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 analyse the scaling properties of turbulent flows using a suite of three-dimensional numerical simulations. We model driven, compressible, isothermal, turbulence with Mach numbers ranging from the subsonic ( $\mathcal {M} \approx 0.5$ ) to the highly supersonic regime ( $\mathcal {M}\approx 16$ ). The forcing scheme consists of both solenoidal (transverse) and compressive (longitudinal) modes in equal parts. We confirm the relation $\sigma _{s}^2 = \ln {(1+b^2\mathcal {M}^2)}$ between the Mach number and the standard deviation of the logarithmic density with b  = 0.33. We find increasing deviations with higher Mach number from the predicted lognormal shape in the high-density wing of the density probability density function. The density spectra follow $\mathcal {D}(k,\,\mathcal {M}) \propto k^{\zeta (\mathcal {M})}$ with scaling exponents depending on the Mach number. We find $\zeta (\mathcal {M}) = \alpha \mathcal {M}^{\beta }$ with coefficients α = –2.1 and β = –0.33. The dependence of the scaling exponent on the Mach number implies a fractal dimension $D=2+1.05 \mathcal {M}^{-0.33}$ .

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: Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive understanding of turbulence. We develop and employ a hierarchical Bayesian fitting method to estimate the parameters describing the scaling relationships of the velocity power spectra of supersonic turbulence. We demonstrate the accuracy and other advantages of this technique compared with ordinary linear regression methods. Using synthetic power spectra, we show that the Bayesian method provides accurate parameter and error estimates. Commonly used normal linear regression methods can provide estimates that fail to recover the underlying slopes, up to 70 per cent of the instances, even when considering the 2 uncertainties. Additionally, we apply the Bayesian methods to analyse the statistical properties of compressible turbulence in three-dimensional numerical simulations. We model driven, isothermal, turbulence with root-mean-square Mach numbers in the highly supersonic regime $\mathcal {M}\approx 15$ . We study the influence of purely solenoidal (divergence-free) and purely compressive (curl-free) forcing on the scaling exponent of the power spectrum. In simulations with solenoidal forcing and 1024 3 resolution, our results indicate that there is no extended inertial range with a constant scaling exponent. The bottleneck effect results in a curved power spectrum at all wave numbers and is more pronounced in the transversal modes compared with the longitudinal modes. Therefore, this effect is stronger in stationary turbulent flows driven by solenoidal forcing compared to the compressive one. The longitudinal spectrum driven with compressive forcing is the only spectrum with constant scaling exponent  = –1.94 ± 0.01, corresponding to slightly shallower slopes than the Burger prediction.

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: Giant molecular clouds (GMCs) are observed to be turbulent, but theory shows that without a driving mechanism turbulence should quickly decay. The question arises by which mechanisms turbulence is driven or sustained. It has been shown that photoionizing feedback from massive stars has an impact on the surrounding GMC and can for example create vast H ii bubbles. We therefore address the question of whether turbulence is a consequence of this effect of feedback on the cloud. To investigate this, we analyse the velocity field of simulations of high-mass star-forming regions by studying velocity structure functions and power spectra. We find that clouds whose morphology is strongly affected by photoionizing feedback also show evidence of driving of turbulence by preserving or recovering a Kolmogorov-type velocity field. On the contrary, control run simulations without photoionizing feedback have a velocity distribution that bears the signature of gravitational collapse and of the dissipation of energy, where the initial Kolmogorov-type structure function is erased.

Description: We present three-dimensional magneto-hydrodynamical simulations of the self-gravitating interstellar medium (ISM) in a periodic (256 pc) 3 box with a mean number density of 0.5 cm –3 . At a fixed supernova rate we investigate the multi-phase ISM structure, H 2 molecule formation and density–magnetic field scaling for varying initial magnetic field strengths (0, 6 x 10 –3 , 0.3, 3 μG). All magnetic runs saturate at mass-weighted field strengths of ~1–3 μG but the ISM structure is notably different. With increasing initial field strengths (from 6 x 10 –3 to 3 μG) the simulations develop an ISM with a more homogeneous density and temperature structure, with increasing mass (from 5 to 85 per cent) and volume filling fractions (VFFs; from 4 to 85 per cent) of warm (300 〈  T 〈 8000 K) gas, with decreasing VFFs from ~35 to ~12 per cent of hot gas ( T 〉 10 5  K) and with a decreasing H 2 mass fraction (from 70 to 〈 1 per cent). Meanwhile, the mass fraction of gas in which the magnetic pressure dominates over the thermal pressure increases by a factor of 10, from 0.07 for an initial field of 6 x 10 –3 μG to 0.7 for a 3 μG initial field. In all but the simulations with the highest initial field strength self-gravity promotes the formation of dense gas and H 2 , but does not change any other trends. We conclude that magnetic fields have a significant impact on the multi-phase, chemical and thermal structure of the ISM and discuss potential implications and limitations of the model.

Description: We report the novel detection of complex high column density tails in the probability distribution functions (PDFs) for three high-mass star-forming regions (CepOB3, MonR2, NGC 6334), obtained from dust emission observed with Herschel . The low column density range can be fitted with a lognormal distribution. A first power-law tail starts above an extinction ( A V ) of ~6–14. It has a slope of α = 1.3–2 for the r –α profile for an equivalent density distribution (spherical or cylindrical geometry), and is thus consistent with free-fall gravitational collapse. Above A V  ~40, 60, and 140, we detect an excess that can be fitted by a flatter power-law tail with α 〉 2. It correlates with the central regions of the cloud (ridges/hubs) of size ~1 pc and densities above 10 4  cm –3 . This excess may be caused by physical processes that slow down collapse and reduce the flow of mass towards higher densities. Possible are: (1) rotation, which introduces an angular momentum barrier, (2) increasing optical depth and weaker cooling, (3) magnetic fields, (4) geometrical effects, and (5) protostellar feedback. The excess/second power-law tail is closely linked to high-mass star-formation though it does not imply a universal column density threshold for the formation of (high-mass) stars.

Description: Giant molecular clouds (GMCs) are observed to be turbulent, but theory shows that without a driving mechanism turbulence should quickly decay. The question arises by which mechanisms turbulence is driven or sustained. It has been shown that photoionizing feedback from massive stars has an impact on the surrounding GMC and can for example create vast H ii bubbles. We therefore address the question of whether turbulence is a consequence of this effect of feedback on the cloud. To investigate this, we analyse the velocity field of simulations of high-mass star-forming regions by studying velocity structure functions and power spectra. We find that clouds whose morphology is strongly affected by photoionizing feedback also show evidence of driving of turbulence by preserving or recovering a Kolmogorov-type velocity field. On the contrary, control run simulations without photoionizing feedback have a velocity distribution that bears the signature of gravitational collapse and of the dissipation of energy, where the initial Kolmogorov-type structure function is erased.