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

¹ University of Hamburg, Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
e-mail: volker.heesen@hs.uni-hamburg.de
² School of Earth and Space Exploration, Arizona State University, PO Box 871404 Tempe, AZ, 85287-1404 USA
³ Fakultät für Physik, Universität Bielefeld, Postfach 100131 33501 Bielefeld, Germany
⁴ Max-Planck-Institute für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁵ School of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, AL10 9AB UK
⁶ Chalmers University of Technology, Dept. of Space, Earth and Environment, Onsala Space Observatory, 439 92 Onsala, Sweden
⁷ Astronomisches Institut der Ruhr-Universität Bochum, 44780 Bochum, Germany
⁸ Astronomical Observatory, Jagiellonian University, ul. Orla 171, 30-244 Kraków, Poland
⁹ SUPA, Institute for Astronomy, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ UK
¹⁰ CSIRO Astronomy and Space Science, PO Box 1130 Bentley, WA, 6102 Australia
¹¹ INAF/Istituto di Radioastronomia, via Gobetti 101, 40129 Bologna, Italy

Received: 19 July 2018
Accepted: 15 October 2018

Abstract

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.