Unifying X-ray Scaling Relations from Galaxies to Clusters
  We examine a sample of $\sim 250 000$ "locally brightest galaxies" selected
from the Sloan Digital Sky Survey to be central galaxies within their dark
matter halos. These were previously stacked by the Planck Collaboration to
measure the Sunyaev-Zel'dovich signal as a function of central galaxy stellar
mass. Here, we stack the X-ray emission from these halos using data from the
ROSAT All-Sky Survey. We detect emission across almost our entire sample,
including emission which we attribute to hot gas around galaxies spanning a
range of 1.2 dex in stellar mass (corresponding to nearly two orders of
magnitude in halo mass) down to $M* = 10^{10.8} M_{\odot}$ ($M_{500} \approx
10^{12.6} M_{\odot}$). Over this range, the X-ray luminosity can be fit by a
power-law, either of stellar mass or of halo mass. A single unified scaling
relation between mass and $L_X$ applies for galaxies, groups, and clusters.
This relation has a steeper slope than expected for self-similarity, in
contrast to the $Y_{SZ}$-$M_{500}$ relation, showing the importance of
non-gravitational heating. If this heating is predominantly due to AGN
feedback, the lack of a break in our relation suggests that AGN feedback is
tightly self-regulated and fairly gentle, in agreement with recent
high-resolution simulations. Our results are consistent with earlier
measurements of the $L_X$-$L_K$ relation for elliptical galaxies and of the
$L_X$-$M_{500}$ relation for optically-selected galaxy clusters. However, our
$L_X$-$M_{500}$ relation lies more than a factor of two below most previous
relations based on X-ray-selected cluster samples. We argue that optical
selection offers a less biased view of the $L_X$-$M_{500}$ relation.
