[Paper Review] Innermost stable circular orbits around strange stars and kHz QPOs in low-mass X-ray binaries

J. L. Zdunik, P. Haensel+2 more|arXiv (Cornell University)|Feb 21, 2000

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper investigates innermost stable circular orbits (ISCO) around rotating strange stars using general relativity and MIT Bag Model equations of state for strange quark matter. It finds that for strange stars above a minimum mass (1.4–1.6 M☉), an ISCO-stellar surface gap always exists, and ISCO frequencies exceed 1.07 kHz for stars above 2.2 M☉ with a solid crust, enabling natural explanation of observed kHz QPOs without fine-tuning of parameters for high-mass models.

ABSTRACT

Exact calculations of innermost stable circular orbit (ISCO) around rotating strange stars are performed within the framework of general relativity. Equations of state (EOS) of strange quark matter based on the MIT Bag Model with massive strange quarks and lowest order QCD interactions, are used. The presence of a solid crust of normal matter on rotating, mass accreting strange stars in LMXBs is taken into account. It is found that, contrary to neutron stars, above some minimum mass a gap always separates the ISCO and stellar surface, independently of the strange star rotation rate. For a given baryon mass of strange star, we calculate the ISCO frequency as function of stellar rotation frequency, from static to Keplerian configuration. For masses close to the maximum mass of static configurations the ISCO frequencies for static and Keplerian configurations are similar. However, for masses significantly lower than the maximum mass of static configurations, the minimum value of the ISCO frequency is reached in the Keplerian limit. Presence of a solid crust increases the ISCO frequency for the Keplerian configuration by about ten percent compared to that for a bare strange star of the same mass.

Motivation & Objective

• To determine the properties of innermost stable circular orbits (ISCO) around rotating strange stars using exact general relativistic calculations.
• To assess whether observed kHz quasi-periodic oscillations (QPOs) in low-mass X-ray binaries (LMXBs) can be explained by ISCO orbital motion around strange stars.
• To examine the impact of a solid crust of normal matter on the ISCO frequency and its consistency with observed QPO frequencies.
• To evaluate whether standard strange quark matter equations of state (EOS) can reproduce observed QPO frequencies without parameter tuning.
• To explore the dependence of ISCO frequency on stellar mass, rotation rate, and EOS parameters, particularly in the Keplerian limit.

Proposed method

• Exact numerical solution of the general relativistic equations for rotating strange stars using the MIT Bag Model with massive strange quarks and lowest-order QCD interactions.
• Incorporation of a solid crust of normal matter on the surface of accreting strange stars in LMXBs, modeled as a thin, rigid shell of non-strange matter.
• Computation of the ISCO radius and frequency as a function of stellar rotation frequency, from static to Keplerian configurations.
• Use of scaling relations derived from the MIT Bag Model to generalize results across different values of the bag pressure B, quark mass, and coupling constant.
• Comparison of ISCO frequencies with observed upper kHz QPOs (e.g., 1.07 kHz in 4U 1820-30 and 1.33 kHz in 4U 0614+91) for various EOS and stellar masses.
• Analysis of the ISCO frequency behavior in the Keplerian limit and its dependence on crust thickness and stellar mass.

Experimental results

Research questions

• RQ1 Does the presence of a gap between the ISCO and the stellar surface persist in rotating strange stars, and how does it depend on mass and rotation?
• RQ2 Can observed kHz QPO frequencies in LMXBs be naturally explained by ISCO orbital motion around strange stars without fine-tuning of EOS parameters?
• RQ3 How does the presence of a solid crust affect the ISCO frequency, particularly near the Keplerian limit?
• RQ4 What stellar masses and rotation rates are required to reproduce the observed 1.07 kHz and 1.33 kHz QPOs in strange star models?
• RQ5 How does the ISCO frequency vary with baryon mass and rotation frequency, especially in the Keplerian regime, for different strange quark matter EOS?

Key findings

• For strange stars above a minimum mass of 1.4–1.6 M☉, a gap always exists between the ISCO and the stellar surface, regardless of rotation rate.
• The ISCO frequency for a 1.8 M☉ strange star with the standard SQM1 EOS always exceeds 1.07 kHz, consistent with the upper QPO frequency in 4U 1820-30.
• For the SQM2 EOS (maximum static mass 2.3 M☉), ISCO frequencies of 1.07 kHz are achieved at rotation rates of 200–300 Hz for stars with mass >2.2 M☉.
• The ISCO frequency at the Keplerian limit decreases with decreasing baryon mass, allowing lower ISCO frequencies for less massive stars.
• The presence of a solid crust increases the ISCO frequency by about 100 Hz compared to a bare strange star of the same mass, especially in rapidly rotating configurations.
• For the SQM2 EOS, ISCO frequencies of ~1 kHz are reached near the Keplerian limit across a broad range of stellar masses, without requiring parameter tuning.