On quintessence star model and strange star

The astronomical observations on the accelerated expansion of the universe generate the possibility that the internal matter of the stars is not only formed by ordinary matter but also by matter with negative pressure. We discuss the existence of stars formed by the coexistence of two types of fluids, one associated to quintessence dark matter described by the radial and tangential pressures $$(P_{rq},P_{tq})$$ ( P rq , P tq ) and the density $$\rho _{q}$$ ρ q characterized by a parameter $$-1<w<-\frac{1}{3}$$ - 1 < w < - 1 3 and ordinary matter described by an anisotropic fluid with radial pressure of a strange star given by the MIT Bag model $$P_r=\frac{1}{3}(c^2\rho -4B_g)$$ P r = 1 3 ( c 2 ρ - 4 B g ) and tangential pressure $$P_t=\frac{1}{3}(c^2\rho -4B_g)-\frac{3}{2}(1+w)c^2\rho _q$$ P t = 1 3 ( c 2 ρ - 4 B g ) - 3 2 ( 1 + w ) c 2 ρ q , in which the effect is reflected of the quintessence dark matter over the ordinary matter. Via a theorem we show that the geometry that describes this interaction is equivalent to that of a perfect fluid with ordinary matter. Taking as geometry the one associated with a model for neutron stars, a physically acceptable and stable model is obtained. The application to the star Her X-1, as a candidate to a strange quark star, generates for us a value of the MIT Bag constant $$B_g = 97.0048\,\mathrm{Mev}/\mathrm{fm}^3$$ B g = 97.0048 Mev / fm 3 , which is found to be inside the expected interval.