Strange quark star I: the maximum gravitational mass and deformation of magnetized spinning model

TL;DR

This study models strange quark stars under strong magnetization and rapid rotation using a density-dependent MIT bag EOS that incorporates Landau quantization. By solving the axisymmetric Einstein equations with the LORENE spectral method, it maps how magnetic field strength and rotation influence the maximum gravitational mass, stellar deformation, total energy, and binding energy. The results show that M_g,max can reach about 2.80 solar masses for f = 1200 Hz and B_c = 5×10^17 G, with deformation up to a ≈ 1.55, placing these stars in the observationally relevant mass range for events like GW190814 and PSR J0952-0607. The work provides analytic fits for M_g,max and a for predicting how magnetic moment and rotation shape equilibrium configurations, and it highlights the relative small role of external magnetic energy in the total energy budget while confirming stable, self-bound configurations across the explored parameter space.

Abstract

We investigate the structural parameters of strange quark stars (SQS) under the influence of strong magnetic fields and varying rotational frequencies. The equation of state is computed using the MIT bag model with a density-dependent bag constant and considering the Landau quantization effect regarding the strong magnetic fields up to $5\times10^{17}\,$G in the interior of SQS. Employing the LORENE library, we calculate the structural parameters under different magnetic field strengths and rotational frequencies. Our models are compared in terms of maximum gravitational mass, deformation parameter, binding energy, and compactness. Our equation of state model demonstrates that the gravitational masses are higher than those computed using a MIT bag model with a fixed bag constant. We find the gravitational masses beyond $2.3 \,M_\odot$, which are compatible with the masses of observed compact objects, such as the ``black widow'' pulsar \emph{PSR J0952-0607}, and the \emph{GW190814} event detected by the LIGO/Virgo collaboration. The deformation parameter and maximum gravitational mass of SQS are characterized by fitted functions accounting for variations in both magnetic field strength and rotational frequency. We find the maximum deformation parameter of 1.55 and the maximum gravitational mass of $2.8\, M_\odot$ in the fast-rotating strongly magnetized model.

Figures (7)

• Figure 1: Pressure as a function of the energy density of SQM in the presence of different magnetic field strengths. The energy density corresponding to the maximum gravitational mass is pointed with the red cross. The curves with four magnetic fields indicated in the legend overlap.
• Figure 2: Gravitational mass $M_{\rm g}$ versus circumferential radius $R_{\rm circ}$ for different rotational frequencies in each panel, with the colors indicating the value of the central magnetic field, as indicated in the color bar.
• Figure 3: Gravitational mass $M_{\rm g}$ versus circumferential radius $R_{\rm circ}$ with different angular momentum ($J = 1.13, 2.26, 3.39\, [{GM_\odot^2/c}]$) in each panel with the colors indicating the value of the central magnetic field.
• Figure 4: Gravitational mass $M_{\rm g}$ as a function of central energy density in the unit of [$\rho_{\rm nuc} c^2$] with different angular momentum ($J = 1.13, 2.26, 3.39\, [{\rm GM_\odot^2/c}]$)in each panel with the colors indicating the value of the central magnetic field.
• Figure 5: Gravitational mass $M^{\rm max}_{\rm g}$ as a function of the magnetic moment $\mu$ at different rotational frequencies $f$. Each color represents one rotational frequency. The dotted lines show the fitted function.