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

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 ( 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 μ m 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.