Rotating proto-neutron stars can be important sources of gravitational waves to be searched for by present-day and future interferometric detectors. It was demonstrated by Imshennik that in extreme cases the rapid rotation of a collapsing stellar core may lead to fission and formation of a binary proto-neutron star which subsequently merges due to gravitational wave emission. In the present paper, we show that such dynamically unstable collapsing stellar cores may be the product of a former merger process of two stellar cores in a common envelope. We applied population synthesis calculations to assess the expected fraction of such rapidly rotating stellar cores which may lead to fission and formation of a pair of proto-neutron stars. We have used the BSE population synthesis code supplemented with a new treatment of stellar core rotation during the evolution via effective core-envelope coupling, characterized by the coupling time, τ c . The validity of this approach is checked by direct MESA calculations of the evolution of a rotating 15 M ⊙ star. From comparison of the calculated spin distribution of young neutron stars with the observed one, reported by Popov and Turolla, we infer the value τ c ≃ 5 × 10 5 years. We show that merging of stellar cores in common envelopes can lead to collapses with dynamically unstable proto-neutron stars, with their formation rate being ∼ 0.1 − 1% of the total core collapses, depending on the common envelope efficiency.

We present a model of a viscously evolving accretion disc around a magnetized neutron star. The model features the varying outer radius of the hot ionized part of the disc due to cooling and the varying inner radius of the disc due to interaction with the magnetosphere. It also includes hindering of accretion on the neutron star because of the centrifugal barrier and irradiation of the outer disc and companion star by X-rays from the neutron star and disc. When setting inner boundary conditions, we take into account that processes at the inner disc occur on a time scale much less than the viscous time scale of the whole disc. We consider three types of outflow from the disc inner edge: zero outflow, one based on MHD calculations, and a very efficient propeller mechanism. The light curves of an X-ray transient after the outburst peak can be calculated by a corresponding, publicly available code. We compare observed light curves of the 2013 burst of Aql X-1 in X-ray and optical bands with modeled ones. We find that the fast drop of the 0.3 − 10 keV flux can be solely explained by a radial shrinking of the hot disc. At the same time, models with the neutron star magnetic field >108 G have better fits because the accretion efficiency behaviour emphasizes the ’knee’ on the light curve. We also find that a plato emission can be produced by a disc-reservoir with stalled accretion.

Her X-1/HZ Her is one of the best studied accreting X-ray pulsars. In addition to the pulsating and orbital periods, the X-ray and optical light curves of the source exhibit an almost periodic 35-day variability caused by a precessing accretion disk. The nature of the observed long-term stability of the 35-day cycle has been debatable. The X-ray pulse frequency of Her X-1 measured by the Fermi/GBM demonstrates periodical variations with X-ray flux at the Main-on state of the source. We explain the observed periodic sub-microsecond pulse frequency changes by the free precession of a triaxial neutron star with parameters previously inferred from an independent analysis of the X-ray pulse evolution over the 35-day cycle. In the Fermi/GBM data, we identified several time intervals with a duration of half a year or longer where the neutron star precession period describing the pulse frequency variations does not change. We found that the NS precession period varies within one per cent in different intervals. Such variations in the free precession period on a year time scale can be explained by $\lesssim 1{{\ \rm per\ cent}}$ changes in the fractional difference between the triaxial neutron star’s moments of inertia due to the accreted mass readjustment or variable internal coupling of the neutron star crust with the core.

Accretion onto magnetized neutron stars is considered using as a case study long-term X-ray and optical observations of HZ Her/Her X-1, an X-ray binary system with a 1.7-day orbital period where disc accretion occurs from the optical donor star (HZ Her) onto a neutron star (Her X-1). On top of orbital variability and pulsating X-ray emission from the neutron star rotating with a period of about one second, a 35-day X-ray modulation of emission is observed. The 35-day variability is due to a tilted precessing accretion disc that periodically screens X-ray emission from the neutron star. The disc precession that occurs in the direction opposite to the orbital motion is determined by the joint action of the tidal torque from the donor and dynamical torque from the gas streams. Several dozen thousand broadband UBV photometric observations of HZ Her have been obtained since 1972. The shape of the orbital light curves of HZ Her also changes with the 35-day cycle phase. The orbital variability can be reproduced in a model that includes a precessing tilted and warped accretion disc around a freely precessing neutron star. The disc is warped near its inner edge due to interaction with the rotating neutron star magnetosphere. The magnetic torque depends on the precessional phase of the neutron star. The X-ray emission flux from the neutron star also depends on the free precession phase that modulates the heating of the optical-star atmosphere and the intensity of gas streams. We show that this model reproduces well both optical observations of HZ Her and the behavior of the 35-day X-ray cycle.

The X-ray binary Her X-1 consists of an accreting neutron star and the optical component HZ Her. The 35-day X-ray superorbital variability of this system is known since its discovery in 1972 by the Uhuru satellite and is believed to be caused by forced precession of a warped accretion disk tilted to the orbital plane. We argue that the observed features of the 35-day optical variability of HZ Her can be explained by free precession of the neutron star with a period close to that of the forced disk. The model parameters include a) the X-ray luminosity of the neutron star; b) the optical flux from the accretion disk; c) the tilt of the inner and outer edges of the accretion disk. A possible synchronization mechanism based on the coupling between the neutron star free precession and the dynamical action of non-stationary gas streams is discussed.