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 (σ HI ≈ 0.8σ 300−8000 K ∼ 10−20 km s −1 , σ Hα ≈ 0.6σ 8000−3×10 5 K ∼ 20 − 30 km 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 (ρ ∼ 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 ρ ∼ 10 −28 − 10 −27 g cm −3 .
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple appoximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P V (ρ) ∝ ρ −1.54 for the (volumeweighted) PDF and P M (ρ) ∝ ρ −0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates. Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured star formation rates are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
We present a detailed parameter study of collapsing turbulent cloud cores, varying the initial density profile and the initial turbulent velocity field. We systematically investigate the influence of different initial conditions on the star formation process, mainly focusing on the fragmentation, the number of formed stars and the resulting mass distributions. Our study compares four different density profiles (uniform, Bonnor–Ebert type, ρ∝r−1.5 and ρ∝r−2), combined with six different supersonic turbulent velocity fields (compressive, mixed and solenoidal, initialized with two different random seeds each) in three‐dimensional simulations using the adaptive‐mesh refinement, hydrodynamics code flash. The simulations show that density profiles with flat cores produce hundreds of low‐mass stars, either distributed throughout the entire cloud or found in subclusters, depending on the initial turbulence. Concentrated density profiles always lead to the formation of one high‐mass star in the centre of the cloud and, if at all, low‐mass stars surrounding the central one. In uniform and Bonnor–Ebert type density distributions, compressive initial turbulence leads to local collapse about 25 per cent earlier than solenoidal turbulence. However, central collapse in the steep power‐law profiles is too fast for the turbulence to have any significant influence. We conclude that (i) the initial density profile and turbulence mainly determine the cloud evolution and the formation of clusters, (ii) the initial mass function (IMF) is not universal for all setups and (iii) that massive stars are much less likely to form in flat density distributions. The IMFs obtained in the uniform and Bonnor–Ebert type density profiles are more consistent with the observed IMF, but shifted to lower masses.
We present a hydrodynamical simulation of the turbulent, magnetized, supernova (SN)-driven interstellar medium (ISM) in a stratified box that dynamically couples the injection and evolution of cosmic rays (CRs) and a self-consistent evolution of the chemical composition. CRs are treated as a relativistic fluid in the advection-diffusion approximation. The thermodynamic evolution of the gas is computed using a chemical network that follows the abundances of H + , H, H 2 , CO, C + , and free electrons and includes (self-)shielding of the gas and dust. We find that CRs perceptibly thicken the disk with the heights of 90% (70%) enclosed mass reaching 1.5 kpc ( 0.2 kpc). The simulations indicate that CRs alone can launch and sustain strong outflows of atomic and ionized gas with mass loading factors of order unity, even in solar neighborhood conditions and with a CR energy injection per SN of 10 50 erg, 10% of the fiducial thermal energy of an SN. The CR-driven outflows have moderate launching velocities close to the midplane ( 100 km s −1 ) and are denser (ρ ∼ 10 −24 − 10 −26 g cm −3 ), smoother, and colder than the (thermal) SN-driven winds. The simulations support the importance of CRs for setting the vertical structure of the disk as well as the driving of winds.
Column-density maps of molecular clouds are one of the most important observables in the context of molecular cloud-and starformation (SF) studies. With the Herschel satellite it is now possible to precisely determine the column density from dust emission, which is the best tracer of the bulk of material in molecular clouds. However, line-of-sight (LOS) contamination from fore-or background clouds can lead to overestimating the dust emission of molecular clouds, in particular for distant clouds. This implies values that are too high for column density and mass, which can potentially lead to an incorrect physical interpretation of the column density probability distribution function (PDF). In this paper, we use observations and simulations to demonstrate how LOS contamination affects the PDF. We apply a first-order approximation (removing a constant level) to the molecular clouds of Auriga and Maddalena (low-mass star-forming), and Carina and NGC 3603 (both high-mass SF regions). In perfect agreement with the simulations, we find that the PDFs become broader, the peak shifts to lower column densities, and the power-law tail of the PDF for higher column densities flattens after correction. All corrected PDFs have a lognormal part for low column densities with a peak at A v ∼ 2 mag, a deviation point (DP) from the lognormal at A v (DP) ∼ 4−5 mag, and a power-law tail for higher column densities. Assuming an equivalent spherical density distribution ρ ∝ r −α , the slopes of the power-law tails correspond to α PDF = 1.8, 1.75, and 2.5 for Auriga, Carina, and NGC 3603. These numbers agree within the uncertainties with the values of α ≈ 1.5, 1.8, and 2.5 determined from the slope γ (with α = 1 − γ) obtained from the radial column density profiles (N ∝ r γ ). While α ∼ 1.5−2 is consistent with a structure dominated by collapse (local free-fall collapse of individual cores and clumps and global collapse), the higher value of α > 2 for NGC 3603 requires a physical process that leads to additional compression (e.g., expanding ionization fronts). From the small sample of our study, we find that clouds forming only low-mass stars and those also forming high-mass stars have slightly different values for their average column density (1.8 × 10 21 cm −2 vs. 3.0 × 10 21 cm −2 ), and they display differences in the overall column density structure. Massive clouds assemble more gas in smaller cloud volumes than low-mass SF ones. However, for both cloud types, the transition of the PDF from lognormal shape into power-law tail is found at the same column density (at A v ∼ 4−5 mag). Low-mass and high-mass SF clouds then have the same low column density distribution, most likely dominated by supersonic turbulence. At higher column densities, collapse and external pressure can form the power-law tail. The relative importance of the two processes can vary between clouds and thus lead to the observed differences in PDF and column density structure.
We study the impact of stellar winds and supernovae on the multi-phase interstellar medium using three-dimensional hydrodynamical simulations carried out with FLASH. The selected galactic disc region has a size of (500 pc) 2 × ±5 kpc and a gas surface density of 10 M pc −2 . The simulations include an external stellar potential and gas self-gravity, radiative cooling and diffuse heating, sink particles representing star clusters, stellar winds from these clusters which combine the winds from individual massive stars by following their evolution tracks, and subsequent supernova explosions. Dust and gas (self-)shielding is followed to compute the chemical state of the gas with a chemical network. We find that stellar winds can regulate star (cluster) formation. Since the winds suppress the accretion of fresh gas soon after the cluster has formed, they lead to clusters which have lower average masses (10 2 −10 4.3 M ) and form on shorter timescales (10 −3 −10 Myr). In particular we find an anti-correlation of cluster mass and accretion time scale. Without winds the star clusters easily grow to larger masses for ∼ 5 Myr until the first supernova explodes. Overall the most massive stars provide the most wind energy input, while objects beginning their evolution as B type stars contribute most of the supernova energy input. A significant outflow from the disk (mass loading 1 at 1 kpc) can be launched by thermal gas pressure if more than 50% of the volume near the disc mid-plane can be heated to T > 3 × 10 5 K. Stellar winds alone cannot create a hot volume-filling phase. The models which are in best agreement with observed star formation rates drive either no outflows or weak outflows.
The SILCC project (SImulating the Life-Cycle of molecular Clouds) aims at a more selfconsistent understanding of the interstellar medium (ISM) on small scales and its link to galaxy evolution. We simulate the evolution of the multi-phase ISM in a (500 pc) 2 × ± 5 kpc region of a galactic disc, with a gas surface density of Σ GAS = 10 M ⊙ /pc 2 . The Flash 4.1 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. We explore SN explosions at different (fixed) rates in high-density regions (peak), in random locations (random), in a combination of both (mixed), or clustered in space and time (clustered). Only random or clustered models with self-gravity (which evolve similarly) are in agreement with observations. Molecular hydrogen forms in dense filaments and clumps and contributes 20% -40% to the total mass, whereas most of the mass (55% -75%) is in atomic hydrogen. The ionised gas contributes <10%. For high SN rates (0.5 dex above Kennicutt-Schmidt) as well as for peak and mixed driving the formation of H 2 is strongly suppressed. Also without self-gravity the H 2 fraction is significantly lower (∼ 5%). Most of the volume is filled with hot gas (∼90% within ±2 kpc). Only for random or clustered driving, a vertically expanding warm component of atomic hydrogen indicates a fountain flow. Magnetic fields have little impact on the final disc structure. However, they affect dense gas (n 10 cm −3 ) and delay H 2 formation. We highlight that individual chemical species, in particular atomic hydrogen, populate different ISM phases and cannot be accurately accounted for by simple temperature-/density-based phase cut-offs.
We present 3D "zoom-in" simulations of the formation of two molecular clouds out of the galactic interstellar medium. We model the clouds -identified from the SILCC simulations -with a resolution of up to 0.06 pc using adaptive mesh refinement in combination with a chemical network to follow heating, cooling, and the formation of H 2 and CO including (self-) shielding. The two clouds are assembled within a few million years with mass growth rates of up to ∼ 10 −2 M yr −1 and final masses of ∼ 50 000 M . A spatial resolution of 0.1 pc is required for convergence with respect to the mass, velocity dispersion, and chemical abundances of the clouds, although these properties also depend on the cloud definition such as based on density thresholds, H 2 or CO mass fraction. To avoid grid artefacts, the progressive increase of resolution has to occur within the free-fall time of the densest structures (1 -1.5 Myr) and 200 time steps should be spent on each refinement level before the resolution is progressively increased further. This avoids the formation of spurious, large-scale, rotating clumps from unresolved turbulent flows. While CO is a good tracer for the evolution of dense gas with number densities n 300 cm −3 , H 2 is also found for n 30 cm −3 due to turbulent mixing and becomes dominant at column densities around 30 -50 M pc −2 . The CO-to-H 2 ratio steadily increases within the first 2 Myr whereas X CO 1 -4 × 10 20 cm −2 (K km s −1 ) −1 is approximately constant since the CO(1-0) line quickly becomes optically thick.
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