摘要：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 (ΣSFR) 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 radioΣSFRmaps using the Condon relation. We compared these maps with hybridΣSFRmaps from a combination of GALEX far-ultraviolet andSpitzer24μm data using plots tracing the relation at the highest angular resolution allowed by our data at 1.2 × 1.2 kpc2resolution.Results.The RC emission is smoothed with respect to the hybridΣSFRowing to the transport of cosmic-ray electrons (CREs) away from star formation sites. This results in a sublinear relation (ΣSFR)RC ∝ [(ΣSFR)hyb]a, wherea = 0.59 ± 0.13 (140 MHz) anda = 0.75 ± 0.10 (1365 MHz). Both relations have a scatter ofσ = 0.3 dex. If we restrict ourselves to areas of young CREs (α > −0.65;Iν ∝ να), the relation becomes almost linear at both frequencies witha ≈ 0.9 and a reduced scatter ofσ = 0.2 dex. We then simulate the effect of CRE transport by convolving the hybridΣSFRmaps with a Gaussian kernel until the RC–SFR relation is linearised; CRE transport lengths arel = 1–5 kpc. Solving the CRE diffusion equation, assuming dominance of the synchrotron and inverse-Compton losses, we find diffusion coefficients ofD = (0.13–1.5) × 1028 cm2 s−1at 1 GeV.Conclusions.A RC–SFR relation at 1.4 GHz can be exploited to measure SFRs at redshiftz ≈ 10 using 140 MHz observations.
关键词：enradiation mechanisms: non-thermalcosmic raysgalaxies: magnetic fieldsgalaxies: star formationradio continuum: galaxies
