Dark matter admixed strange quark stars in the Starobinsky model

We compute the mass-to-radius profiles for dark matter admixed strange quark stars in the Starobinsky model of modified gravity. For quark matter, we assume the MIT bag model, while self-interacting dark matter inside the star is modeled as a Bose-Einstein condensate with a polytropic equation of state. We numerically integrate the structure equations in the Einstein frame, adopting the two-fluid formalism, and we treat the curvature correction term nonperturbatively. The effects on the properties of the stars of the amount of dark matter as well as the higher curvature term are investigated. We find that strange quark stars (in agreement with current observational constraints) with the highest masses are equally affected by dark matter and modified gravity.

Figure 1

Mass-to-radius profile for DM admixed strange quark star (with $K_{\chi }=4/B$ and $f_{\chi }=0.1$) in a $f(R)$ theory of gravity with three different values of the $a$ parameter: $a={10}^{77}$ (red curve), $a={10}^{78}$ (blue curve), and $a={10}^{79}$ (magenta curve). The profiles of a strange quark star in GR ($a=0$) without DM (gray curve) and with DM (black curve) are also shown for comparison.

Figure 2

Mass-to-radius profile for DM admixed strange quark star (with $K_{\chi }=150/B$ and $f_{\chi }=0.05$) in a $f(R)$ theory of gravity with three different values of the $a$ parameter: $a=5\times {10}^{76}$ (red curve), $a={10}^{80}$ (blue curve), and $a={10}^{88}$ (magenta curve).

Figure 3

Scalar field $\varphi$ as a function of the dimensionless star radius $r/R_{*}$. The compact star is an admixed DM strange quark star for which $K_{\chi }=150/B$ and $f_{\chi }=0.05$. The scalar field is shown for three different values of $a$: $a=5\times {10}^{76}$ (red), $a=3\times {10}^{77}$ (blue), and $a={10}^{78}$ (magenta) and central total pressure $P(0)=B$ (or 0.36% of DM).

Figure 4

Same as Fig. 3 but for the two metric functions [Eq. (10)]: $e^{2\nu }$ (blue curve) and $e^{2\lambda }$ (red curve). The metric functions coincide for all three values of $a$ (see Fig. 3), so there is only one set of curves.

Figure 5

Same as Fig. 3 but for the normalized pressure $P_i/B$ ($i=s$, $\chi$) of the fluids. Shown are the curves of the total pressure in black, the quark pressure in blue, and the DM pressure in red. The metric functions coincide for all three values of $a$ (see Fig. 3), so there is only one set of curves. Note that the curve corresponding to the DM pressure (red curve) has been scaled to $10:1$ for better visualization.

Figure 6

Mass-to-radius profiles for two DM admixed strange quark stars in an $f(R)$ theory of gravity (with $a={10}^{77})$: model $A$ (black curve) with $K_{\chi }=4/B$ and $f_{\chi }=0.09$ and model $B$ (magenta curve) with $K_{\chi }=150/B$ and $f_{\chi }=0.05$. For comparison, we also show the same models of DM admixed strange quark stars in GR ($a=0$), model A (blue curve) and model B (orange curve). The same strange quark star without DM in GR is also shown for comparison (gray curve).