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

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 (up to $\sim$\,200\,$h^{-1}$\,kpc), where close galaxy-galaxy interactions are not dominant. We apply our selection criteria to two volume-limited samples of galaxies from SDSS DR6 with $M_{r}-5 \log_{10} h \leq$ -19 and -20 to study the effects of the environment of very sparse groups on galaxy colour. For satellite galaxies in a group of two, we find a red excess attributed to star formation quenching of 0.15\,$\pm$\,0.01 and 0.14\,$\pm$\,0.01 for the -19 and -20 samples, respectively, relative to isolated galaxies of the same stellar mass. Assuming N=1 systems are the progenitors of N=2 systems, 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 in agreement with the observations. The observations also reveal that central galaxies in a group of two have a slight blue excess of 0.06\,$\pm$\,0.02 and 0.02\,$\pm$\,0.01 for the -19 and -20 samples, respectively, relative to N=1 populations of the same stellar mass. Our results demonstrate that even the environment of very sparse groups of luminous galaxies influence galaxy evolution and in-depth studies of these simple systems are an essential step towards understanding galaxy evolution in general.