A weak gravitational lensing recalibration of the scaling relations
  linking the gas properties of dark halos to their mass
  We use weak gravitational lensing to measure mean mass profiles around
Locally Brightest Galaxies (LBGs). These are selected from the SDSS/DR7
spectroscopic and photometric catalogues to be brighter than any neighbour
projected within 1.0 Mpc and differing in redshift by $<1000$ km/s. Most ($>
83\%$) are expected to be the central galaxies of their dark matter halos.
Previous stacking analyses have used this LBG sample to measure mean
Sunyaev-Zeldovich flux and mean X-ray luminosity as a function of LBG stellar
mass. In both cases, a simulation of the formation of the galaxy population was
used to estimate effective halo mass for LBGs of given stellar mass, allowing
the derivation of scaling relations between the gas properties of halos and
their mass. By comparing results from a variety of simulations to our lensing
data, we show that this procedure has significant model dependence reflecting:
(i) the failure of any given simulation to reproduce observed galaxy abundances
exactly; (ii) a dependence on the cosmology underlying the simulation; and
(iii) a dependence on the details of how galaxies populate halos. We use our
lensing results to recalibrate the scaling relations, eliminating most of this
model dependence and explicitly accounting both for residual modelling
uncertainties and for observational uncertainties in the lensing results. The
resulting scaling relations link the mean gas properties of dark halos to their
mass over an unprecedentedly wide range, $10^{12.5}<M_{500}/
\mathrm{M_\odot}<10^{14.5}$, and should fairly and robustly represent the full
halo population.
