{Star-forming dwarf galaxies: the correlation between far-infrared and radio fluxes}

The correlation between far-infrared and radio fluxes connects star formation and magnetic fields in galaxies and has been confirmed over a wide range in luminosities in the far-infrared to radio domain, both in the local Universe and even at redshifts of z ~ 2. Recent investigations have indicated that it may even hold in the regime of local dwarf galaxies, and we therefore explore here the expected behavior in the regime of star formation surface densities below 0.1 M⊙ kpc-2 yr-1. We derive two conditions that can be particularly relevant for inducing a change in the expected correlation: a critical star formation surface density to maintain the correlation between star formation rate and the magnetic field, and a critical star formation surface density below which cosmic-ray diffusion losses dominate their injection through supernova explosions. For rotation periods shorter than 1.5 × 107(H/ kpc)2 yr, with H the scale height of the disk, the first correlation will break down before diffusion losses are relevant because higher star formation rates are required to maintain the correlation between star formation rate and magnetic field strength. For high star formation surface densities ΣSFR, we derive a characteristic scaling of the nonthermal radio to the far-infrared and infrared emission with ΣSFR1/3 , corresponding to a scaling of the nonthermal radio luminosity Ls with the infrared luminosity Lth as Lth4/3 . The latter is expected to change when the above processes are no longer steadily maintained. In the regime of long rotation periods, we expect a transition toward a steeper scaling with ΣSFR2/3, implying Ls ∝ Lth5/3 , while the regime of fast rotation is expected to show a considerably enhanced scatter because a well-defined relation between star formation and magnetic field strength is not maintained. The scaling relations above explain the increasing thermal fraction of the radio emission observed within local dwarfs and can be tested with future observations by LOFAR as well as the Square Kilometer Array (SKA) and its precursor radio telescopes.