The VLA Frontier Field Survey: A Comparison of the Radio and UV/Optical Size of 0.3 ≲ z ≲ 3 Star-forming Galaxies

o 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 ≲ z ≲ 3 with a median stellar mass of $\mathrm{log}({M}_{\star }/{M}_{\odot })\approx 10.4$. 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: MACS J0416.1−2403, MACS J0717.5+3745, and MACS J1149.5+2223. Radio continuum sizes are derived from 3 and 6 GHz radio images (≲0farcs6 resolution, ≈0.9 μJy 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 Advanced Camera for Surveys and Wide Field Camera 3 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 $\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 10$, we find that the radio/UV/optical emission tends to be more compact in galaxies with high star formation rates (≳100 M⊙ 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⋆/M⊙) > 10 increases by a factor of 1.5–2 from z ≈ 3 to z ≈ 0.3, 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 ≲ z ≲ 3 tend to harbor centrally enhanced star formation activity relative to their outer disks.