We use a hybrid approach that combines high-resolution simulations of the formation of a Milky Way-like halo with a semi-analytic model of galaxy formation to study the mass content of dwarf galaxies in the concordance $Lambda$CDM cosmology. We find that the mass within 600 pc of dark matter haloes hosting luminous satellites has a median value of $sim 3.2times 10^7$ Msun with very little object-to-object scatter. In contrast, the present day total luminosities of the model satellites span nearly five orders of magnitude. These findings are in very good agreement with the results recently reported in the literature for the dwarf spheroidal galaxies of the Milky Way. In our model, dwarf irregular galaxies like the Small Magellanic Cloud, are predicted to have similar or slightly larger dark matter mass within 600 pc.
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