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Constraining twin-star existence in a four-parameter Maxwell equation of state

Shamim Haque1,2,*, Atharva Shinde1,*, Asim Kumar Saha1, Tuhin Malik3, and Ritam Mallick1,†

  • *These authors contributed equally to this work.
  • †Contact author: mallick@iiserb.ac.in
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Phys. Rev. D 114, 103016 – Published 9 November, 2026

DOI: https://doi.org/10.1103/62q1-5bv7

Abstract

Twin stars (TSs) are predicted to exist in nature if the hadron-to-quark phase transition is strong enough to form a new branch of hybrid stars, separated from the branch of neutron stars. It is essential to study the hybrid equation of states (EoSs) that can form TSs, with a primary focus on estimating the onset of the phase transition and its strength. We systematically study the TS scenario by adopting a four-parameter Maxwell-CSS approach to construct a large ensemble of Maxwell-type hybrid EoSs. Within this framework, we report the conditions on our parameter space imposed by the Tolman-Oppenheimer-Volkoff (TOV) solutions. For a fixed transition energy density and speed of sound for quark matter, we define distinct ranges of transition pressures based on the allowed strengths of discontinuity. Below a maximum transition pressure, a range of discontinuity exists that increases as the transition pressure decreases. Thereby, we identify the loci of the limits on discontinuities as the TS existence boundaries. Based on the causality limit, the TS existence boundaries can be truncated. Strong constraints on this picture are drawn from the CET, GW170817 and NICER. Within our considered model, we computed conditional extrema surviving the adopted 2σ filters—the maximum mass for TSs to be 2.05M⊙, the allowed strongest discontinuity in rest-mass density to be 7.76ρsat, and the upper bound on transition rest-mass density to be 4.03ρsat. Subsequently, we compute the implications of the stiffness of the quark matter EoS on this picture. Different confidence levels for observational constraints are considered to assess the extent to which Maxwell-type EOSs remain compatible with the observations.

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Phys. Rev. D 114, 103016– Published 9 November, 2026
  • Received 29 January 2026
  • Accepted 23 October 2026
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