Calibrating the relation of low-frequency radio continuum to star formation rate at 1 kpc scale with LOFAR

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 kpc² 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) × 10²⁸ cm² 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.

Radio continuum flux densities and fits files are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/622/A8