the inner pairings typically have separations of a few au and mass ratios concentrated towards unity, whereas the outer pairings have separations of order 100 au and a flatter distribution of mass ratios. The binary statistics are compatible with observations of young embedded populations, and – if wider orbits are disrupted preferentially by external perturbations – with observations of mature field populations. With no radiative feedback, the results are similar to those from simulations with episodic feedback. With continuous radiative feedback, brown dwarfs are underproduced, the number of multiple systems is too low, and the statistical properties of multiple systems are at variance with observation. This suggests that star formation in Ophiuchus may only be representative of global star formation if accretion on to protostars, and hence radiative feedback, is episodic.

Description: We present synthetic ALMA observations of Keplerian, protostellar discs in the Class 0 stage studying the emission of molecular tracers like 13 CO, C 18 O, HCO + , H 13 CO + , N 2 H + , and H 2 CO. We model the emission of discs around low- and intermediate-mass protostars. We show that under optimal observing conditions ALMA is able to detect the discs already in the earliest stage of protostellar evolution, although the emission is often concentrated to the innermost 50 au. Therefore, a resolution of a few 0.1 arcsec might be too low to detect Keplerian discs around Class 0 objects. We also demonstrate that under optimal conditions for edge-on discs Keplerian rotation signatures are recognisable, from which protostellar masses can be inferred. For this we here introduce a new approach, which allows us to determine protostellar masses with higher fidelity than before. Furthermore, we show that it is possible to reveal Keplerian rotation even for strongly inclined discs and that ALMA should be able to detect possible signs of fragmentation in face-on discs. In order to give some guidance for future ALMA observations, we investigate the influence of varying observing conditions and source distances. We show that it is possible to probe Keplerian rotation in inclined discs with an observing time of 2 h and a resolution of 0.1 arcsec, even in the case of moderate weather conditions. Furthermore, we demonstrate that under optimal conditions, Keplerian discs around intermediate-mass protostars should be detectable up to kpc distances.

Description: We study the connection of star formation to atomic (H i ) and molecular hydrogen (H 2 ) in isolated, low-metallicity dwarf galaxies with high-resolution ( m gas = 4 M , N ngb = 100) smoothed particle hydrodynamics simulations. The model includes self-gravity, non-equilibrium cooling, shielding from a uniform and constant interstellar radiation field, the chemistry of H 2 formation, H 2 -independent star formation, supernova feedback and metal enrichment. We find that the H 2 mass fraction is sensitive to the adopted dust-to-gas ratio and the strength of the interstellar radiation field, while the star formation rate is not. Star formation is regulated by stellar feedback, keeping the gas out of thermal equilibrium for densities n 〈 1 cm –3 . Because of the long chemical time-scales, the H 2 mass remains out of chemical equilibrium throughout the simulation. Star formation is well correlated with cold ( T ≤ 100 K) gas, but this dense and cold gas – the reservoir for star formation – is dominated by H i , not H 2 . In addition, a significant fraction of H 2 resides in a diffuse, warm phase, which is not star-forming. The interstellar medium is dominated by warm gas (100 K 〈 T ≤ 3 x 10 4  K) both in mass and in volume. The scaleheight of the gaseous disc increases with radius while the cold gas is always confined to a thin layer in the mid-plane. The cold gas fraction is regulated by feedback at small radii and by the assumed radiation field at large radii. The decreasing cold gas fractions result in a rapid increase in depletion time (up to 100 Gyr) for total gas surface densities $\Sigma _{\rm \rm H\,\small {I}+H_2} \lesssim$ 10 M pc –2 , in agreement with observations of dwarf galaxies in the Kennicutt–Schmidt plane.