| Abstract
| - Abstract. We study the evolution of low-mass X-ray binaries hosting a neutron star and of millisecond binary radio pulsars using numerical simulations that take into account the detailed evolution of the companion star, of the binary system, and of the neutron star. According to general relativity, when energy is released during accretion or due to magnetodipole radiation during the pulsar phase, the system loses gravitational mass. Moreover, the neutron star can collapse to a black hole if its mass exceeds a critical limit, which depends on the equation of state of ultradense matter and is typically ∼2 M⊙. These facts have some interesting consequences. (i) In a millisecond radio pulsar the mass-energy is lost with a specific angular momentum that is smaller than the specific angular momentum of the system, resulting in a positive contribution to the orbital period derivative. If this contribution is dominant and can be measured, we can extract information about the moment of inertia of the neutron star, since the energy loss rate depends on it. Such a measurement can help to put constraints on the equation of state of ultradense matter. (ii) In low-mass X-ray binaries below the bifurcation period (∼18 h), the neutron star survives the ‘period gap’ only if its mass is smaller than the maximum non-rotating mass when the companion becomes fully convective and accretion pauses. Since in such evolutions ∼0.8 M⊙ can be accreted on to the neutron star, short-period (P ⩽ 2 h) millisecond X-ray pulsars such as SAX J1808.4 − 3658 can be formed only if either a large part of the accreting matter has been ejected from the system, or the equation of state of ultradense matter is very stiff. (iii) In low-mass X-ray binaries above the bifurcation period, the mass-energy loss lowers the mass transfer rate. As a side effect, the inner core of the companion star becomes ∼1 per cent bigger than in a system with a non-collapsed primary. As a result of this difference, the final orbital period of the system is 20 per cent longer than if the mass-energy loss effect is not taken into account.
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