The different fates of a low-mass X-ray binary - I. Conservative mass transfer

We study the evolution of a low-mass X-ray binary by coupling a binary stellar evolution code with a general relativistic code that describes the behaviour of the neutron star. We assume the neutron star to be low-magnetized (B~ 108 G). In the systems investigated in this paper, our computations show that during the binary evolution, the companion transfers as much as 1 Msolar to the neutron star, with an accretion rate of ~10-9 Msolar yr-1. This is sufficient to keep the inner rim of the accretion disc in contact with the neutron star surface, thus preventing the onset of a propeller phase capable of ejecting a significant fraction of the matter transferred by the companion. In this scenario we find that, for neutron stars governed by equations of state from soft up to moderately stiff, an accretion induced collapse to a black hole is almost unavoidable. The collapse to a black hole can occur either during the accretion phase or after the end of the mass transfer when the neutron star is left in a supramassive sequence. In this last case, the collapse is driven by energy losses of the fast spinning magneto-dipole rotator (pulsar). For extremely supramassive neutron stars, these energy losses cause a spin-up. Consequently, the pulsar will have a much shorter lifetime than that of a canonical, spinning down radio pulsar. This complex behaviour strongly depends on the equation of state for ultradense matter and therefore could be used to constrain the internal structure of the neutron star. In the hypothesis that the r-modes of the neutron star are excited during the accretion process, the gravitational waves emission limits the maximum spin attainable by a neutron star to roughly 2 ms. In this case, if the mass transfer is conservative, the collapse to a black hole during the accretion phase is even more common since the maximum mass achievable before the collapse to a black hole during accretion is smaller due to the limited spin frequency.