Strange quark star II: the minimal and maximal gravitational mass and the Keplerian configuration

TL;DR

This work examines minimal and maximal gravitational masses and the Keplerian (mass-shedding) configurations of rapidly rotating strange quark stars using a density-dependent MIT bag model EOS. The authors solve the Einstein equations for axisymmetric, stationary spacetimes with the LORENE spectral method to compute rotating SQS across $f$ in the range $1100$–$1300$ Hz, revealing a rotating maximum mass up to $\sim2.87\,M_\odot$ and a rotating minimum mass down to $\sim0.25\,M_\odot$, while the static maximum mass is $\approx2.35\,M_\odot$. Keplerian frequencies derived from full models agree with analytic Haensel-type fits within a few percent, and the mass limits are compatible with observed pulsars, including $M\gtrsim2\,M_\odot$ systems and GW190814 scenarios. The results underscore the role of rotation in supporting more massive SQS and provide constraints on the EOS, with future work aimed at magnetized configurations and alternative EOSs.

Abstract

We employ the MIT bag model with density-dependent bag constant for the equation of state (EOS) to estimate the gravitational mass and Keplerian frequency of rapidly rotating strange quark stars (SQS). In a companion paper we discuss the structural parameters of such rotating stars under the influence of strong magnetic fields. We use the LORENE library to compute the structural parameters at different rotational frequencies in the range of 1100-1300~Hz for a non-magnetized SQS. While there is no minimum limit for the mass of slowly rotating self-bound stars, by computing the maximum rotational frequency, known as the mass-shedding limit, we show that SQS must have a minimum mass to sustain high rotational frequencies. The mass-shedding frequency in our EOS model is lower than that estimated from the MIT bag model EOS with a fixed bag constant. The Keplerian frequency in our model depends linearly on the gravitational mass at the mass-shedding limit (and similarly on the minimum mass) with the slope of 0.08~${\rm kHz}/M_\odot$. We obtain mass limits aligned with the observational data for both the heaviest and the lightest observed pulsars.

Figures (3)

• Figure 1: The pressure $P$ versus density $\varepsilon$ for two MIT bag models: one with a fixed bag constant $\mathcal{B}^{\rm fixed}_{\rm bag} = 60 \, {\rm MeV/fm^3}$, with red dashed line and one with a density-dependent bag constant $\mathcal{B}_{\rm bag}(\rho)$, with blue solid line.
• Figure 2: The gravitational mass $M_{\rm g}$ versus circumferential radius radius $R_{\rm circ}$ is presented with color-coded filled circles for each frequency. Each marker indicates a computed configuration defined by its central enthalpy, while each color-coded sequence of markers corresponds to a distinct rotational frequency.
• Figure 3: The frequency versus the minimum gravitational mass $M^{\rm min}_{\rm g}$ and mass-shedding $M^{\rm shed}_{\rm g}$ (Keplerian configurations) with blue circles and red triangles, respectively, from our computations are shown along the values from the expression for $f_{\rm Kep}$ by Haensel_2009 with black stars. The blue and red dashed lines are fitted functions on $M^{\rm min}_{\rm g}$ and $M^{\rm shed}_{\rm g}$, respectively.