We investigate how star formation quenching proceeds within central and satellite galaxies using spatially resolved spectroscopy from the SDSS-IV MaNGA DR15. We adopt a complete sample of star formation rate surface densities ($Sigma_{rm SFR}$), derived in Bluck et al. (2020), to compute the distance at which each spaxel resides from the resolved star forming main sequence ($Sigma_{rm SFR} - Sigma_*$ relation): $Delta Sigma_{rm SFR}$. We study galaxy radial profiles in $Delta Sigma_{rm SFR}$, and luminosity weighted stellar age (${rm Age_L}$), split by a variety of intrinsic and environmental parameters. Via several statistical analyses, we establish that the quenching of central galaxies is governed by intrinsic parameters, with central velocity dispersion ($sigma_c$) being the most important single parameter. High mass satellites quench in a very similar manner to centrals. Conversely, low mass satellite quenching is governed primarily by environmental parameters, with local galaxy over-density ($delta_5$) being the most important single parameter. Utilising the empirical $M_{BH}$ - $sigma_c$ relation, we estimate that quenching via AGN feedback must occur at $M_{BH} geq 10^{6.5-7.5} M_{odot}$, and is marked by steeply rising $Delta Sigma_{rm SFR}$ radial profiles in the green valley, indicating `inside-out quenching. On the other hand, environmental quenching occurs at over-densities of 10 - 30 times the average galaxy density at z$sim$0.1, and is marked by steeply declining $Delta Sigma_{rm SFR}$ profiles, indicating `outside-in quenching. Finally, through an analysis of stellar metallicities, we conclude that both intrinsic and environmental quenching must incorporate significant starvation of gas supply.
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