We investigate the roles of two classes of quenching mechanisms for central
and satellite galaxies in the SDSS (z<0.075): those involving the halo and
those involving the formation of a compact centre. For central galaxies with
inner compactness Ξ£1kpcββΌ109β9.4Mββkpcβ2,
the quenched fraction fqβ is strongly correlated with Ξ£1kpcβ
with only weak halo mass Mhβ dependence. However, at higher and lower
Ξ£1kpcβ, sSFR is a strong function of Mhβ and mostly
independent of Ξ£1kpcβ. In other words, Ξ£1kpcββΌ109β9.4Mββkpcβ2 divides galaxies into those with high sSFR
below and low sSFR above this range. In both the upper and lower regimes,
increasing Mhβ shifts the entire sSFR distribtuion to lower sSFR
without a qualitative change in shape. This is true even at fixed Mββ, but
varying Mββ at fixed Mhβ adds no quenching information. Most of the
quenched centrals with Mhβ>1011.8Mββ are dense (Ξ£1kpcβ>109Β Mββkpcβ2), suggesting compaction-related
quenching maintained by halo-related quenching. However, 21% are diffuse,
indicating only halo quenching. For satellite galaxies in the outskirts of
halos, quenching is a strong function of compactness and a weak function of
host Mhβ. In the inner halo, Mhβ dominates quenching, with
βΌ90% of the satellites being quenched once Mhβ>1013Mββ. This regional effect is greatest for the least massive
satellites. As demonstrated via semi-analytic modelling with simple
prescriptions for quenching, the observed correlations can be explained if
quenching due to central compactness is rapid while quenching due to halo mass
is slow.Comment: 16 pages, 11 figures, MNRAS accepte