Quark stars admixed with dark matter

Compact stars consisting of massless quark matter and fermionic dark matter are studied by solving the Tolman-Oppenheimer-Volkoff equations for two fluids separately. Dark matter is further investigated by incorporating interfermionic interactions among the dark matter particles. The properties of stars made of quark matter particles and self-interacting and free dark matter particles are explored by obtaining their mass-radius relations. The regions of stability for such a compact star are determined, and it is demonstrated that the maximum stable total mass of such a star decreases approximately linearly with an increasing dark matter fraction.

Figure 1

Mass ($M_{\text{quark}}$) vs radius ($R_{\text{quark}}$) curve for quark stars for two different bag values.

Figure 2

Plot of the mass ($M_{\text{dark}}$) vs radius ($R_{\text{dark}}$) for a free gas of fermions of mass 100 GeV at zero temperature. This graph corresponds to the mass-radius curve of the dark matter composed of free fermionic particles.

Figure 3

Plot of mass $M_{\mathrm{int}}$ vs radius $R_{\mathrm{int}}$ for strongly self-interacting dark matter fermionic particles ($y={10}^3$).

Figure 4

Plot of mass ($M_{\text{quark}}$) vs central energy density (${\epsilon }_{0,\text{quark}}$) of quark matter for three different central energy densities of dark matter (${\epsilon }_{0,\text{dark}}$).

Figure 5

Plot of radius ($R_{\text{quark}}$) vs central energy density (${\epsilon }_{0,\text{quark}}$) of quark matter for different central energy densities of dark matter (${\epsilon }_{0,\text{dark}}$).

Figure 6

Plot of mass ($M_{\text{dark}}$) vs central energy density (${\epsilon }_{0,\text{dark}}$) of dark matter for different central energy densities of quark matter (${\epsilon }_{0,\text{quark}}$).

Figure 7

Plot of radius ($R_{\text{dark}}$) vs central energy density (${\epsilon }_{0,\text{dark}}$) of dark matter for different central energy densities of quark matter (${\epsilon }_{0,\text{quark}}$).

Figure 8

Contour plot with [$\frac{{\epsilon }_{0,\text{quark}}}{4B}$, $\frac{{\epsilon }_{0,\text{dark}}}{m_f^4}$, and $M_{\text{total}}$ (in $M_{\odot }$)] as the $x$, $y$, and $z$ axes, respectively. The region marked as A represents the stable region for the formation of a quark star admixed with dark matter, while all the points in region B are unstable for such a formation.

Figure 9

Plot for the mass of the quark component ($M_{\text{quark}}$) vs the quark central density ${\epsilon }_{0,\text{quark}}$ for three different dark matter central densities (${\epsilon }_{0,\text{intdark}}$). It is visible that as ${\epsilon }_{0,\text{intdark}}$ is increased the maximum stable quark mass ($M_{\text{quark},\max }$) is reduced and is now attained at a higher ${\epsilon }_{0,\text{quark}}$.

Figure 10

Plot for the radius of the quark component ($R_{\text{quark}}$) vs the quark central density ${\epsilon }_{0,\text{quark}}$ for different dark matter central densities (${\epsilon }_{0,\text{intdark}}$).

Figure 11

Plot for the mass of the dark component ($M_{\mathrm{int}}$) vs the dark central density ${\epsilon }_{0,\text{intdark}}$ of different quark matter central densities (${\epsilon }_{0,\text{quark}}$). It is visible that the dark matter mass profile is not altered very much with changing ${\epsilon }_{0,\text{quark}}$.

Figure 12

Plot for the radius of the dark component ($R_{\mathrm{int}}$) vs the dark central density ${\epsilon }_{0,\text{intdark}}$ for different quark matter central densities (${\epsilon }_{0,\text{quark}}$).

Figure 13

Contour plot with [$\frac{{\epsilon }_{0,\text{quark}}}{4B}$, $\frac{{\epsilon }_{0,\text{intdark}}}{m_f^4}$, $M_{\text{total}}$ (in $M_{\odot }$)] as the $x$, $y$, and $z$ axes, respectively. The region marked as A represents the stable region for the formation of a quark star admixed with dark matter, while all the points in region B are unstable to such a formation. $\frac{{\epsilon }_{0,\text{quark}}}{4B}$ starts from 1.0 in the plot because the energy density of quark matter cannot be zero according to the equation of state (6).

Figure 14

Plot showing the dependence of the maximum total mass vs the dark matter content for a quark star admixed with dark matter. The slope of the plot is $-3.62$. It shows that the maximum total mass decreases with increasing dark matter content in the star. The red line shows the linear fit.