We have recently used the Faint Images of the Radio Sky at Twenty-centimeters (FIRST) survey to show that red quasars have fundamentally different radio properties to typical blue quasars: a significant (factor $sim3$) enhancement in the radio-detection fraction, which arises from systems around the radio-quiet threshold with compact ($<5$) radio morphologies. To gain greater insight into these physical differences, here we use the DR14 Sloan Digital Sky Survey (SDSS) and more sensitive, higher resolution radio data from the Very Large Array (VLA) Stripe 82 (S82) and VLA-COSMOS 3 GHz (C3GHz) surveys. With the S82 data, we perform morphological analyses at a resolution and depth three times that of the FIRST radio survey, and confirm an enhancement in radio-faint and compact red quasars over typical quasars; we now also find tentative evidence for an enhancement in red quasars with slightly extended radio structures ($16-43$ kpc at $z=1.5$). These analyses are complemented by C3GHz, which is deep enough to detect radio emission from star-formation processes. From our data we find that the radio enhancement from red quasars is due to AGN activity on compact scales ($< 43$ kpc) for radio-intermediate-radio-quiet sources ($-5<R<-3.4$, where $R=L_{1.4GHz}/L_{6 mu m}$), which decreases at $R<-5$ as the radio emission from star-formation starts to dilute the AGN component. Overall our results argue against a simple orientation scenario and are consistent with red quasars representing a younger, earlier phase in the overall evolution of quasars.
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