On the Evolution of Low‐Mass X‐Ray Binaries under the Influence of a Donor Stellar Wind Induced by X‐Rays from the Accretor

Abstract

In a low-mass X-ray binary (LMXB), an intense stellar wind from the mass donor may be a consequence of the absorption of X-rays from the mass-accreting neutron star or black hole, and such a wind could change the evolution of these binaries dramatically compared with the evolution of cataclysmic variables (CVs), which are close binaries in which the accretor is a white dwarf. An analytical study and numerical models show that, in the closest and brightest LMXBs, a relativistic companion can capture up to D10% of the mass lost in the induced stellar wind (ISW) from the main-sequence or subgiant donor, and this is enough to keep the X-ray luminosity of a typical LMXB on the level of L X D 5000 L _ and to accelerate the rotation of an old neutron star with a low magnetic Ðeld into the millisecond-period range. A self-sustained ISW may exist even if the donor does not Ðll its Roche lobe, but the system can be bright only if the radius of the donor is a substantial fraction of the (L X [ 100 L _) (Z 0.8) Roche lobe radius. A lower limit on the Roche lobe Ðlling factor follows from the circumstance that both the rate at which work must be done to lift wind matter o † the donor and the rate at which E0 wind E0 abs the donor absorbs X-ray energy are proportional to (the ISW mass-loss rate) and from the require-M 0 ISW ment that in order for energy to be conserved. E0 wind \ E0 abs The observed number (D100) of bright LMXBs in our Galaxy can be understood as the product of a relatively short lifetime (a few ] 107 yr) and a small theoretical birthrate (D2 ] 10~6È8 ] 10~6 yr~1), which is comparable to semiempirical estimates of the birthrate of LMXBs and millisecond pulsars (D2 ] 10~6 yr~1). The theoretical lifetime is D10È60 times shorter than when the ISW is not taken into account, and the theoretical birthrate is D3È6 times smaller, because of the fact that the ISW acts to expand the orbit and reduce the number of systems that can evolve through an X-ray bright stage under the inÑuence of a magnetic stellar wind (MSW) when the donor is a main-sequence star (CV-like LMXBs), or under the inÑuence of nuclear evolution when the donor is a subgiant or giant with a degenerate helium core (Algol-like LMXBs) of mass in the range M He \ 0.13È0.45 M _. The observed concentration of LMXBs in the 3È24 hr orbital period range corresponds to a similar concentration in the CV distribution and could be interpreted as evidence that the MSW in LMXBs operates at a strength not too di †erent from its strength in CVs. For 0.3È1 main-sequence donors, if M _ the radius of the donor is larger than D70% of the Roche lobe radius, the tendency of the ISW to force orbital expansion can balance the braking inÑuence of the MSW and prevent an LMXB with a main-sequence donor from evolving to periods less than D3 hr. When a main-sequence donor becomes completely convective (donor mass D0.1È0.3 depending on the mass-loss rate) and the MSW shuts o †, M _ , orbital angular momentum loss due to gravitational wave radiation (GWR) is unable to counter the tendency toward expansion, and this may explain the apparent absence of short-period hr) (P orb \ 3 LMXBs with main-sequence donors. This contrasts with the CV family in which the number of systems in the Galaxy with hr (with donor mass ¹0.3 and with evolution driven only by P orb D 1.3È2 M _ GWR) is larger by a factor of D100 than the number of systems with hr. P orb [ 3 In Algol-like LMXBs in the Galactic disk, the timescale for the evaporation (caused by the ISW) of the donor with a low-mass, degenerate helium core can be smaller than the timescale for the radial expansion of the donor owing to nuclear evolution, and the donor may never Ðll its Roche lobe. However, if progenitor binaries are initially wide enough, the donor may escape evaporation as a main-sequence star, and signiÐcant mass transfer may not occur until the secondary evolves into a giant with a degenerate helium core of large mass and Ðlls its Roche lobe. In globular clusters, as a result of capture and exchange reactions, semidetached Algol-like LMXBs can be formed in which the donor can Ðll its Roche lobe even when its degenerate helium core is of small mass, and Roche lobe mediated mass transfer driven by the nuclear evolution of the donor can dominate over capture from the ISW. The numerical models formally imply the possible presence in the Galaxy of D104 dim (L X D 1È100 long-period LMXBs or radio pulsars with low-mass (D0.05 companions. Since there are few, if L _), M _) any, known observational counterparts of these systems, it is necessary to invoke a mechanism or mechanisms to destroy their formal progenitors. Possible destruction mechanisms include : (1) evaporation driven by the radiation from the rapidly rotating pulsar into which the accretor has been transformed by accretion during the bright LMXB phase, and (2) a dynamical instability arising when the 955 956 IBEN, TUTUKOV, & FEDOROVA Vol. 486 donor is almost completely convective and Ðlls its Roche lobe. In the case of dynamical disruption, the donor may be transformed into the envelope of a object with a neutron star or Thorne-Z 0 ytkow (1975) black hole core or into a planet-forming disk around the neutron star or black hole. A few short-period hr) LMXBs do exist, and, in them, the donor may be a helium white (P orb \ 3 dwarf of mass less than D0.09 An ISW operating before the donor Ðlls its Roche lobe may be M _. responsible for reducing the mass of the white dwarf from an initial value of º0.13 to a value of M _ ¹0.09 thus permitting stable mass exchange (at a rate smaller than the Eddington limiting rate) M _ , and evolution to longer periods to occur after the donor Ðlls its Roche lobe. Another scenario relies on the collapse of a massive oxygen-neon white dwarf, which has accreted from a Roche lobe Ðlling helium white dwarf. Problems that must be explored further in order to acquire a better understanding of the evolution of LMXBs include the formation of a corona around an irradiated low-mass main-sequence or degenerate dwarf star, accretion of ISW matter by a neutron star or black hole companion, the e †ect of an ISW on the MSW, formation of millisecond pulsars, complete evaporation of low-mass donors, disruption by tidal forces of a low-mass main-sequence star or a degenerate dwarf companion into a gas disk around the accretor, and the formation of planetary systems in the disk around neutron stars and or black holes in post-LMXB systems.