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Observed kinematical data of 40 Local Group (LG) members are used to derivethe dark matter halo mass of such galaxies. Haloes are selected from thetheoretically expected LG mass function and two different density profiles areassumed, a standard universal cuspy model and a mass dependent profile whichaccounts for the effects of baryons in modifying the dark matter distributionwithin galaxies. The resulting relations between stellar and halo mass arecompared with expectations from abundance matching.  Using a universal cuspy profile, the ensemble of LG galaxies is fit inrelatively low mass haloes, leaving "dark" many massive haloes of\mhalo$\gtrsim$10$^{10}$\msun: this reflects the "too big to fail" problem andresults in a \mstar-\mhalo\ relation that differs from abundance matchingpredictions. Moreover, the star formation efficiency of isolated LG galaxiesincreases with decreasing halo mass when adopting a cuspy model. By contrast,using the mass dependent density profile, dwarf galaxies with\mstar$\gtrsim$10$^{6}$\msun are assigned to more massive haloes, which have acentral cored distribution of dark matter: the "too big to fail" problem isalleviated, the resultant \mstar-\mhalo\ relation follows abundance matchingpredictions down to the completeness limit of current surveys, and the starformation efficiency of isolated members decreases with decreasing halo mass,in agreement with theoretical expectations.  Finally, the cusp/core space of LG galaxies is presented, providing aframework to understand the non-universality of their density profiles.

Expanded haloes, abundance matching and too-big-to-fail in the Local Group