  We obtain more straightforwardly some features of dark matter distribution in
the halos of galaxies by considering the spherically symmetric space-time,
which satisfies the flat rotational curve condition, and the geometric equation
of state resulting from the modified gravity theory. In order to measure the
equation of state for dark matter in the galactic halo, we provide a general
formalism taking into account the modified $f(X)$ gravity theories. Here,
$f(X)$ is a general function of $X \in \{ R, \mathcal{G}, T \}$, where $R,
\mathcal{G}$ and $T$ are the Ricci scalar, the Gauss-Bonnet scalar and the
torsion scalar, respectively. These theories yield that the flat rotation
curves appear as a consequence of the additional geometric structure
accommodated by those of modified gravity theories. Constructing a geometric
equation of state $w_{_X} \equiv p_{_X} / \rho_{_X}$ and inspiring by some
values of the equation of state for the ordinary matter, we infer some
properties of dark matter in galactic halos of galaxies.
