  We have compiled a large sample of isolated central galaxies from the Sloan
Digital Sky Survey, which do not have a neighbour of comparable brightness
within a projected distance of 1 Mpc. We use the colours, luminosities and
surface brightnesses of satellite galaxies in the vicinity of these objects to
estimate their atomic gas content and to derive the average total mass of HI
gas contained in satellites as a function of projected radius from the primary.
Recent calibrations of merging timescales from N-body simulations are used to
estimate the rate at which this gas will accrete onto the primaries. Our
estimated accretion rates fall short of those needed to maintain the observed
level of star formation in these systems by nearly two orders of magnitude.
Nevertheless, there are strong correlations between the total mass of gas in
satellites and the colours and specific star formation rates of central
galaxies of all stellar masses. The correlations are much weaker if we consider
the total stellar mass in the satellites, rather than their total gas mass. We
ask why star formation in the central galaxies should be correlated with gas
contained in satellites at projected separations of a Mpc or more, well outside
the virial radius of the dark matter halos of these systems. We suggest that
gas-rich satellites trace an underlying reservoir of ionized gas that is
accreted continuously, and that provides the fuel for ongoing star formation in
galaxies in the local Universe.
