The VLA Frontier Field Survey: A Comparison of the Radio and UV/optical
  size of $0.3 \lesssim z \lesssim 3$ star-forming galaxies
  To investigate the growth history of galaxies, we measure the rest-frame
radio, ultraviolet (UV), and optical sizes of 98 radio-selected, star-forming
galaxies (SFGs) distributed over $0.3 \lesssim z \lesssim 3$ and median stellar
mass of $\log(M_\star/ \rm M_\odot)\approx10.4$. We compare the size of galaxy
stellar disks, traced by rest-frame optical emission, relative to the overall
extent of star formation activity that is traced by radio continuum emission.
Galaxies in our sample are identified in three Hubble Frontier Fields:
MACSJ0416.1$-$2403, MACSJ0717.5+3745, and MACSJ1149.5+2223. Radio continuum
sizes are derived from 3 GHz and 6 GHz radio images ($\lesssim 0$''$.6$
resolution, $\approx0.9\, \rm \mu Jy\, beam^{-1}$ noise level) from the Karl G.
Jansky Very Large Array. Rest-frame UV and optical sizes are derived using
observations from the Hubble Space Telescope and the ACS and WFC3 instruments.
We find no clear dependence between the 3 GHz radio size and stellar mass of
SFGs, which contrasts with the positive correlation between the UV/optical size
and stellar mass of galaxies. Focusing on SFGs with $\log(M_\star/\rm
M_\odot)>10$, we find that the radio/UV/optical emission tends to be more
compact in galaxies with high star-formation rates ($\rm SFR\gtrsim
100\,M_\odot\,yr^{-1}$), suggesting that a central, compact starburst (and/or
an Active Galactic Nucleus) resides in the most luminous galaxies of our
sample. We also find that the physical radio/UV/optical size of radio-selected
SFGs with $\log(M_\star/\rm M_\odot)>10$ increases by a factor of $1.5-2$ from
$z\approx 3$ to $z\approx0.3$, yet the radio emission remains two-to-three
times more compact than that from the UV/optical. These findings indicate that
these massive, {radio-selected} SFGs at $0.3 \lesssim z \lesssim 3$ tend to
harbor centrally enhanced star formation activity relative to their
outer-disks.
