  Due to ram-pressure stripping, jellyfish galaxies are thought to lose large
amounts, if not all, of their interstellar medium. Nevertheless, some, but not
all, observations suggest that jellyfish galaxies exhibit enhanced star
formation compared to control samples, even in their ram pressure-stripped
tails. We use the TNG50 cosmological gravity+magnetohydrodynamical simulation,
with an average spatial resolution of 50-200 pc in the star-forming regions of
galaxies, to quantify the star formation activity and rates (SFRs) of more than
700 jellyfish galaxies at $z=0-1$ with stellar masses
$10^{8.3-10.8}\,\mathrm{M}_\odot$ in hosts with mass
$10^{10.5-14.3}\,\mathrm{M}_\odot$. We extract their global SFRs, the SFRs
within their main stellar body vs. within the tails, and we follow the
evolution of the star formation along their individual evolutionary tracks. We
compare the findings for jellyfish galaxies to those of diversely-constructed
control samples, including against satellite and field galaxies with matched
redshift, stellar mass, gas fraction and host halo mass. According to TNG50,
star formation and ram-pressure stripping can indeed occur simultaneously
within any given galaxy, and frequently do so. Moreover, star formation can
also take place within the ram pressure-stripped tails, even though the latter
is typically subdominant. However, TNG50 does not predict elevated
population-wide SFRs in jellyfish compared to analog satellite galaxies with
the same stellar mass or gas fraction. Simulated jellyfish galaxies do undergo
bursts of elevated star formation along their history but, at least according
to TNG50, these do not translate into a population-wide enhancement at any
given epoch.
