Can Dark Matter Be Explained by a New Nonrelativistic Fermion?

[somebody-nobody]

The mass of sun is determined by measuring the distance of a planet from the sun,the speed of that planet around the sun ,and then using Newtons law of gravity.In the same fashion one can determine the distribution of mass in a galaxy by observing the position adn motion of the stars in that galaxy.Astronomers have done this and determined that 1)90% of the mass of a typical galaxy is a dark matter2)unlike the visible matter,the dark matter has a spherically symetric distribution centered on the galaxy,but somewhat larger than the visible stars in the galaxy?
Lets assume that this dark matter is a new species of a particle.Like neutrinos new particle has no electrical or strong charge so it does not interact with normal matter.We will further assume that new particle is a fermion,and that is a centered around each galay in a gravitationally bound,nonrelativisti degenerate gas.

take the mass of a typical galaxy 10^10 solar masses adn the radius to be 10^5 light years.

1)What is the rest mass energy of new particle
2) what is the Fermi energy
3)is our assumption tha tnew particel is norelativistic validated?What ar the implications if it is not

DO i calculate rest mass as a E=mc^2

where m=90%mass of galaxy

 

[somebody-nobody]

2b)

for Fermi energy I guess tha ti need to use formula:

E=(h^2/2m)(3n/pi)

but than i have problem finding n