Abstract
(Abrigded) Observations of galaxies up to z 2 show a tight correlation between far-infrared and radio continuum emission. We explain the far-infrared - radio continuum correlation by relating star formation and magnetic field strength in terms of turbulent magnetic field amplification, where turbulence is injected by supernova explosions from massive stars. We calculate the expected amount of turbulence in galaxies based on their star formation rates, and infer the expected magnetic field strength due to turbulent dynamo amplification. We estimate the timescales for cosmic ray energy losses via synchrotron emission, inverse Compton scattering, ionization and bremsstrahlung emission, probing up to which redshift strong synchrotron emission can be maintained. We find that the correlation between star formation rate and magnetic field strength in the local Universe can be understood as a result of turbulent magnetic field amplification. If the typical gas density in the interstellar medium increases at high z, we expect an increase of the magnetic field strength and the radio emission, as indicated by current observations. Such an increase would imply a modification of the far-infrared - radio correlation. We expect a breakdown when inverse Compton losses start dominating over synchrotron emission. For a given star formation surface density, we calculate the redshift where the breakdown occurs, yielding z (Sigma_SFR/0.0045 M_solar kpc^{-2} yr^{-1})^{1/(6-alpha/2)}. In this relation, the parameter \alpha describes the evolution of the characteristic ISM density in galaxies as (1+z)^\alpha. Both the possible raise of the radio emission at high redshift and the final breakdown of the far-infrared -- radio correlation at a critical redshift will be probed by the Square Kilometre Array (SKA) and its pathfinders, while the typical ISM density in galaxies will be probed with ALMA.
Highlights
While non-thermal radio emission arises due to synchrotron emission of cosmic ray electrons in the interstellar magnetic fields, far-infrared radiation is generated by dust grains heated by UV radiation from massive stars, which typically dominate the Lyman continuum luminosity
We explain the far-infrared – radio continuum correlation by relating star formation and magnetic field strength in terms of turbulent magnetic field amplification, where turbulence is injected by supernova explosions from massive stars
Both the possible raise of the radio emission at high redshift and the final breakdown of the far-infrared – radio correlation at a critical redshift will be probed by the Square Kilometre Array (SKA) and its pathfinders, while the typical interstellar medium (ISM) density in galaxies will be probed with ALMA
Summary
While non-thermal radio emission arises due to synchrotron emission of cosmic ray electrons in the interstellar magnetic fields, far-infrared radiation is generated by dust grains heated by UV radiation from massive stars, which typically dominate the Lyman continuum luminosity. In order to explore whether the far-infrared – radio correlation will hold on an approximate level, we calculate the timescales of the characteristic energy losses of the cosmic ray electrons, assuming that the correlation is only established when synchrotron emission yields the shortest timescale Based on this assumption, we derive a critical magnetic field strength which is required for efficient synchrotron emission at a given redshift, corresponding to a critical star formation rate in our model. With a typical synchrotron spectral index αsyn ∼ 0.9, this ratio would scale as Σ0S.F3R, implying a dependence on the star formation rate, similar to that of the magnetic field (18), and a non-linear far-infrared – radio correlation, as claimed already by Niklas & Beck (1997). Based on a comparison of the different energy loss timescales, we assess when such a correlation is expected to break down
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