  The infrared-radio correlation (IRRC) of star-forming galaxies can be used to
estimate their star formation rate (SFR) based on the radio continuum
luminosity at MHz-GHz frequencies. For its application in future deep radio
surveys, it is crucial to know whether the IRRC persists at high redshift z.
Previous works have reported that the 1.4 GHz IRRC correlation of star-forming
galaxies is nearly z-invariant up to z=4, but depends strongly on stellar mass
M. This should be taken into account for SFR calibrations based on radio
luminosity. To understand the physical cause behind the M dependence of the
IRRC and its properties at higher z, we constructed a phenomenological model
for galactic radio emission. Our model is based on a dynamo-generated magnetic
field and a steady-state cosmic ray population. It includes a number of free
parameters as well as observed scaling relations. We find that the resulting
spread of the infrared-to-radio luminosity ratio, q(z, M), with respect to M is
mostly determined by the scaling of the galactic radius with M, while the
absolute value of the q(z, M) curves decreases with more efficient conversion
of supernova energy to magnetic fields and cosmic rays. Decreasing the slope of
the cosmic ray injection spectrum, aCR, results in higher radio luminosity,
decreasing the absolute values of the q(z, M) curves. Our model reproduces the
observed dependence of the IRRC on M and z when the efficiency of
supernova-driven turbulence is 5%, 10% of the kinetic energy is converted into
magnetic energy, and aCR = 3. For galaxies with intermediate to high M
(10^9.5-10^11 M_sun), our model results in an IRRC that is nearly independent
of z. For galaxies with lower M (M=10^8.5 M_sun), we find that the IR-to-radio
flux ratio increases with increasing redshift. This matches the observational
data in that mass bin which currently, however, only extends to z~1.5.
