  Regardless of the formation mechanism, an exotic object, Double Degenerate
Star (DDS), is introduced and investigated, which is composed of baryonic
matter and some unknown fermion dark matter. Different from the simple White
Dwarfs (WDs), there are additional gravitational force provided by the unknown
fermion component inside DDSs, which may strongly affect the structure and the
stability of such kind of objects. Many possible and strange observational
phenomena connecting with them are concisely discussed. Similar to the normal
WD, this object can also experience thermonuclear explosion as type Ia
supernova explosion when DDS's mass exceeds the maximum mass that can be
supported by electron degeneracy pressure. However, since the total mass of
baryonic matter can be much lower than that of WD at Chandrasekhar mass limit,
the peak luminosity should be much dimmer than what we expect before, which may
throw a slight shadow on the standard candle of SNIa in the research of
cosmology.
