We use galaxy-galaxy lensing to study the dark matter halos surrounding a sample of Locally Brightest Galaxies (LBGs) selected from the Sloan Digital Sky Survey. We measure mean halo mass as a function of the stellar mass and colour of the central galaxy. Mock catalogues constructed from semi-analytic galaxy formation simulations demonstrate that most LBGs are the central objects of their halos, greatly reducing interpretation uncertainties due to satellite contributions to the lensing signal. Over the full stellar mass range, $10.3 < log [M_*/M_odot] < 11.6$, we find that passive central galaxies have halos that are at least twice as massive as those of star-forming objects of the same stellar mass. The significance of this effect exceeds $3sigma$ for $log [M_*/M_odot] > 10.7$. Tests using the mock catalogues and on the data themselves clarify the effects of LBG selection and show that it cannot artificially induce a systematic dependence of halo mass on LBG colour. The bimodality in halo mass at fixed stellar mass is reproduced by the astrophysical model underlying our mock catalogue, but the sign of the effect is inconsistent with recent, nearly parameter-free age-matching models. The sign and magnitude of the effect can, however, be reproduced by halo occupation distribution models with a simple (few-parameter) prescription for type-dependence.
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