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It is usually thought that a single equation of state (EoS) model correctly represents cores of all compact stars. Here we emphasize that two families of compact stars, viz., neutron stars and strange stars, can coexist in nature, and that neutron stars can get converted to strange stars through the nucleation process of quark matter in the stellar center. From our fully general relativistic numerical computations of the structures of fast-spinning compact stars, known as millisecond pulsars, we find that such a stellar conversion causes a simultaneous spin-up and decrease in gravitational mass of these stars. This is a new type of millisecond pulsar evolution through a new mechanism, which gives rise to relatively lower mass compact stars with higher spin rates. This could have implication for the observed mass and spin distributions of millisecond pulsars. Such a stellar conversion can also rescue some massive, spin-supported millisecond pulsars from collapsing into black holes. Besides, we extend the concept of critical mass $M_{rm cr}$ for the neutron star sequence (Berezhiani et al. 2003; Bombaci et al. 2004) to the case of fast-spinning neutron stars, and point out that neutron star EoS models cannot be ruled out by the stellar mass measurement alone. Finally, we emphasize the additional complexity for constraining EoS models, for example, by stellar radius measurements using X-ray observations, if two families of compact stars coexist.
The spin-down of a neutron star, e.g. due to magneto-dipole losses, results in compression of the stellar matter and induces nuclear reactions at phase transitions between different nuclear species in the crust. We show that this mechanism is effecti
An understanding of spin frequency ($ u$) evolution of neutron stars in the low-mass X-ray binary (LMXB) phase is essential to explain the observed $ u$-distribution of millisecond pulsars (MSPs), and to probe the stellar and binary physics, includin
We analyse the phenomenological implications of the two-families scenario on the merger of compact stars. That scenario is based on the coexistence of both hadronic stars and strange quark stars. After discussing the classification of the possible me
The maximum mass of a neutron star has important implications across multiple research fields, including astrophysics, nuclear physics and gravitational wave astronomy. Compact binary millisecond pulsars (with orbital periods shorter than about a day
Bose-Einstein condensates (BECs) have been proposed as candidate states of matter for the interior of neutron stars. Specifically, Chavanis and Harko obtained the mass-radius relation for a BEC star and proposed that the recently discovered neutron s