Halo mass and assembly history exposed in the faint outskirts: the stellar and dark matter haloes of Illustris galaxies

We use the Illustris simulations to gain insight into the build-up of the outer, low-surface brightness regions which surround galaxies. We characterize the stellar haloes by means of the logarithmic slope of the spherically averaged stellar density profiles, alpha(STARS) at z = 0, and we relate these slopes to the properties of the underlying dark matter (DM) haloes, their central galaxies, and their assembly histories. We analyse a sample of similar to 5000 galaxies resolved with more than 5 x 10(4) particles each, and spanning a variety of morphologies and halo masses (3 x 10(11) <= M-vir less than or similar to 10(14) M-circle dot). We find a strong trend between stellar halo slope and total halo mass, where more massive objects have shallower stellar haloes than the less massive ones (-5.5 +/- 0.5 < alpha(STARS) < -3.5 +/- 0.2 in the studied mass range). At fixed halo mass, we show that disc-like, blue, young, and more massive galaxies are surrounded by significantly steeper stellar haloes than elliptical, red, older, and less massive galaxies. Overall, the stellar density profiles fall off much more steeply than the underlying DM, and no clear trend holds between stellar slope and DM halo concentration. However, DM haloes which formed more recently, or which accreted larger fractions of stellar mass from infalling satellites, exhibit shallower stellar haloes than their older analogues with similar masses, by up to Delta alpha(STARS) similar to 0.5-0.7. Our findings, combined with the most recent measurements of the strikingly different stellar power-law indices for M31 and the Milky Way, appear to favour a massive M31, and a Milky Way characterized by a much quieter accretion history over the past 10 Gyr than its companion.