We examine the star formation properties of bright (~0.1 L*) satellites around isolated ~L* hosts in the local Universe using spectroscopically confirmed systems in the Sloan Digital Sky Survey DR7. Our selection method is carefully designed with the aid of N-body simulations to avoid groups and clusters. We find that satellites are significantly more likely to be quenched than a stellar mass-matched sample of isolated galaxies. Remarkably, this quenching occurs only for satellites of hosts that are themselves quenched: while star formation is unaffected in the satellites of star-forming hosts, satellites around quiescent hosts are more than twice as likely to be quenched than stellar-mass matched field samples. One implication of this is that whatever shuts down star formation in isolated, passive L* galaxies also plays at least an indirect role in quenching star formation in their bright satellites. The previously-reported tendency for "galactic conformity" in color/morphology may be a by-product of this host-specific quenching dichotomy. The S��rsic indices of quenched satellites are statistically identical to those of field galaxies with the same specific star formation rates, suggesting that environmental and secular quenching give rise to the same morphological structure. By studying the distribution of pairwise velocities between the hosts and satellites, we find dynamical evidence that passive host galaxies reside in dark matter halos that are ~45% more massive than those of star-forming host galaxies of the same stellar mass. We emphasize that even around passive hosts, the mere fact that galaxies become satellites does not typically result in star formation quenching: we find that only ~30% of ~0.1 L* galaxies that fall in from the field are quenched around passive hosts, compared with ~0% around star forming hosts.

14 pages, 9 figures