The far-infrared - radio correlation in dwarf galaxies
  The far-infrared - radio correlation connects star formation and magnetic
fields in galaxies, and has been confirmed over a large range of far-infrared
luminosities. Recent investigations indicate that it may even hold in the
regime of local dwarf galaxies, and we explore here the expected behavior in
the regime of star formation surface densities below 0.1 M_sun 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 over their injection via supernova
explosions. For rotation periods shorter than 1.5x10^7 (H/kpc)^2 yrs, with H
the scale height of the disk, the first correlation will break down before
diffusion losses are relevant, as higher star formation rates are required to
maintain the correlation between star formation rate and magnetic field
strength. For high star formation surface densities Sigma_SFR, we derive a
characteristic scaling of the non-thermal radio to the far-infrared / infrared
emission with Sigma_SFR^{1/3}, corresponding to a scaling of the non-thermal
radio luminosity L_s with the infrared luminosity L_{th} as L_{th}^{4/3}. 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
towards a steeper scaling with Sigma_SFR^{2/3}, implying L_s~L_th^{5/3}, while
the regime of fast rotation is expected to show a considerably enhanced
scatter. These scaling relations explain the increasing thermal fraction of the
radio emission observed within local dwarfs, and can be tested with future
observations by the SKA and its precursor radio telescopes.
