We examine a sample of 250 000 'locally brightest galaxies' selected from the Sloan Digital Sky Survey to be central galaxies within their dark matter haloes. We stack the X-ray emission from these haloes, as a function of the stellar mass of the central galaxy, 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 (M 500 10 12.6 M ). Over this range, the X-ray luminosity can be fit by a power law, either of stellar mass or of halo mass. From this, we infer a single unified scaling relation between mass and L X which applies for galaxies, groups, and clusters. This relation has a slope steeper than expected for self-similarity, showing the importance of non-gravitational heating. Assuming this non-gravitational heating is predominately due to AGN feedback, the lack of a break in the relation shows that AGN feedback is tightly self-regulated and fairly gentle, in agreement with the predictions of recent high-resolution simulations. Our relation is consistent with established measurements of the L X -L K relation for elliptical galaxies as well as the L X -M 500 relation for optically selected galaxy clusters. However, our L X -M 500 relation has a normalization more than a factor of 2 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 for mass-selected clusters.
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