  We estimate minimum energy magnetic fields (B_min) for a sample of galaxies
with measured gas surface densities, spanning from normal spirals to
starbursts. We show that the ratio of the minimum energy magnetic pressure to
the total pressure in the ISM decreases substantially with increasing surface
density; for Arp 220 this ratio is ~10^-4. Therefore, if the minimum energy
estimate is applicable, magnetic fields in starbursts are dynamically weak
compared to gravity, in contrast to normal spiral galaxies. We argue, however,
that rapid cooling of relativistic electrons in starbursts invalidates the
minimum energy estimate. We critically assess a number of independent
constraints on the magnetic field strength in starbursts. In particular, we
argue that the existence of the FIR-radio correlation implies that the
synchrotron cooling timescale for cosmic ray electrons is much shorter than
their escape time from the galactic disk; this in turn implies that the true
magnetic field in starbursts is significantly larger than B_min. The strongest
argument against such large fields is that one might expect starbursts to have
steep radio spectra indicative of strong synchrotron cooling, which is not
observed. We show, however, that ionization and bremsstrahlung losses can
flatten the nonthermal spectra of starburst galaxies even in the presence of
rapid cooling, providing much better agreement with observed spectra. We
further demonstrate that ionization and bremsstrahlung losses are likely to be
important in shaping the radio spectra of most starbursts at GHz frequencies,
thereby preserving the linearity of the FIR-radio correlation. We thus conclude
that magnetic fields in starbursts are significantly larger than B_min. We
highlight several observations that can test this conclusion.
