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Obtaining reliable distance estimates to gas clouds within the Milky Way is challenging in the absence of certain tracers. The kinematic distance approach has been used as an alternative, derived from the assumption of circular trajectories around the Galactic centre. Consequently, significant errors are expected in regions where gas flow deviates from purely circular motions. We aim to quantify the systematic errors that arise from the kinematic distance method in the presence of a Galactic potential that is non-axisymmetric. We investigate how these errors differ in certain regions of the Galaxy and how they relate to the underlying dynamics. We perform 2D isothermal hydrodynamical simulation of the gas disk with the moving-mesh code Arepo, adding the capability of using an external potential provided by the Agama library for galactic dynamics. We introduce a new analytic potential of the Milky Way, taking elements from existing models and adjusting parameters to match recent observational constraints. We find significant errors in the kinematic distance estimate for gas close to the Sun, along sight lines towards the Galactic centre and anti-centre, and significant deviations associated with the Galactic bar. Kinematic distance errors are low within the spiral arms as gas resides close to local potential minima and the resulting line-of-sight velocity is close to what is expected for an axisymmetric potential. Interarm regions exhibit large deviations at any given Galactic radius. This is caused by the gas being sped up or slowed down as it travels into or out of the spiral arm. We are able to define 'zones of avoidance' in the lv-diagram, where the kinematic distance method is particularly unreliable and should only be used with caution. We report a power law relation between the kinematic distance error and the deviation of the project line-of-sight velocity from circular motion., Comment: 23 pages, 22 figures, 6 tables, submitted to A&A

Molecular clouds (MC) are structures of dense gas in the interstellar medium (ISM), that extend from ten to a few hundred parsecs and form the main gas reservoir available for star formation. Hydrodynamical simulations of varying complexity are a promising way to investigate MC evolution and their properties. However, each simulation typically has a limited range in resolution and different cloud extraction algorithms are used, which complicates the comparison between simulations. In this work, we aim to extract clouds from different simulations covering a wide range of spatial scales. We compare their properties, such as size, shape, mass, internal velocity dispersion and virial state. We apply the Hop cloud detection algorithm on (M)HD numerical simulations of stratified ISM boxes and isolated galactic disk simulations that were produced using Flash Ramses and Arepo We find that the extracted clouds are complex in shape ranging from round objects to complex filamentary networks in all setups. Despite the wide range of scales, resolution, and sub-grid physics, we observe surprisingly robust trends in the investigated metrics. The mass spectrum matches in the overlap between simulations without rescaling and with a high-mass slope of $\mathrm{d} N/\mathrm{d}\ln M\propto-1$ in accordance with theoretical predictions. The internal velocity dispersion scales with the size of the cloud as $\sigma\propto R^{0.75}$ for large clouds ($R\gtrsim3\,\mathrm{pc}$). For small clouds we find larger sigma compared to the power-law scaling, as seen in observations, which is due to supernova-driven turbulence. Almost all clouds are gravitationally unbound with the virial parameter scaling as $\alpha_\mathrm{vir}\propto M^{-0.4}$, which is slightly flatter compared to observed scaling, but in agreement given the large scatter., Comment: 22 pages, 16 figures, proposed for acceptance in A&A

We present a numerical study of the evolution of power-law tails (PLTs) in the (column-)density distributions ($N$-PDF, $\rho$-PDF) in contracting star-forming clumps in primordial gas, without and with some initial rotational and/or turbulent support. In all considered runs multiple PLTs emerge shortly after the formation of the first protostar. The first PLT (PLT 1) in the $\rho$-PDF is a stable feature with slope $q_1\simeq -1.3$ which corresponds -- under the condition of preserved spherical symmetry -- to the outer envelope of the protostellar object with density profile $\rho\propto l^{-2}$ in the classical Larson-Penston collapse model, where $l$ is the radius. The second PLT (PLT 2) in the $\rho$-PDF is stable in the pure-infall runs but fluctuates significantly in the runs with initial support against gravity as dozens of protostars form and their mutual tidal forces change the density structure. Its mean slope, $\langle q_2\rangle\simeq -2$, corresponds to a density profile of $\rho\propto l^{-3/2}$ which describes a core in free fall in the classical Larson-Penston collapse model or an attractor solution at scales with dominating protostellar gravity. PLT 1 and PLT 2 in the $N$-PDFs are generally consistent with the observational data of Galactic low-mass star-forming regions from {\it Herschel} data. In the runs with initial support against gravity a third PLT (PLT~3) in the $\rho$-PDFs appears simultaneously with or after the emergence of PLT 2. It is very shallow, with mean slope of $\langle q_3\rangle\simeq -1$, and is associated with the formation of thin protostellar accretion disks., Comment: 14 pages, 12 figures; accepted for publication in MNRAS (main journal)

Cosmic rays (CRs) are dynamically important for the formation and evolution of galaxies by regulating star formation and by powering galactic outflows. However, to what extent CRs regulate galaxy formation depends on the coupling strength of CRs with the ambient plasma and the effective CR transport speed along the magnetic field. Moreover, both properties sensitively depend on the CR momentum, which is largely unexplored in three-dimensional hydrodynamical simulations. We perform magneto-hydrodynamical simulations of entire galaxies with masses ranging from $10^{10}$ to $10^{12}\,\mathrm{M}_\odot$ and compare dynamically coupled CRs in the grey approximation with a spectrally resolved model that includes CR momenta from $0.1\,\mathrm{GeV}~c^{-1}$ to $100\,\mathrm{TeV}~c^{-1}$. We find that hadronic cooling of CRs dominates over Alfv\'{e}n cooling, with the latter emulating CR losses as a result of streaming of CRs down their pressure gradient. While star formation rates and galaxy morphologies are only mildly affected by the spectral CR modelling, mass loading factors of galactic outflows can differ by up to a factor of four in dwarf galaxies. All simulated low-mass halos ($M=10^{10}$, $10^{11}$, and $3\times10^{11}\,\mathrm{M}_\odot$) drive strong outflows, where CR transport is temporally dominated by advection. In contrast, the Milky Way-mass galaxy with $M=10^{12}\,\mathrm{M}_\odot$ does not drive sustained outflows, so that CR transport is entirely dominated by diffusion. The effective energy weighted diffusion coefficients vary by two orders of magnitude from the canonical energy-weighted values of $\langle{D}\rangle_{e_\mathrm{cr}}\sim10^{28}\,\mathrm{cm^2\,s^{-1}}$ in the disc up to $3\times10^{29}\,\mathrm{cm^2\,s^{-1}}$ in the circumgalactic medium, where we observe substantial temperature and CR pressure differences between our grey and spectral CR models., Comment: 28 pages, MNRAS, accepted

Cosmic rays (CRs) are ubiquitous in the interstellar medium (ISM) of nearby galaxies, but many of their properties are not well-constrained. Gamma-ray observations provide a powerful tool in this respect, allowing us to constrain both the interaction of CR protons with the ISM and their transport properties. To help better understand the link between observational signatures and CR physics, we use a series of magneto-hydrodynamical (MHD) AREPO simulations of isolated galaxies performed using spectrally-resolved CR transport in every computational cell, with subsequent gamma-ray emission calculated using the CRAYON+ (Cosmic RAY emissiON) code. In each of our simulated halos, modelling the energy-dependent spatial diffusion of CRs leads to a more extended distribution of high-energy (~100 GeV) gamma rays compared to that predicted by a 'grey' steady-state model, which is especially visible in the corresponding emission maps and radial profiles. Despite this, the total gamma-ray spectra can often be well approximated by the steady-state model, although recovering the same spectral index typically requires a minor variation of the energy dependence of the diffusion coefficient. Our simulations reproduce the observed spectral indices and gamma-ray spectra of nearby star-forming galaxies and also match recent observations of the far infrared--gamma-ray relation. We find, however, that the spectrally resolved model yields marginally smaller luminosities for lower star formation rates compared to grey simulations of CRs. Our work highlights the importance of modelling spectrally resolved CR transport for an accurate prediction of spatially resolved high-energy gamma-ray emission, as will be probed by the upcoming Cherenkov Telescope Array observatory., Comment: 18 pages, 11 figures, submitted to MNRAS, comments are welcome!

We present magnetohydrodynamic (MHD) simulations of the star-forming multiphase interstellar medium (ISM) in stratified galactic patches with gas surface densities $\Sigma_\mathrm{gas} =$ 10, 30, 50, and 100 $\mathrm{M_\odot\,pc^{-2}}$. The SILCC project simulation framework accounts for non-equilibrium thermal and chemical processes in the warm and cold ISM. The sink-based star formation and feedback model includes stellar winds, hydrogen-ionising UV radiation, core-collapse supernovae, and cosmic ray (CR) injection and diffusion. The simulations follow the observed relation between $\Sigma_\mathrm{gas}$ and the star formation rate surface density $\Sigma_\mathrm{SFR}$. CRs qualitatively change the outflow phase structure. Without CRs, the outflows transition from a two-phase (warm and hot at 1 kpc) to a single-phase (hot at 2 kpc) structure. With CRs, the outflow always has three phases (cold, warm, and hot), dominated in mass by the warm phase. The impact of CRs on mass loading decreases for higher $\Sigma_\mathrm{gas}$ and the mass loading factors of the CR-supported outflows are of order unity independent of $\Sigma_\mathrm{SFR}$. Similar to observations, vertical velocity dispersions of the warm ionised medium (WIM) and the cold neutral medium (CNM) correlate with the star formation rate as $\sigma_\mathrm{z} \propto \Sigma_\mathrm{SFR}^a$, with $a \sim 0.20$. In the absence of stellar feedback, we find no correlation. The velocity dispersion of the WIM is a factor $\sim 2.2$ higher than that of the CNM, in agreement with local observations. For $\Sigma_\mathrm{SFR} \gtrsim 1.5 \times 10^{-2}\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$ the WIM motions become supersonic., Comment: 20 pages, 12 figures, accepted by MNRAS

We present a study of the filamentary structure in the atomic hydrogen (HI) emission at the 21 cm wavelength toward the Galactic plane using the observations in the HI4PI survey. Using the Hessian matrix method across radial velocity channels, we identified the filamentary structures and quantified their orientations using circular statistics. We found that the regions of the Milky Way's disk beyond 10 kpc and up to roughly 18 kpc from the Galactic center display HI filamentary structures predominantly parallel to the Galactic plane. For regions at lower Galactocentric radii, we found that the HI filaments are mostly perpendicular or do not have a preferred orientation with respect to the Galactic plane. We interpret these results as the imprint of supernova feedback in the inner Galaxy and Galactic rotation in the outer Milky Way. We found that the HI filamentary structures follow the Galactic warp and that they highlight some of the variations interpreted as the effect of the gravitational interaction with satellite galaxies. In addition, the mean scale height of the filamentary structures is lower than that sampled by the bulk of the HI emission, thus indicating that the cold and warm atomic hydrogen phases have different scale heights in the outer galaxy. Finally, we found that the fraction of the column density in HI filaments is almost constant up to approximately 18 kpc from the Galactic center. This is possibly a result of the roughly constant ratio between the cold and warm atomic hydrogen phases inferred from the HI absorption studies. Our results indicate that the HI filamentary structures provide insight into the dynamical processes shaping the Galactic disk. Their orientations record how and where the stellar energy input, the Galactic fountain process, the cosmic ray diffusion, and the gas accretion have molded the diffuse interstellar medium in the Galactic plane., Comment: 33 pages. 39 figures. Accepted for publication in Astronomy & Astrophysics (06MAY2022)

The interstellar medium (ISM) is a turbulent, highly structured multi-phase medium. State-of-the-art cosmological simulations of the formation of galactic discs usually lack the resolution to accurately resolve those multi-phase structures. However, small-scale density structures play an important role in the life cycle of the ISM, and determine the fraction of cold, dense gas, the amount of star formation and the amount of radiation and momentum leakage from cloud-embedded sources. Here, we derive a $statistical\, model$ to calculate the unresolved small-scale ISM density structure from coarse-grained, volume-averaged quantities such as the $gas\, clumping\, factor$, $\mathcal{C}$, and mean density $\left<\rho\right>_V$. Assuming that the large-scale ISM density is statistically isotropic, we derive a relation between the three-dimensional clumping factor, $\mathcal{C}_\rho$, and the clumping factor of the $4\pi$ column density distribution on the cloud surface, $\mathcal{C}_\Sigma$, and find $\mathcal{C}_\Sigma=\mathcal{C}_\rho^{2/3}$. Applying our model to calculate the covering fraction, i.e., the $4\pi$ sky distribution of optically thick sight-lines around sources inside interstellar gas clouds, we demonstrate that small-scale density structures lead to significant differences at fixed physical ISM density. Our model predicts that gas clumping increases the covering fraction by up to 30 per cent at low ISM densities compared to a uniform medium. On the other hand, at larger ISM densities, gas clumping suppresses the covering fraction and leads to increased scatter such that covering fractions can span a range from 20 to 100 per cent at fixed ISM density. All data and example code is publicly available at GitHub., Comment: 16 pages with 8 figures, 14 pages main text with 7 figures, 1 page references, 1 page appendix with 1 figure, accepted by MNRAS on April 1st 2022

We analyse observational signatures of magnetic fields for simulations of a Milky-Way like disc with supernova-driven interstellar turbulence and self-consistent chemical processes. In particular, we post-process two simulations data sets of the SILCC Project for two initial amplitudes of the magnetic field, $B_0 = $ 3 and 6 $\mu$G, to study the evolution of Faraday rotation measures (RM) and synchrotron luminosity. For calculating the RM, three different models of the electron density $n_e$ are considered. A constant electron density, and two estimations based on the density of ionized species and the fraction of the total gas, respectively. Our results show that the RM profiles are extremely sensitive to the $n_e$ models, which assesses the importance of accurate electron distribution observations/estimations for the magnetic fields to be probed using Faraday RMs. As a second observable of the magnetic field, we estimate the synchrotron luminosity in the simulations using a semi-analytical cosmic ray model. We find that the synchrotron luminosity decreases over time, which is connected to the decay of magnetic energy in the simulations. The ratios between the magnetic, the cosmic ray, and the thermal energy density indicate that the assumption of equipartition does not hold for most regions of the ISM. In particular, for the ratio of the cosmic ray to the magnetic energy the assumption of equipatition could lead to a wrong interpretation of the observed synchrotron emission., Comment: 21 pages, 15 figures, published in MNRAS

Recently, cosmic ray (CR) feedback has been identified as a critical process in galaxy formation but most previous simulations have integrated out the energy-dependence of the CR distribution, despite its large extent over more than twelve decades in particle energy. To improve upon this simplification, we present the implementation and first application of spectrally resolved CRs which are coupled to the magneto-hydrodynamics in simulations of galaxy formation. The spectral model for the CRs enables more accurate cooling of CRs and allows for an energy-dependent spatial diffusion, for which we introduce a new stable numerical algorithm that proves essential in highly dynamical systems. We perform galaxy formation simulations with this new model and compare the results to a grey CR approach with a simplified diffusive transport and effective cooling that assumes steady-state spectra. We find that the galaxies with spectrally resolved CRs differ in morphology, star formation rate, and strength and structure of the outflows. Interestingly, the first outflow front is driven by CRs with average momenta of $\sim200-600\,\mathrm{Gev}~c^{-1}$. The subsequent formation of outflows, which reach mass loading factors of order unity, are primarily launched by CRs of progressively smaller average momenta of $\sim8-15\,\mathrm{GeV}~c^{-1}$. The CR spectra in the galactic centre quickly approach a steady state, which does not significantly vary over time. In the outer disc and outflow regions, the spectral shape approaches steady state only after $\sim2\,\mathrm{Gyr}$ of evolution. Furthermore, the shapes of the approximate steady state spectra differ for individual regions of the galaxy, which highlights the importance of actively including the full CR spectrum., Comment: 21 pages, 13 figures, published in MNRAS, erratum added

Magnetic fields are an important component of the interstellar medium (ISM) and exhibit strongly varying field strengths and a non-trivial correlation with the gas density. Its dynamical impact varies between individual regions of the ISM and correlates with the orientation of the field with respect to the gas structures. Using high-resolution magneto-hydrodynamical simulations of the ISM we explore the connection between the orientation of the field and the dynamical state of the gas. We find that the onset of gravitational instability in molecular gas above a density of $\rho\sim10^{-21}\,\mathrm{g\,cm^{-3}}$ $(n\sim400\,\mathrm{cm^{-3}})$ coincides with an alignment of the magnetic field lines and the gas flow. At this transition the gradient of the density changes from mainly perpendicular to preferentially parallel to the field lines. A connection between the three-dimensional alignment and projected two-dimensional observables is non-trivial, because of a large dispersion of the magnetic field orientation along the line of sight. The turbulent correlation lengths can be small compared to the typical integration lengths. As a consequence the small scale signal of the orientation can sensitively depend on the line of sight or the dynamical state of the cloud, can fluctuate stochastically or be completely averaged out. With higher spatial resolution more small scale structures are resolved, which aggravates the link between magneto-hydrodynamical quantities and projected observables., Comment: 20 pages, 16 figures, MNRAS accepted, corrected typos, updated references

An extinction-free estimator of the star-formation rate (SFR) of galaxies is critical for understanding the high-redshift universe. To this end, the nearly linear, tight correlation of far-infrared (FIR) and radio luminosity of star-forming galaxies is widely used. While the FIR is linked to massive star formation, which also generates shock-accelerated cosmic ray (CR) electrons and radio synchrotron emission, a detailed understanding of the underlying physics is still lacking. Hence, we perform three-dimensional magneto-hydrodynamical (MHD) simulations of isolated galaxies over a broad range of halo masses and SFRs using the moving-mesh code AREPO, and evolve the CR proton energy density self-consistently. In post-processing, we calculate the steady-state spectra of primary, shock-accelerated and secondary CR electrons, which result from hadronic CR proton interactions with the interstellar medium. The resulting total radio luminosities correlate with the FIR luminosities as observed and are dominated by primary CR electrons if we account for anisotropic CR diffusion. The increasing contribution of secondary emission up to 30 per cent in starbursts is compensated by the larger bremsstrahlung and Coulomb losses. CR electrons are in the calorimetric limit and lose most of their energy through inverse Compton interactions with star-light and cosmic microwave background (CMB) photons while less energy is converted to synchrotron emission. This implies steep steady-state synchrotron spectra in starbursts. Interestingly, we find that thermal free-free emission hardens the total radio spectra at high radio frequencies and reconciles calorimetric theory with observations while free-free absorption explains the observed low-frequency flattening towards the central regions of starbursts., Comment: 24 pages, 15 figures, submitted to MNRAS, comments are welcome

In star-forming galaxies, the far-infrared (FIR) and radio-continuum luminosities obey a tight empirical relation over a large range of star-formation rates (SFR). We examine magneto-hydrodynamic galaxy simulations with cosmic rays (CRs), accounting for their advective and anisotropic diffusive transport. We show that gravitational collapse of the proto-galaxy generates a corrugated accretion shock, which injects turbulence and drives a small-scale magnetic dynamo. As the shock propagates outwards and the associated turbulence decays, the large velocity shear between the supersonically rotating cool disc with respect to the (partially) pressure-supported hot circumgalactic medium excites Kelvin-Helmholtz surface and body modes. Those inject turbulence and drive multiple small-scale dynamos, which exponentially amplify magnetic fields. They grow in scale to reach equipartition with thermal and CR energies in Milky Way-mass galaxies. In small galaxies, the magnetic energy saturates at the turbulent energy while it fails to reach equipartition with thermal and CR energies. We solve for steady-state spectra of CR protons, secondary electrons/positrons from hadronic CR-proton interactions with the interstellar medium, and primary shock-accelerated electrons at supernovae. The radio-synchrotron emission is dominated by primary electrons, irradiates the magnetised disc, bulge, and bubble-shaped magnetically-loaded outflows of our simulated Milky Way-mass galaxy. Our star-forming and star-bursting galaxies with saturated magnetic fields match the global FIR-radio correlation (FRC) across four orders of magnitude. Its intrinsic scatter arises due to (i) different magnetic saturation levels that result from different seed magnetic fields, (ii) different radio synchrotron luminosities for different specific SFRs at fixed SFR and (iii) a varying radio intensity with galactic inclination. (abridged), Comment: 37 pages, 26 figures, accepted for publication in MNRAS

The $\gamma$-ray emission of star-forming (SF) galaxies is attributed to hadronic interactions of cosmic ray (CR) protons with the interstellar gas and contributions from CR electrons via bremsstrahlung and inverse Compton (IC) scattering. The relative importance of these processes in different galaxy types is still unclear. We model these processes in three-dimensional magneto-hydrodynamical (MHD) simulations of the formation of isolated galactic discs using the moving-mesh code AREPO, including dynamically coupled CR protons and adopting different CR transport models. We calculate steady-state CR spectra and also account for the emergence of secondary electrons and positrons. This allows us to produce detailed $\gamma$-ray maps, luminosities and spectra of our simulated galaxies at different evolutionary stages. Our simulations with anisotropic CR diffusion and a low CR injection efficiency at supernovae (SNe, $\zeta_{\mathrm{SN}}=0.05$) can successfully reproduce the observed far infrared (FIR)-$\gamma$-ray relation. Starburst galaxies are close to the calorimetric limit, where CR protons lose most of their energy due to hadronic interactions and hence, their $\gamma$-ray emission is dominated by neutral pion decay. However, in low SF galaxies, the increasing diffusive losses soften the CR proton spectra due to energy-dependent diffusion, and likewise steepen the pionic $\gamma$-ray spectra. In turn, IC emission hardens the total spectra and can contribute up to $\sim40$ per cent of the total luminosity in low SF galaxies. Furthermore, in order to match the observed $\gamma$-ray spectra of starburst galaxies, we require a weaker energy dependence of the CR diffusion coefficient, $D\propto{E}^{0.3}$, in comparison to Milky Way-like galaxies., Comment: 20 pages, 11 figures, accepted to MNRAS

Current-day cosmic ray (CR) propagation studies use static Milky-Way models and fit parametrized source distributions to data. Instead, we use three-dimensional magneto-hydrodynamical (MHD) simulations of isolated galaxies with the moving-mesh code AREPO that self-consistently accounts for hydrodynamic effects of CR protons. In post-processing, we calculate their steady-state spectra, taking into account all relevant loss processes. We show that this steady-state assumption is well justified in the disc and generally for regions that emit non-thermal radio and gamma rays. Additionally, we model the spectra of primary electrons, accelerated by supernova remnants, and secondary electrons and positrons produced in hadronic CR proton interactions with the gas. We find that proton spectra above 10 GeV only weakly depend on galactic radius, while they acquire a radial dependence at lower energies due to Coulomb interactions. Radiative losses steepen the spectra of primary CR electrons in the central galactic regions while diffusive losses dominate in the outskirts. Secondary electrons exhibit a steeper spectrum than primaries because they originate from the transported steeper CR proton spectra. Consistent with Voyager-1 and AMS-02 data, our models (i) show a turn-over of proton spectra below GeV energies due to Coulomb interactions so that electrons start to dominate the total particle spectra and (ii) match the shape of the positron fraction up to 10 GeV. We conclude that our steady-state CR modeling in MHD-CR galaxy simulations is sufficiently realistic to capture the dominant transport effects shaping their spectra, arguing for a full MHD treatment to accurately model CR transport in the future., Comment: 23 pages, 17 figures, accepted to MNRAS

We present simulations of the multi-phase interstellar medium (ISM) at solar neighbourhood conditions including thermal and non-thermal ISM processes, star cluster formation, and feedback from massive stars: stellar winds, hydrogen ionising radiation computed with the novel TreeRay radiative transfer method, supernovae (SN), and the injection of cosmic rays (CR). N-body dynamics is computed with a 4th-order Hermite integrator. We systematically investigate the impact of stellar feedback on the self-gravitating ISM with magnetic fields, CR advection and diffusion and non-equilibrium chemical evolution. SN-only feedback results in strongly clustered star formation with very high star cluster masses, a bi-modal distribution of the ambient SN densities, and low volume-filling factors (VFF) of warm gas, typically inconsistent with local conditions. Early radiative feedback prevents an initial starburst, reduces star cluster masses and outflow rates. Furthermore, star formation rate surface densities of $\Sigma_{\dot{M}_\star} = 1.4-5.9 \times 10^{-3}$ $\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$, VFF$_\mathrm{warm} = 60-80$ per cent as well as thermal, kinetic, magnetic, and cosmic ray energy densities of the model including all feedback mechanisms agree well with observational constraints. On the short, 100 Myr, timescales investigated here, CRs only have a moderate impact on star formation and the multi-phase gas structure and result in cooler outflows, if present. Our models indicate that at low gas surface densities SN-only feedback only captures some characteristics of the star-forming ISM and outflows/inflows relevant for regulating star formation. Instead, star formation is regulated on star cluster scales by radiation and winds from massive stars in clusters, whose peak masses agree with solar neighbourhood estimates., Comment: 23 pages, 16 figures, accepted by MNRAS, corrected an incorrect reference

Molecular outflows contributing to the matter cycle of star forming galaxies are now observed in small and large systems at low and high redshift. Their physical origin is still unclear. In most theoretical studies only warm ionised/neutral and hot gas outflowing from the interstellar medium is generated by star formation. We investigate an in-situ H$_2$ formation scenario in the outflow using high-resolution simulations, including non-equilibrium chemistry and self-gravity, of turbulent, warm, and atomic clouds with densities 0.1, 0.5 and $1\,\mathrm{cm}^{-3}$ exposed to a magnetised hot wind. For cloud densities $\gtrsim 0.5\,\mathrm{cm}^{-3}$ a magnetised wind triggers H$_2$ formation before cloud dispersal. Up to 3 per cent of the initial cloud mass can become molecular on $\sim 10\,\mathrm{Myr}$ time scales. The effect is stronger for winds with perpendicular $B$-fields and intermediate density clouds ($n_\mathrm{c}\sim 0.5\,\mathrm{cm}^{-3}$). Here H$_2$ formation can be boosted by up to one order of magnitude compared to isolated cooling clouds independent of self-gravity. Self-gravity preserves the densest clouds way past their $\sim 15\,\mathrm{Myr}$ cloud crushing time scales. This model could provides a plausible in-situ origin for the observed molecular gas. Warm ionised gas is also generated, almost independent of the cloud density. The amount solely depend on the magnetic field configuration in the wind. For low density clouds ($0.1\,\mathrm{cm}^{-3}$), the forming warm ionised gas can be as much as 60 per cent of the initially atomic cloud mass. This could contribute to observations of outflows with ionised gas sensitive tracers., Comment: 23 pages, MNRAS accepted

Supernova remnants (SNRs) are believed to be the source of Galactic cosmic rays (CRs). SNR shocks accelerate CR protons and electrons which reveal key insights into the non-thermal physics by means of their synchrotron and $\gamma$-ray emission. The remnant SN 1006 is an ideal particle acceleration laboratory because it is observed across all electromagnetic wavelengths from radio to $\gamma$-rays. We perform three-dimensional (3D) magnetohydrodynamics (MHD) simulations where we include CR protons and follow the CR electron spectrum. By matching the observed morphology and non-thermal spectrum of SN 1006 in radio, X-rays and $\gamma$-rays, we gain new insight into CR electron acceleration and magnetic field amplification. 1. We show that a mixed leptonic-hadronic model is responsible for the $\gamma$-ray radiation: while leptonic inverse-Compton emission and hadronic pion-decay emission contribute equally at GeV energies observed by Fermi, TeV energies observed by imaging air Cherenkov telescopes are hadronically dominated. 2. We show that quasi-parallel acceleration (i.e., when the shock propagates at a narrow angle to the upstream magnetic field) is preferred for CR electrons and that the electron acceleration efficiency of radio-emitting GeV electrons at quasi-perpendicular shocks is suppressed at least by a factor ten. This precludes extrapolation of current one-dimensional plasma particle-in-cell simulations of shock acceleration to realistic SNR conditions. 3. To match the radial emission profiles and the $\gamma$-ray spectrum, we require a volume-filling, turbulently amplified magnetic field and that the Bell-amplified magnetic field is damped in the immediate post-shock region. Our work connects micro-scale plasma physics simulations to the scale of SNRs., Comment: 18 pages, 18 figures, published in MNRAS

Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms., Comment: 86 pages, 4 figures. To appear in Space Science Reviews, topical collection Star formation

Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work., Comment: 53 pages, 7 figures, preprint of a review to appear in Space Science Reviews Topical collection "Star formation". Changes in this version: updated comments line to to acceptance of the paper by the journal

In recent years, exciting developments have taken place in the identification of the role of cosmic rays in star-forming environments. Observations from radio to infrared wavelengths and theoretical modelling have shown that low-energy cosmic rays (<1 TeV) play a fundamental role in shaping the chemical richness of the interstellar medium, determining the dynamical evolution of molecular clouds. In this review we summarise in a coherent picture the main results obtained by observations and by theoretical models of propagation and generation of cosmic rays, from the smallest scales of protostars and circumstellar discs, to young stellar clusters, up to Galactic and extragalactic scales. We also discuss the new fields that will be explored in the near future thanks to new generation instruments, such as: CTA, for the $\gamma$-ray emission from high-mass protostars; SKA and precursors, for the synchrotron emission at different scales; and ELT/HIRES, JWST, and ARIEL, for the impact of cosmic rays on exoplanetary atmospheres and habitability., Comment: Submitted to Space Science Reviews topical collection Star formation

Cosmic ray (CR) protons are an important component in many astrophysical systems. Processes like CR injection, cooling, adiabatic changes as well as active CR transport through the medium strongly modify the CR momentum distribution and have to be taken into account in hydrodynamical simulations. We present an efficient novel numerical scheme to accurately compute the evolution of the particle distribution function by solving the Fokker-Planck equation with a low number of spectral bins (10 - 20), which is required to include a full spectrum for every computational fluid element. The distribution function is represented by piecewise power laws and is not forced to be continuous, which enables an optimal representation of the spectrum. The Fokker-Planck equation is solved with a two-moment approach evolving the CR number and energy density. The low numerical diffusion of the scheme reduces the numerical errors by orders of magnitude in comparison to classical schemes with piecewise constant spectral representations. With this method not only the spectral evolution of CRs can be computed accurately in magnetohydrodynamic simulations but also their dynamical impact as well as CR ionisation. This allows for more accurate models for astrophysical plasmas, like the interstellar medium, and direct comparisons with observations., Comment: 16 pages, MNRAS accepted, corrected typo in eq. (63)

We present a new approach to extract the power-law part of a density/column-density probability density function (rho-pdf/N-pdf) in star-forming clouds. It is based on the mathematical method bPLFIT of Virkar & Clauset (2014) and assesses the power-law part of an arbitrary distribution, without any assumptions about the other part of this distribution. The slope and deviation point are derived as averaged values as the number of bins is varied. Neither parameter is sensitive to spikes and other local features of the tail. This adapted bPLFIT method is applied to two different sets of data from numerical simulations of star-forming clouds at scales 0.5 and 500 pc and displays rho-pdf and N-pdf evolution in agreement with a number of numerical and theoretical studies. Applied to Herschel data on the regions Aquila and Rosette, the method extracts pronounced power-law tails, consistent with those seen in simulations of evolved clouds., Comment: Accepted for publication in MNRAS; 15 pages, 13 figures

Cosmic ray (CR) electrons reveal key insights into the non-thermal physics of the interstellar medium, galaxies, galaxy clusters, and active galactic nuclei by means of their inverse Compton {\gamma}-ray emission and synchrotron emission in magnetic fields. While magnetohydrodynamical (MHD) simulations with CR protons capture their dynamical impact on these systems, only few computational studies include CR electron physics because of the short cooling time-scales and complex hysteresis effects, which require a numerically expensive, high-resolution spectral treatment. Since CR electrons produce important non-thermal observational signatures, such a spectral CR electron treatment is important to link MHD simulations to observations. We present an efficient post-processing code for Cosmic Ray Electron Spectra that are evolved in Time (CREST) on Lagrangian tracer particles. The CR electron spectra are very accurately evolved on comparably large MHD time steps owing to an innovative hybrid numerical-analytical scheme. CREST is coupled to the cosmological MHD code AREPO and treats all important aspects of spectral CR electron evolution such as adiabatic expansion and compression, Coulomb losses, radiative losses in form of inverse Compton, bremsstrahlung and synchrotron processes, diffusive shock acceleration and reacceleration, and Fermi-II reacceleration. After showing various code validations of idealized one-zone simulations, we study the coupling of CREST to MHD simulations. We demonstrate that the CR electron spectra are efficiently and accurately evolved in shock-tube and Sedov-Taylor blast wave simulations. This opens up the possibility to produce self-consistent synthetic observables of non-thermal emission processes in various astrophysical environments., Comment: 19 pages, 14 figures, 11 pages, 9 figures, published in MNRAS

Mrk 71/NGC 2366 is the closest Green Pea (GP) analog and candidate Lyman Continuum (LyC) emitter. Recently, 11 LyC-leaking GPs have been detected through direct observations of the ionizing continuum, making this the most abundant class of confirmed LyC-emitters at any redshift. High resolution, multi-wavelength studies of GPs can lead to an understanding of the method(s), through which LyC escapes from these galaxies. The proximity of Mrk 71/NCG 2366 offers unprecedented detail on the inner workings of a GP analog, and enables us to identify the mechanisms of LyC escape. We use 5825-7650{\AA} integral field unit PMAS observations to study the kinematics and physical conditions in Mrk 71. An electron density map is obtained from the [S II] ratio. A fortuitous second order contamination by the [O II]3727 doublet enables the construction of an electron temperature map. Resolved maps of sound speed, thermal broadening, "true" velocity dispersion, and Mach number are obtained and compared to the high resolution magneto-hydrodynamic SILCC simulations. Two regions of increased velocity dispersion indicative of outflows are detected to the north and south of the super star cluster, knot B, with redshifted and blueshifted velocities, respectively. We confirm the presence of a faint broad kinematical component, which is seemingly decoupled from the outflow regions, and is fainter and narrower than previously reported in the literature. Within uncertainties, the low- and high-ionization gas move together. Outside of the core of Mrk 71, an increase in Mach numbers is detected, implying a decrease in gas density. Simulations suggest this drop in density can be as high as ~4 dex, down to almost optically thin levels, which would imply a non-zero LyC escape fraction along the outflows... [abridged], Comment: Accepted for publication in A&A. 17 pages, 16 figures, 4 tables

Magnetic fields are ubiquitously observed in the interstellar medium (ISM) of present-day star-forming galaxies with dynamically relevant energy densities. Using three-dimensional magneto-hydrodynamic (MHD) simulations of the supernova (SN) driven ISM in the flux-freezing approximation (ideal MHD) we investigate the impact of the magnetic field on the chemical and dynamical evolution of the gas, fragmentation and the formation of molecular clouds. We follow the chemistry with a network of six species (H$^{+}$, H, H$_2$, C$^+$, CO, free electrons) including local shielding effects. We find that magnetic fields thicken the disc by a factor of a few to a scale height of $\sim100\,\mathrm{pc}$, delay the formation of dense (and molecular) gas by $\sim25\,\mathrm{Myr}$ and result in differently shaped gas structures. The magnetised gas fragments into fewer clumps, which are initially at subcritical mass-to-flux ratios, $M/\Phi\approx0.3(M/\Phi)_\mathrm{crit}$, and accrete gas preferentially parallel to the magnetic field lines until supercritial mass-to-flux ratios of up to order 10 are reached. The accretion rates onto molecular clouds scale with $\dot{M}\propto M^{1.5}$. The median of the inter-cloud velocity dispersion is $\sim2-5\,\mathrm{km\,s}^{-1}$ and lower than the internal velocity dispersion in the clouds ($\sim3-7\,\mathrm{km\,s}^{-1}$). However, individual cloud-cloud collisions occur at speeds of a few $10\,\mathrm{km\,s}^{-1}$., Comment: 31 pages, 26 figures, MNRAS accepted

Recent magneto-hydrodynamic simulations of the star-forming interstellar medium (ISM) with parsec scale resolution indicate that relativistic cosmic rays support the launching of galactic outflows on scales of a few kpc. If these fundamental constituents of the ISM are injected at the sites of supernova (SN) explosions, the outflows are smoother, colder, and denser than the highly structured, hot-phase driven outflows forming, e.g., by thermal SN energy injection alone. In this Letter we present computations of resonant Lyman-$\alpha$ (Ly$\alpha$) radiation transfer through snapshots of a suite of stratified disk simulations from the SILCC project. For a range of thermal, radiative, and kinetic feedback models only simulations including non-thermal cosmic rays produce Ly$\alpha$ spectra with enhanced red peaks and strong absorption at line center -- similar to observed systems. The absence of cosmic ray feedback leads to spectra incompatible with observations. We attribute this to the smoother neutral gas distribution of cosmic ray supported outflows within a few kpc from the disk midplane., Comment: 6 pages, 4 figures; accepted for publication in ApJL

We investigate the impact of cosmic rays (CRs) on galactic outflows from a multi-phase interstellar medium with solar neighbourhood conditions. The three-dimensional magneto-hydrodynamical simulations include CRs as a relativistic fluid in the advection-diffusion approximation. The thermal and chemical state of the ISM is computed with a non-equilibrium chemical network. We find that CRs (injected with 10 \% of the supernova energy) efficiently support the launching of outflows and strongly affect their phase structure. Outflows leaving the midplane are denser ($\rho \sim 10^{-26}\,\mathrm{g\,cm}^{-3}$), colder ($\sim 10^4\,\mathrm{K}$), and slower ($\sim 30\,\mathrm{km\,s}^{-1}$) if CRs are considered in addition to thermal SNe. The CR supported outflows are also smoother, in particular at larger heights ($> 1\,\mathrm{kpc}$ above the midplane) without the direct impact of SN explosions. Approximately $5\% - 25\%$ of the injected CR energy is lost via hadronic cooling. Smaller diffusion coefficients lead to slightly larger hadronic losses but allow for steeper CR pressure gradients, stronger outflows and larger accelerations. Up to a height of $z \sim1\,\mathrm{kpc}$ there are large volumes in approximate pressure equilibrium between thermal and CR component. At larger altitudes the CR pressure is $10-100$ times as large as the thermal counterpart. More than $\sim 1\,\mathrm{kpc}$ away from the midplane, CRs provide the dominant gas acceleration mechanism., Comment: 28 pages, submitted to MNRAS, movies at http://girichidis.com/

The large vertical scale heights of the diffuse ionised gas (DIG) in disc galaxies are challenging to model, as hydrodynamical models including only thermal feedback seem to be unable to support gas at these heights. In this paper, we use a three dimensional Monte Carlo radiation transfer code to post-process disc simulations of the Simulating the Life-Cycle of Molecular Clouds (SILCC) project that include feedback by cosmic rays. We show that the more extended discs in simulations including cosmic ray feedback naturally lead to larger scale heights for the DIG which are more in line with observed scale heights. We also show that including a fiducial cosmic ray heating term in our model can help to increase the temperature as a function of disc scale height, but fails to reproduce observed DIG nitrogen and sulphur forbidden line intensities. We show that, to reproduce these line emissions, we require a heating mechanism that affects gas over a larger density range than is achieved by cosmic ray heating, which can be achieved by fine tuning the total luminosity of ionising sources to get an appropriate ionising spectrum as a function of scale height. This result sheds a new light on the relation between forbidden line emissions and temperature profiles for realistic DIG gas distributions., Comment: 14 pages, 11 figures, accepted for publication in Montly Notices of the Royal Astronomical Society

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, $6\times 10^{-3}$, 0.3, 3 $\mu$G). All magnetic runs saturate at mass weighted field strengths of $\sim$ 1 $-$ 3 $\mu$G but the ISM structure is notably different. With increasing initial field strengths (from $6\times 10^{-3}$ to 3 $\mu$G) the simulations develop an ISM with a more homogeneous density and temperature structure, with increasing mass (from 5% to 85%) and volume filling fractions (from 4% to 85%) of warm (300 K $<$ T $<$ 8000 K) gas, with decreasing volume filling fractions (VFF) from $\sim$ 35% to $\sim$ 12% of hot gas (T $> 10^5$ K) and with a decreasing H$_{2}$ mass fraction (from 70% to $<$ 1%). 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 $6\times 10^{-3}$ $\mu$G to 0.7 for a 3 $\mu$G 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., Comment: submitted

We present three-dimensional radiation-hydrodynamical simulations of the impact of stellar winds, photoelectric heating, photodissociating and photoionising radiation, and supernovae on the chemical composition and star formation in a stratified disc model. This is followed with a sink-based model for star clusters with populations of individual massive stars. Stellar winds and ionising radiation regulate the star formation rate at a factor of ~10 below the simulation with only supernova feedback due to their immediate impact on the ambient interstellar medium after star formation. Ionising radiation (with winds and supernovae) significantly reduces the ambient densities for most supernova explosions to rho < 10^-25 g cm^-3, compared to 10^-23 g cm^-3 for the model with only winds and supernovae. Radiation from massive stars reduces the amount of molecular hydrogen and increases the neutral hydrogen mass and volume filling fraction. Only this model results in a molecular gas depletion time scale of 2 Gyr and shows the best agreement with observations. In the radiative models, the Halpha emission is dominated by radiative recombination as opposed to collisional excitation (the dominant emission in non-radiative models), which only contributes ~1-10 % to the total Halpha emission. Individual massive stars (M >= 30 M_sun) with short lifetimes are responsible for significant fluctuations in the Halpha luminosities. The corresponding inferred star formation rates can underestimate the true instantaneous star formation rate by factors of ~10., Comment: submitted to MNRAS, movies https://hera.ph1.uni-koeln.de/~silcc/

Dust grains are an important component of the interstellar medium (ISM) of galaxies. We present the first direct measurement of the residence times of interstellar dust in the different ISM phases, and of the transition rates between these phases, in realistic hydrodynamical simulations of the multi-phase ISM. Our simulations include a time-dependent chemical network that follows the abundances of H^+, H, H_2, C^+ and CO and take into account self-shielding by gas and dust using a tree-based radiation transfer method. Supernova explosions are injected either at random locations, at density peaks, or as a mixture of the two. For each simulation, we investigate how matter circulates between the ISM phases and find more sizeable transitions than considered in simple mass exchange schemes in the literature. The derived residence times in the ISM phases are characterised by broad distributions, in particular for the molecular, warm and hot medium. The most realistic simulations with random and mixed driving have median residence times in the molecular, cold, warm and hot phase around 17, 7, 44 and 1 Myr, respectively. The transition rates measured in the random driving run are in good agreement with observations of Ti gas-phase depletion in the warm and cold phases in a simple depletion model, although the depletion in the molecular phase is under-predicted. ISM phase definitions based on chemical abundance rather than temperature cuts are physically more meaningful, but lead to significantly different transition rates and residence times because there is no direct correspondence between the two definitions., Comment: submitted to MNRAS, movies https://hera.ph1.uni-koeln.de/~silcc/

The halo of the Milky Way contains a hot plasma with a surface brightness in soft X-rays of the order $10^{-12}$erg cm$^{-2}$ s$^{-1}$ deg$^{-2}$. The origin of this gas is unclear, but so far numerical models of galactic star formation have failed to reproduce such a large surface brightness by several orders of magnitude. In this paper, we analyze simulations of the turbulent, magnetized, multi-phase interstellar medium including thermal feedback by supernova explosions as well as cosmic-ray feedback. We include a time-dependent chemical network, self-shielding by gas and dust, and self-gravity. Pure thermal feedback alone is sufficient to produce the observed surface brightness, although it is very sensitive to the supernova rate. Cosmic rays suppress this sensitivity and reduce the surface brightness because they drive cooler outflows. Self-gravity has by far the largest effect because it accumulates the diffuse gas in the disk in dense clumps and filaments, so that supernovae exploding in voids can eject a large amount of hot gas into the halo. This can boost the surface brightness by several orders of magnitude. Although our simulations do not reach a steady state, all simulations produce surface brightness values of the same order of magnitude as the observations, with the exact value depending sensitively on the simulation parameters. We conclude that star formation feedback alone is sufficient to explain the origin of the hot halo gas, but measurements of the surface brightness alone do not provide useful diagnostics for the study of galactic star formation., Comment: ApJ Letters in press

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, H2, 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) and are denser (\rho~1e-24 - 1e-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., Comment: 7 pages, 5 figures, ApJL, accepted

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, H2, 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_HI ~ 0.8\sigma_(300-8000K) ~ 10-20km/s, \sigma_H\alpha ~ 0.6\sigma_(8000-3e5K) ~ 20-30km/s), and strong outflows with mass loading factors 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 (\rho ~ 1e-25-1e-24g/cc) and slow (v ~ 20-40km/s) but there is a high-velocity tail of up to v ~ 500km/s with \rho ~ 1e-28-1e-27g/cc., Comment: 26 pages, MNRAS, accepted

We model driven, compressible, isothermal, turbulence with Mach numbers ranging from the subsonic ($\mathcal{M} \approx 0.65$) to the highly supersonic regime ($\mathcal{M}\approx 16 $). The forcing scheme consists both solenoidal (transverse) and compressive (longitudinal) modes in equal parts. We find a relation $\sigma_{s}^2 = \mathrm{b}\log{(1+\mathrm{b}^2\mathcal{M}^2)}$ between the Mach number and the standard deviation of the logarithmic density with $\mathrm{b} = 0.457 \pm 0.007$. 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 a coefficient $\alpha$ that varies slightly with resolution, whereas $\beta$ changes systematically. We extrapolate to the limit of infinite resolution and find $\alpha = -1.91 \pm 0.01,\, \beta =-0.30\pm 0.03$. The dependence of the scaling exponent on the Mach number implies a fractal dimension $D=2+0.96 \mathcal{M}^{-0.30}$. We determine how the scaling parameters depend on the wavenumber and find that the density spectra are slightly curved. This curvature gets more pronounced with increasing Mach number. We propose a physically motivated fitting formula $\mathcal{D}(k) = \mathcal{D}_0 k^{\zeta k^{\eta}}$ by using simple scaling arguments. The fit reproduces the spectral behaviour down to scales $k\approx 80$. The density spectrum follows a single power-law $\eta = -0.005 \pm 0.01$ in the low Mach number regime and the strongest curvature $\eta = -0.04 \pm 0.02$ for the highest Mach number. These values of $\eta$ represent a lower limit, as the curvature increases with resolution., Comment: 12 pages, 11 figures, MNRAS, submitted

We present a novel implementation of cosmic rays (CR) in the magneto-hydrodynamic code FLASH. CRs are described as separate fluids with different energies. CR advection, energy dependent anisotropic diffusion with respect to the magnetic field and adiabatic losses to follow the evolution of spectra are taken into account. We present a first study of the transport and immediate (~150 kyr) dynamical impact of CRs on the turbulent magnetised interstellar medium around supernova remnants on scales up to 80 pc. CR diffusion quickly leads to an efficient acceleration of low-density gas (mainly perpendicular to the magnetic field) with accelerations up to two orders of magnitude above the thermal values. Peaked (at 1 GeV) CR injection spectra have a stronger impact on the dynamics than power-law spectra. For realistic magnetic field configurations low energy CRs (with smaller diffusion coefficients) distribute anisotropically with large spatial variations of a factor of ten and more. Adiabatic losses can change the local spectra perceptibly but do not have an integral effect on the dynamics at the spatial and temporal scales considered here. We discuss the potential global impact of CRs and anisotropic transport on the dynamical structure of the ISM and also detail the limitations of the model., Comment: 22 pages, submitted to MNRAS, comments welcome

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% of the instances, even when considering the 2std.dev. uncertainties. Additionally, we apply the Bayesian methods to analyse the statistical properties of compressible turbulence in 3D numerical simulations. We model driven, isothermal, turbulence with rms Mach numbers in the highly supersonic regime M~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 z=-1.94 +- 0.01, corresponding to slightly shallower slopes than the Burger's prediction., Comment: 10 pages, 6 figures

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 pages

The probability density function (PDF) of the gas density in subsonic and supersonic, isothermal, driven turbulence is analyzed with a systematic set of hydrodynamical grid simulations with resolutions up to 1024^3 cells. We performed a series of numerical experiments with root mean square (r.m.s.) Mach number M ranging from the nearly incompressible, subsonic (M=0.1) to the highly compressible, supersonic (M=15) regime. We study the influence of two extreme cases for the driving mechanism by applying a purely solenoidal (divergence-free) and a purely compressive (curl-free) forcing field to drive the turbulence. We find that our measurements fit the linear relation between the r.m.s. Mach number and the standard deviation of the density distribution in a wide range of Mach numbers, where the proportionality constant depends on the type of the forcing. In addition, we propose a new linear relation between the standard deviation of the density distribution and the standard deviation of the velocity in compressible modes, i.e. the compressible component of the r.m.s. Mach number. In this relation the influence of the forcing is significantly reduced, suggesting a linear relation between the standard deviation of the density distribution and the standard deviation of the velocity in compressible modes, independent of the forcing, ranging from the subsonic to the supersonic regime., Comment: 8 pages,6 figures, The Astrophysical Journal (submitted)

We investigate the formation of protostellar clusters during the collapse of dense molecular cloud cores with a focus on the evolution of potential and kinetic energy, the degree of substructure, and the early phase of mass segregation. Our study is based on a series of hydrodynamic simulations of dense cores, where we vary the initial density profile and the initial turbulent velocity. In the three-dimensional adaptive mesh refinement simulations, we follow the dynamical formation of filaments and protostars until a star formation efficiency of 20%. Despite the different initial configurations, the global ensemble of all protostars in a setup shows a similar energy evolution and forms sub-virial clusters with an energy ratio $E_\mathrm{kin}/|E_\mathrm{pot}|\sim0.2$. Concentrating on the innermost central region, the clusters show a roughly virialised energy balance. However, the region of virial balance only covers the innermost $\sim10-30%$ of all the protostars. In all simulations with multiple protostars, the total kinetic energy of the protostars is higher than the kinetic energy of the gas cloud, although the protostars only contain 20% of the total mass. The clusters vary significantly in size, mass, and number of protostars, and show different degrees of substructure and mass segregation. Flat density profiles and compressive turbulent modes produce more subclusters then centrally concentrated profiles and solenoidal turbulence. We find that dynamical relaxation and hence dynamical mass segregation is very efficient in all cases from the very beginning of the nascent cluster, i.e., during a phase when protostars are constantly forming and accreting., Comment: 19 pages, MNRAS accepted

We investigate the impact of different initial conditions for the initial density profile and the initial turbulence on the formation process of protostellar clusters. We study the collapse of dense molecula r cloud cores with three-dimensional adaptive mesh refinement simulations. We focus our discussion on the distribution of the gas among the protostellar objects in the turbulent dynamical cores. Despite the large variations in the initial configurations and the resulting gas and cluster morphology we find that all stellar clusters follow a very similar gas accretion behaviour. Once secondary protostars begin to form, the central region of a cluster is efficiently shielded from further accretion. Hence, objects located close to the centre are starved of material, as indicated by a strong decrease of the central acc retion rate. This Fragmentation Induced Starvation occurs not only in rotationally supported discs and filaments, but also in more spherically symmetric clusters with complex chaotic motions., Comment: 15 pages, MNRAS, in press, small changes (referee's suggestions and comments)

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, $\rho\propto r^{-1.5}$, and $\rho\propto r^{-2}$), combined with six different supersonic turbulent velocity fields (compressive, mixed, and solenoidal, initialised 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% 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., Comment: 20 pages, MNRAS in press