Beyond halo mass: galactic conformity as a smoking gun of central galaxy assembly bias

Quenched central galaxies tend to reside in a preferentially quenched large-scale environment, a phenomenon that has been dubbed galactic conformity. Remarkably, this tendency persists out to scales far larger than the virial radius of the halo hosting the central. Therefore, conformity manifestly violates the widely adopted assumption that the dark matter halo mass M-vir exclusively governs galaxy occupation statistics. This paper is the first in a series studying the implications of the observed conformity signal for the galaxy-dark matter connection. We show that recent measurements of conformity on scales r similar to 1-5 Mpc imply that central galaxy quenching statistics cannot be correctly predicted with the knowledge of Mvir alone. We also demonstrate that ejected (or 'backsplash') satellites cannot give rise to the signal. We then invoke the age matching model, which is predicated on the co-evolution of galaxies and haloes. We find that this model produces a strong signal, and that central galaxies are solely responsible. We conclude that large-scale 'two-halo' conformity represents a smoking gun of central galaxy assembly bias, and indicates that contemporary models of satellite quenching have systematically overestimated the influence of post-infall processes.