Compact stars with strongly coupled quark matter in a strong magnetic field

Some time ago we derived from the QCD Lagrangian an equation of state (EOS) for cold quark matter which can be considered an improved version of the MIT bag model EOS. Compared to the latter, our equation of state reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to nonperturbative effects. Later we applied this EOS to the study of compact stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. We found maximum masses of the sequences with more than two solar masses, in agreement with recent experimental observations. In the present work we include the magnetic field in the equation of state and study how it changes the stability conditions and the mass-radius curves.

Figure 1

Dependence of the EOS on the magnetic field. (a) Parallel pressure. (b) Perpendicular pressure.

Figure 2

Splitting between the parallel and perpendicular pressures as a function of the magnetic field for mQCD and for the MIT bag model.

Figure 3

Stability windows defined by the conditions (26, 27, 28, 29).

Figure 4

Stability diagram: baryon density ratio as function of magnetic field. The points in the light grey area satisfy the conditions (26, 27, 28). Points in the dark grey area satisfy also the condition (29).

Figure 5

Mass-radius diagrams. Two values of the magnetic fields with ${\mathcal{B}}_{\mathrm{QCD}}$ and $\xi$ allowed by the stability conditions at ${\rho }_B=2.6{\rho }_0$. The largest masses are 2.05 (mQCD) and 1.89 (MIT). In these cases $p_{\parallel }=p_{\perp }$ which permits the use of TOV.

Figure 6

Mass-radius diagram for a fixed value of the magnetic field and the baryon density with $p_{\parallel }<p_{\perp }$. (a) Fixed $\xi$. For ${\mathcal{B}}_{\mathrm{QCD}}=53{\mathrm{MeV}/\mathrm{fm}}^3$ the largest masses are 2.22 and 2.04 (along the dotted lines), calculated with the perpendicular and parallel pressures, respectively. Analogously for ${\mathcal{B}}_{\mathrm{QCD}}=61{\mathrm{MeV}/\mathrm{fm}}^3$ the largest masses are 2.06 and 1.93 (along the solid lines). (b) Fixed ${\mathcal{B}}_{\mathrm{QCD}}$. For $\xi =0.0015{\mathrm{MeV}}^{-1}$ the largest masses are 2.20 and and 2.06 (along the dotted lines), calculated with perpendicular and parallel pressures, respectively. Analogously for MIT $(\xi =0{\mathrm{MeV}}^{-1})$ the largest masses are 2.08 and 1.92 (along the solid lines).

Figure 7

Effect of the pressure anisotropy on the star masses computed with the TOV equations. The chemical potentials obey the stability conditions (26, 27, 28, 29), given by ${\nu }_u=300$ MeV, ${\nu }_d={\nu }_s=316.5$ MeV, and ${\mu }_e=16.5$ MeV.