We calculate the evolution of close binary systems (CBSs) formed by a neutron star (behaving as a radio pulsar) and a normal donor star, evolving either to helium white dwarf (HeWD) or ultra short orbital period systems. We consider X-ray irradiation feedback and evaporation due to radio pulsar irradiation. We show that irradiation feedback leads to cyclic mass transfer episodes, allowing CBSs to be observed in-between as binary radio pulsars under conditions in which standard, non-irradiated models predict the occurrence of a low mass Xray binary. This behavior accounts for the existence of a family of eclipsing binary systems known as redbacks. We predict that redback companions should almost fill their Roche lobe, as observed in PSR J1723-2837. This state is also possible for systems evolving with larger orbital periods. Therefore, binary radio pulsars with companion star masses usually interpreted as larger than expected to produce HeWDs may also result in such quasi -Roche Lobe Overflow states, rather than hosting a carbon-oxygen WD.We found that CBSs with initial orbital periods P i < 1 day evolve into redbacks. Some of them produce low mass HeWDs, and a subgroup with shorter P i become black widows (BWs). Thus, BWs descent from redbacks, although not all redbacks evolve into BWs.There is mounting observational evidence favoring that BW pulsars are very massive ( 2 M ⊙ ). As they should be redback descendants, redback pulsars should also be very massive, since most of the mass is transferred before this stage.CBSs with P i > 1 day, standard calculations that lead to the formation of HeWDs predicts the occurrence of companions to radio pulsars only in the neighborhood of P(M 2 ) relation.Currently, companions to radio pulsars more massive than predicted by the P(M 2 ) relation are considered as CO or HeCO WDs (Tauris et al. 2000;Podsiadlowski et al. 2002).Two separate classes of interacting binary systems with a radio pulsar have been identified, they are called redbacks and BWs. Redbacks are eclipsing binary systems with 0.1 day < P < 1 day and 0.2 M ⊙ < M 2 < 0.4 M ⊙ . BWs have P in the same range of values, but much lower companion masses (M 2 < 0.05 M ⊙ ). 1 We denote the corresponding quantities of the NS and donor star with subscripts 1 and 2, respectively.

The existence of millisecond pulsars with planet-mass companions in close orbits is challenging from the stellar evolution point of view. We calculate in detail the evolution of binary systems self-consistently, including mass transfer, evaporation, and irradiation of the donor by X-ray feedback, demonstrating the existence of a new evolutionary path leading to short periods and compact donors as required by the observations of PSR J1719-1438. We also point out the alternative of an exotic nature of the companion planet-mass star.

We present a numerical code intended for calculating stellar evolution in close binary systems. In doing so, we consider that mass transfer episodes occur when the stellar size overflows the corresponding Roche lobe. In such a situation we equate the radius of the star to the equivalent radius of the Roche lobe. This equation is handled implicitly together with those corresponding to the whole structure of the star. We describe in detail the necessary modifications to the standard Henyey technique for treating the mass-loss rate implicitly together with thin outerlayer integrations.We have applied this code to the calculation of the formation of low-mass, helium white dwarfs in low-mass close binary systems. We find that the global numerical convergence properties are fairly good. In particular, the onset and end of mass transfer episodes are computed automatically.

We present a set of calculations of the evolution of low‐mass, solar composition stars in close binary systems together with a canonical 1.4‐M⊙, neutron star (NS). We restrict the initial mass and period values to those that give rise to the formation of ultracompact systems or low‐mass helium white dwarf (He WD) stars. Specifically, we computed the evolution of 40 systems for which the initial masses of the normal (donor) stars were of 1.00, 1.25, 1.50, 1.75, 2.00, 2.50, 3.00 and 3.50 M⊙, while the range of initial periods covered in this work was from 0.5 to 12 d. Calculations were performed employing the binary hydro code developed by the present authors, which handles the mass transfer rate in a fully implicit way together with state‐of‐the‐art physical ingredients and diffusion processes. In this work we have assumed the standard scheme for the orbital evolution of the binary, considering the usual processes that produce angular momentum losses: mass loss from the system, magnetic braking and gravitational radiation. In the main part of this work we assume that the NS is able to retain only half of the matter coming from the donor star. The range of final masses has been from 0.01961 to 0.34351 M⊙ and periods from 39 min to 187 d. 26 out of the 40 considered systems give rise to the formation of a He WD as a compact remnant. In performing a comparison of our results with observations, we have employed three WD–NS systems, which are among the best known ones. These are PSR J0437−4715, PSR J1012+5307 and PSR B1855+09. In order to obtain good agreement between models and observations we have had to assume that the NS is able to retain only ≈10 per cent of the material released by the donor star. Otherwise, for the cases of PSR J0437−4715 and PSR B1855+09 we would be in conflict with the observed NS masses. For these two objects we have been able to fit WD and NS masses, the orbital period and also the time‐scale for cooling of the WD with the evolution of one binary system. For the case of PSR J1012+5307, the problem is more delicate because the object has a mass near the threshold for the occurrence of thermonuclear flashes and the initial period is close to bifurcation point.