On the evolution of the density pdf in strongly self-gravitating systems

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 $\mathrm{P}_v(\rho)\propto\rho^{-1.54}$ for the (volume-weighted) PDF and $\mathrm{P}_m(\rho)\propto\rho^{-0.54}$ 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.Comment: accepted for publication, 13 page

Simulations of cosmic ray propagation

We review numerical methods for simulations of cosmic ray (CR) propagation on galactic and larger scales. We present the development of algorithms designed for phenomenological and self-consistent models of CR propagation in kinetic description based on numerical solutions of the Fokker-Planck equation. The phenomenological models assume a stationary structure of the galactic interstellar medium and incorporate diffusion of particles in physical and momentum space together with advection, spallation, production of secondaries and various radiation mechanisms. The self-consistent propagation models of CRs include the dynamical coupling of the CR population to the thermal plasma. The CR transport equation is discretized and solved numerically together with the set of magneto-hydrodynamic (MHD) equations in various approaches treating the CR population as a separate relativistic fluid within the two-fluid approach or as a spectrally resolved population of particles evolving in physical and momentum space. The relevant processes incorporated in self-consistent models include advection, diffusion and streaming well as adiabatic compression and several radiative loss mechanisms. We discuss applications of the numerical models for the interpretation of CR data collected by various instruments. We present example models of astrophysical processes influencing galactic evolution such as galactic winds, the amplification of large-scale magnetic fields and instabilities of the interstellar medium.Comment: 99 pages, 13 figures, to be published in the Living Reviews of Computational Astrophysic

Understanding star formation in molecular clouds I. Effects of line-of-sight contamination on the column density structure

Column-density maps of molecular clouds are one of the most important observables in the context of molecular cloud- and star-formation (SF) studies. With the Herschel satellite it is now possible to determine the column density from dust emission. We use observations and simulations to demonstrate how LOS contamination affects the column density probability distribution function (PDF). We apply a first-order approximation (removing a constant level) to the molecular clouds of Auriga, Maddalena, Carina and NGC3603. 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 flattens after correction. All PDFs have a lognormal part for low column densities with a peak at Av~2, a deviation point (DP) from the lognormal at Av(DP)~4-5, and a power-law tail for higher column densities. Assuming a density distribution rho~r^-alpha, the slopes of the power-law tails correspond to alpha(PDF)=1.8, 1.75, and 2.5 for Auriga, Carina, and NGC3603 (alpha~1.5-2 is consistent gravitational collapse). We find that low-mass and high-mass SF clouds 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 Av~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.Comment: A&A accepted, 15.12. 201

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

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 simulate the evolution of the multi-phase ISM in a 500 pc x 500 pc x 10 kpc region of a galactic disc, with a gas surface density of $\Sigma_{_{\rm GAS}} = 10 \;{\rm M}_\odot/{\rm pc}^2$. The Flash 4.1 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 ($\sim$ 5%). Most of the volume is filled with hot gas ($\sim$90% within $\pm$2 kpc). Only for random or clustered driving, a vertically expanding warm component of atomic hydrogen indicates a fountain flow. Magnetic fields have little impact on the final disc structure. However, they affect dense gas ($n\gtrsim 10\;{\rm 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.Comment: 30 pages, 23 figures, submitted to MNRAS. Comments welcome! For movies of the simulations and download of selected Flash data see the SILCC website: http://www.astro.uni-koeln.de/silc

The SILCC project: III. Regulation of star formation and outflows by stellar winds and supernovae

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)$^2$ x $\pm$ 5 kpc and a gas surface density of 10 M$_{\odot}$/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 indi- vidual 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$_{\odot}$) 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 $\gtrsim$ 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 > 3x10$^5$ 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.Comment: 23 pages; submitted to MNRA

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

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 (500pc)2×±5kpc 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 H2 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 H2 is strongly suppressed. For decreasing SN rates, the H2 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 H2 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 H2 formation. Most of the volume is filled with hot gas (∼80 per cent within ±150pc). 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-off

Synthetic dust polarization emission maps at 353 GHz for an observer placed inside a Local Bubble-like cavity

We present a study of synthetic observations of polarized dust emission at 353 GHz as seen by an observer within a cavity in the interstellar medium (ISM). The cavity is selected from a magnetohydrodynamic simulation of the local ISM with time-dependent chemistry, star formation, and stellar feedback in form of supernova explosions with physical properties comparable to the Local Bubble ones. We find that the local density enhancement together with the coherent magnetic field in the cavity walls makes the selected candidate a translucent polarization filter to the emission coming from beyond its domains. This underlines the importance of studying the Local Bubble in further detail. The magnetic field lines inferred from synthetic dust polarization data are qualitatively in agreement with the all-sky maps of polarized emission at 353 GHz from the Planck satellite in the latitudes interval 15deg <= |b| <= 65deg. As our numerical simulation allows us to track the Galactic midplane only out to distances of 250 pc, we exclude the region |b|<15deg from our analysis. At large Galactic latitudes, our model exhibits a high degree of small-scale structures. On the contrary, the observed polarization pattern around the Galactic poles is relatively coherent and regular, and we argue that the global toroidal magnetic field of the Milky Way is important for explaining the data at |b| > 65deg. We show that from our synthetic polarization maps, it is difficult to distinguish between an open and a closed Galactic cap using the inferred magnetic field morphology alone

The influence of the turbulent perturbation scale on prestellar core fragmentation and disk formation

The collapse of weakly turbulent prestellar cores is a critical stage in the process of star formation. Being highly non-linear and stochastic, the outcome of collapse can only be explored theoretically by performing large ensembles of numerical simulations. Standard practice is to quantify the initial turbulent velocity field in a core in terms of the amount of turbulent energy (or some equivalent) and the exponent in the power spectrum (n \equiv -d log Pk /d log k). In this paper, we present a numerical study of the influence of the details of the turbulent velocity field on the collapse of an isolated, weakly turbulent, low-mass prestellar core. We show that, as long as n > 3 (as is usually assumed), a more critical parameter than n is the maximum wavelength in the turbulent velocity field, {\lambda}_MAX. This is because {\lambda}_MAX carries most of the turbulent energy, and thereby influences both the amount and the spatial coherence of the angular momentum in the core. We show that the formation of dense filaments during collapse depends critically on {\lambda}_MAX, and we explain this finding using a force balance analysis. We also show that the core only has a high probability of fragmenting if {\lambda}_MAX > 0.5 R_CORE (where R_CORE is the core radius); that the dominant mode of fragmentation involves the formation and break-up of filaments; and that, although small protostellar disks (with radius R_DISK <= 20 AU) form routinely, more extended disks are rare. In turbulent, low-mass cores of the type we simulate here, the formation of large, fragmenting protostellar disks is suppressed by early fragmentation in the filaments.Comment: 11 pages, 7 figures; accepted for publication by MNRA

Modelling the supernova-driven ISM in different environments

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=0.5-30cm−3 and SN rates 1-720Myr−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≳106K) filling >90 per cent of the volume. This gas reaches high pressures (10450 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 remnant