Context. Radio continuum (RC) emission in galaxies allows us to measure star formation rates (SFRs) unaffected by extinction due to dust, of which the low-frequency part is uncontaminated from thermal (free-free) emission. Aims. We calibrate the conversion from the spatially resolved 140 MHz RC emission to the SFR surface density (Σ SFR ) at 1 kpc scale. Radio spectral indices give us, by means of spectral ageing, a handle on the transport of cosmic rays using the electrons as a proxy for GeV nuclei. Methods. We used recent observations of three galaxies (NGC 3184, 4736, and 5055) from the LOFAR Two-metre Sky Survey (LoTSS), and archival LOw-Frequency ARray (LOFAR) data of NGC 5194. Maps were created with the facet calibration technique and converted to radio Σ SFR maps using the Condon relation. We compared these maps with hybrid Σ SFR maps from a combination of GALEX far-ultraviolet and Spitzer 24 µm data using plots tracing the relation at the highest angular resolution allowed by our data at 1.2 × 1.2-kpc 2 resolution. Results. The RC emission is smoothed with respect to the hybrid Σ SFR owing to the transport of cosmic-ray electrons (CREs) away from star formation sites. This results in a sublinear relation (Σ SFR ) RC ∝ [(Σ SFR ) hyb ] a , where a = 0.59 ± 0.13 (140 MHz) and a = 0.75 ± 0.10 (1365 MHz). Both relations have a scatter of σ = 0.3 dex. If we restrict ourselves to areas of young CREs (α > −0.65; I ν ∝ ν α ), the relation becomes almost linear at both frequencies with a ≈ 0.9 and a reduced scatter of σ = 0.2 dex. We then simulate the effect of CRE transport by convolving the hybrid Σ SFR maps with a Gaussian kernel until the RC-SFR relation is linearised; CRE transport lengths are l = 1-5 kpc. Solving the CRE diffusion equation, assuming dominance of the synchrotron and inverse-Compton losses, we find diffusion coefficients of D = (0.13-1.5) × 10 28 cm 2 s −1 at 1 GeV. Conclusions. A RC-SFR relation at 1.4 GHz can be exploited to measure SFRs at redshift z ≈ 10 using 140 MHz observations.

The circumgalactic medium (CGM) of nearby star-forming galaxies shows clear indications of O VI absorption accompanied by little to no detectable N V absorption. This unusual spectral signature, accompanied by highly non-uniform absorption from lower ionization state species, indicates that the CGM must be viewed as a dynamic, multiphase medium, such as occurs in the presence of turbulence. Motivated by previous isotropic turbulent simulations, we carry out chemodynamical simulations of stratified media in a Navarro-Frenk-White (NFW) gravitational potential with a total mass of 10 12 M and turbulence that decreases radially. The simulations assume a metallicity of 0.3 Z , a redshift zero metagalatic UV background, and they track ionizations, recombinations, and species-by-species radiative cooling using the MAIHEM package. We compare a suite of ionic column densities with the COS-Halos sample of low-redshift star-forming galaxies. Turbulence with an average onedimensional velocity dispersion ≈ 40 km s −1 , corresponding to an energy injection rate of ≈ 4 × 10 49 erg yr −1 , produces a CGM that matches many of the observed ionic column densities and ratios. In this simulation, the N N V /N O VI ratio is suppressed from its equilibrium value due to a combination of radiative cooling and cooling from turbulent mixing. This level of turbulence is consistent with expectations from observations of better constrained, highermass systems, and could be sustained by energy input from supernovae, gas inflows, and dynamical friction from dark matter subhalos. We also conduct a higher resolution ≈ 40 km s −1 run which yields smaller-scale structures, but remains in agreement with observations.

Single-phase photoionization equilibrium (PIE) models are often used to infer the underlying physical properties of galaxy halos probed in absorption with ions at different ionization potentials. To incorporate the effects of turbulence, we use the MAIHEM code to model an isotropic turbulent medium exposed to a redshift zero metagalactic UV background, while tracking the ionizations, recombinations, and species-by-species radiative cooling for a wide range of ions. By comparing observations and simulations over a wide range of turbulent velocities, densities, and metallicity with a Markov chain Monte Carlo technique, we find that MAIHEM models provide an equally good fit to the observed low-ionization species compared to PIE models, while reproducing at the same time high-ionization species such as Si IV and O VI. By including multiple phases, MAIHEM models favor a higher metallicity (Z/Z ≈ 40%) for the circumgalactic medium compared to PIE models. Furthermore, all of the solutions require some amount of turbulence (σ 3D 26 km s −1 ). Correlations between turbulence, metallicity, column density, and impact parameter are discussed alongside mechanisms that drive turbulence within the halo.

Absorption-line measurements of the circumgalactic medium (CGM) display a highly nonuniform distribution of lower ionization state species accompanied by more widespread higher ionization state material. This suggests that the CGM is a dynamic, multiphase medium, such as arises in the presence of turbulence. To better understand this evolution, we perform hydrodynamic and magnetohydrodynamic (MHD) simulations of the CGM surrounding Milky Way–like galaxies. In both cases, the CGM is initially in hydrostatic balance in a 1012 M ⊙ dark matter gravitational potential, and the simulations include rotation in the inner halo and turbulence that decreases radially. They also track ionizations, recombinations, and species-by-species radiative cooling in the presence of the redshift-zero UV background, employing the MAIHEM nonequilibrium chemistry package. We find that after 9 Gyr of evolution, the presence of a magnetic field leads to an overall hotter CGM, with cool gas in the center where magnetic pressure dominates. While the non-MHD run produces more cold clouds overall, we find similar Si iv/O vi and N v/O vi ratios between the MHD and non-MHD runs, which are both very different from their equilibrium values. The non-MHD halo develops cool, low angular momentum filaments above the central disk, in comparison to the MHD run that has more efficient angular momentum transport, especially for the cold gas, which forms a more ordered and extended disk late into its evolution.

The circumgalactic medium (CGM) of nearby star-forming galaxies shows clear indications of O vi absorption accompanied by little to no detectable N v absorption. This unusual spectral signature, accompanied by highly nonuniform absorption from lower-ionization-state species, indicates that the CGM must be viewed as a dynamic, multiphase medium, such as occurs in the presence of turbulence. Motivated by previous isotropic turbulent simulations, we carry out chemodynamical simulations of stratified media in a Navarro–Frenk–White (NFW) gravitational potential with a total mass of 1012 M ⊙ and turbulence that decreases radially. The simulations assume a metallicity of 0.3 Z ⊙ and a redshift-zero metagalatic UV background, and they track ionizations, recombinations, and species-by-species radiative cooling using the MAIHEM package. We compare a suite of ionic column densities with the COS-Halos sample of low-redshift star-forming galaxies. Turbulence with an average one-dimensional velocity dispersion of ≈40 km s−1, corresponding to an energy injection rate of ≈4 × 1049 erg yr−1, produces a CGM that matches many of the observed ionic column densities and ratios. In this simulation, the N N V /N O VI ratio is suppressed from its equilibrium value due to a combination of radiative cooling and cooling from turbulent mixing. This level of turbulence is consistent with expectations from observations of better constrained, higher-mass systems and could be sustained by energy input from supernovae, gas inflows, and dynamical friction from dark matter subhalos. We also conduct a higher resolution ≈40 km s−1 run, which yields smaller-scale structures but remains in agreement with observations.