2019A&A...622A...8H

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 1kpc 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 1.2x1.2kpc² 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 (140MHz) and a=0.75±0.10 (1365MHz). Both relations have a scatter of σ=0.3dex. 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=0.2dex. 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=1-5kpc. Solving the CRE diffusion equation, assuming dominance of the synchrotron and inverse-Compton losses, we find diffusion coefficients of D=(0.13-1.5)x10²⁸cm²/s at 1GeV.
Conclusions. A RC-SFR relation at 1.4GHz can be exploited to measure SFRs at redshift z≥10 using 140MHz observations.