Groups of two galaxies in SDSS: implications of colours on star formation quenching time-scales

(Abrigded) Using hybrid N-body/semi-analytic substructure simulations, we have devised a method to select galaxies that are isolated in their dark matter halo (N=1 systems) and galaxies that reside in a group of exactly two (N=2 systems). Our N=2 systems are widely-separated with comoving projected separations up to ~200 h^-1 kpc, where close galaxy-galaxy interactions are not the dominant physical process at work. We apply our selection criteria to two volume-limited sample of galaxies from the NYU VAGC based on SDSS DR6 with M_r-5log_10 h < -19 and -20. The effects of a simple change in environment on star formation properties are isolated by correcting the populations for contamination by systems in richer environments and by eliminating differences in stellar mass. For satellite galaxies in groups of two, we find a red excess of 0.15 +/- 0.01 and 0.14 +/- 0.01 for the -19 and -20 samples, respectively, relative to isolated galaxies of like stellar mass. A simple galaxy formation model that assumes (1) N=1 galaxies are the progenitors of N=2 galaxies in a statistical sense and (2) cold gas is instantaneously and completely removed from an infalling satellite galaxy immediately upon accretion into another halo predicts a red excess of 0.62 +/- 0.01 and 0.54 +/- 0.01 for the -19 and -20 samples, respectively. Thus, an immediate-rapid star formation quenching scenario is inconsistent with these observations. A delayed-then-rapid star formation quenching scenario with a delay time of 3.3 and 3.7 Gyr for the -19 and -20 samples, respectively, yields a red excess prediction that agrees with the observations.