Two conditions for galaxy quenching: Compact centres and massive haloes

We investigate the roles of two classes of quenching mechanisms for central and satellite galaxies in the Sloan Digital Sky Survey (z < 0.075): those involving the halo and those involving the formation of a compact centre. For central galaxies with inner compactness Σ_{1 kpc} ~ 10^9-9.4M_⊙ kpc^-2, the quenched fraction f_q is strongly correlated with Σ_{1 kpc} with only weak halo mass M_h dependence. However, at higher and lower Σ_{1 kpc}, specific star formation rate (sSFR) is a strong function of M_h and mostly independent of Σ_{1 kpc}. In other words, Σ_{1 kpc} ~ 10^9-9.4M_⊙ kpc^-2 divides galaxies into those with high sSFR below and low sSFR above this range. In both the upper and lower regimes, increasing M_h shifts the entire sSFR distribution to lower sSFR without a qualitative change in shape. This is true even at fixed M_*, but varying M_* at fixed M_h adds no quenching information. Most of the quenched centrals with M_h > 1011.8M_⊙ are dense (Σ_{1 kpc} > 10⁹M_⊙ kpc^-2), suggesting compaction-related quenching maintained by halo-related quenching. However, 21 per cent are diffuse, indicating only halo quenching. For satellite galaxies in the outskirts of haloes, quenching is a strong function of compactness and a weak function of host M_h. In the inner halo, M_h dominates quenching, with ~90 per cent of the satellites being quenched once M_h > 1013M_⊙. 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.