According to the recycling scenario, millisecond pulsars (MSPs) have evolved from low-mass X-ray binaries (LMXBs). Their orbits are expected to be circular due to tidal interactions during binary evolution, as observed in most binary MSPs. There are some peculiar systems that do not fit this picture. Three recent examples are the PSRs J2234+06, J1946+3417, and J1950+2414, all of which are MSPs in eccentric orbits but with mass functions compatible with expected He white dwarf (WD) companions. It has been suggested these MSPs may have formed from delayed accretion-induced collapse of massive WDs, or the eccentricity may be induced by dynamical interaction between the binary and a circumbinary disk. Assuming that the core density of accreting neutron stars (NSs) in LMXBs may reach the density of quark deconfinement, which can lead to phase transition from NSs to strange quark stars, we show that the resultant MSPs are likely to have an eccentric orbit, due to the sudden loss of the gravitational mass of the NS during the transition. The eccentricities can be reproduced with a reasonable estimate of the mass loss. This scenario might also account for the formation of the youngest known X-ray binary Cir X–1, which also possesses a low-field compact star in an eccentric orbit.
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