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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)