I discovered the object "Dark Matter Dominated Neutron Star" (DDNS) which is a neutron star like core made of ordinary and dark matter. Outside the core it contains an extensive dark matter envelope. This object break the universal relation of scaled moment of inertia, which is valid in a neutron star with pure ordinary matter.

The effective gravity is larger due to dark matter, the effective Chandrasekhar mass of the star is lower. A drop of the Chandrasekhar mass by ~40% is found for the admixture with 1 GeV dark matter particles. The lowered Chandrasekhar mass will affect its explosion as Type Ia supernova.

Some neutron stars in binary system are found with an exceptionally low mass. Such low mass can be marginally explained by the standard stellar evolutionary models. We show that a lower mass neutron star can be robustly formed. This may be the origin of those low mass neutron stars (e.g. J1807-2500 c. and J0453+1559 in the figure). 

The direct consequence of a lower Chandrasekhar mass due to presence of dark matter is that the universality of the initial model for Type Ia supernova is broken. 

A Type Ia supernova model with a lower Chandrasekhar mass is weaker with a lower Ni-56 production. The diversity can explain some Type Iax supernova, such as SN 1998de, SN 2011ay and so on in the figure.