When dark matter is a perfect fluid , using the equation of state can get the density profile in the static and spherically symmetric space-time .
If the equation of state is independent of the scaling transformation , its lower order approximation can naturally lead to a special case , i.e . p = \zeta \rho + 2 \epsilon V _ { rot } ^ { 2 } \rho , where p and \rho are the the pressure and density , V _ { rot } is the rotation velocity of galaxy , \zeta and \epsilon are positive constants .
Then we use this equation of state to derive the mass density profiles of dark matter halos .
It can obtain a profile which is similar to the pseudo-isothermal halo model when \epsilon is around 0.15 .
It can perfectly fit the observed rotation curves of low surface brightness ( LSB ) galaxies .
When \zeta = 0 , there exits a power law density in the very outer region which surround a black hole , and its power index is - \frac { 1 + 4 \epsilon } { 4 \epsilon } .
The term \zeta \rho can lead to a constant-density core .

keywords : galaxy : dark matter–galaxy : rotation curves