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The relation between magnetic field strength B and gas density n in the interstellar medium is of fundamental importance to many areas of astrophysics, from protostellar disks to galaxy evolution. We present and compare Bayesian analyses of the B - n relation for a comprehensive observational data set, as well as a large body of numerical MHD simulations. We extend the original Zeeman relation of Crutcher et al. (2010) with a large body of magnetic data that includes 700 observations with the Davis-Chandrasekhar-Fermi method. By using a new multiparameter Bayesian analysis we present a new, more general, time-averaged observational relation: B \propto n^{0.27 \pm 0.017} for n \leq n_0 and B \propto n^{0.54 \pm 0.18} for n \geq n_0, with n_0 = 924^(+145-144) cm^-3. We perform a separate analysis on 19 numerical magnetohydrodynamics simulations that cover a wide range of scales, resolutions, initial conditions, and completed with a variety of codes: arepo, flash, pencil, and ramses. The power law exponents derived from the simulations depend on several physical factors including: dynamo effects, time scales, turbulence, and the initial seed field strength. In particular, early-time simulations where the density, velocity and magnetic fields are unevolved do not match the observational scalings. The simulations that trace the observed density range best, the evolved dwarf galaxy and Milky Way like galaxy simulations, settle into a near consistent exponent of = 0.5 in the dense gas, with variability in the diffuse gas exponent., Comment: 23 figures, 28 pages, submitted to MNRAS, Comments welcome

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