We study the equilibrium structures of white dwarfs with dark matter cores formed by non-self-annihilating dark matter DM particles with mass ranging from 1 GeV to 100 GeV, which are assumed to form an ideal degenerate Fermi gas inside the stars. For DM particles of mass 10 GeV and 100 GeV, we find that stable stellar models exist only if the mass of the DM core inside the star is less than O(10^-3) Msun and O(10^-6) Msun, respectively. The global properties of these stars, and in particular the corresponding Chandrasekhar mass limits, are essentially the same as those of traditional white dwarf models without DM. Nevertheless, in the 10 GeV case, the gravitational attraction of the DM core is strong enough to squeeze the normal matter in the core region to densities above neutron drip, far above those in traditional white dwarfs. For DM with particle mass 1 GeV, the DM core inside the star can be as massive as around 0.1 Msun and affects the global structure of the star significantly. In this case, the radius of a stellar model with DM can be about two times smaller than that of a traditional white dwarf. Furthermore, the Chandrasekhar mass limit can also be decreased by as much as 40%. Our results may have implications on to what extent type Ia supernovae can be regarded as standard candles - a key assumption in the discovery of dark energy.
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