Using the Sloan Digital Sky Survey, we adopt the sSFR-$Sigma_{1kpc}$ diagram as a diagnostic tool to understand quenching in different environments. sSFR is the specific star formation rate, and $Sigma_{1kpc}$ is the stellar surface density in the inner kpc. Although both the host halo mass and group-centric distance affect the satellite population, we find that these can be characterised by a single number, the quenched fraction, such that key features of the sSFR-$Sigma_{1kpc}$ diagram vary smoothly with this proxy for the environment. Particularly, the sSFR of star-forming galaxies decreases smoothly with this quenched fraction, the sSFR of satellites being 0.1 dex lower than in the field. Furthermore, $Sigma_{1kpc}$ of the transition galaxies (i.e., the green valley or GV) decreases smoothly with the environment, by as much as 0.2 dex for $M_* = 10^{9.75-10} M_{odot}$ from the field, and decreasing for satellites in larger halos and at smaller radial distances within same-mass halos. We interpret this shift as indicating the relative importance of todays field quenching track vs. the cluster quenching track. These environmental effects in the sSFR-$Sigma_{1kpc}$ diagram are most significant in our lowest mass range ($9.75 < log M_{*}/M_{odot} < 10$). One feature that is shared between all environments is that at a given $M_{*}$ quenched galaxies have about 0.2-0.3 dex higher $Sigma_{1kpc}$ than the star-forming population. These results indicate that either $Sigma_{1kpc}$ increases (subsequent to satellite quenching), or $Sigma_{1kpc}$ for individual galaxies remains unchanged, but the original $M_*$ or the time of quenching is significantly different from those now in the GV.
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