Formation And Evolution Of X-ray Binaries

X-ray binaries are a class of binary systems, in which the accretor is a compact star (i.e., black hole, neutron star, or white dwarf). They are one of the most important objects in the universe, which can be used to study not only binary evolution but also accretion disks and compact stars. Statistical investigations of these binaries help understand the formation and evolution of galaxies, and sometimes provide useful constraints on the cosmological models. The goal of this thesis is to investigate the formation and evolution processes of X-ray bina-ries including Be/X-ray binaries, low-mass X-ray binaries, ultraluminous X-ray Sources, and cataclysmic variables.In Chapter 1 we give a brief review on the basic knowledge of binary evolution, including stellar evolution, binary interaction, formation and evolution of X-ray binaries.In Chapter 2 we discuss the formation of Be stars through binary interaction. Be stars are rapidly rotating B type stars. The origin of their rapid rotation is not certain, but binary interaction remains to be a possibility. In this Chapter we investigate the formation of Be stars resulting from mass transfer in binaries in the Galaxy. We calculate the binary evolution with both stars evolving simultaneously and consider different possible mass accretion histories for the accretor. From the calculated results we obtain the critical mass ratios qcr that determine the stability of mass transfer. We also numerically calculate the parameter λ in common envelope evolution, and then incorporate both qcr and λ into the population synthesis calculations. We present the predicted numbers and characteristics of Be stars in binary systems with different types of companions, including helium stars, white dwarfs, neutron stars, and black holes. We find that in Be/neutron star binaries the Be stars can have a lower limit of mass ～8M⊙ if they are formed by stable (i.e., without the occurrence of common envelope evolution) and nonconservative mass transfer. We demonstrate that isolated Be stars may originate from both mergers of two main-sequence stars and disrupted Be binaries during the supernova explosions of the primary stars, but mergers seem to play a much more important role. Finally the fraction of Be stars which have involved binary interactions in all B type stars can be as high as-13%-30%, implying that most of Be stars may result from binary interaction.In Chapter 3 we show the evolution of intermediate- and low-mass X-ray binaries and the formation of millisecond pulsars. We present a systematic study of the evolution of intermediate-and low-mass X-ray binaries consisting of an accreting neutron star of mass 1.0-1.8M⊙ and a donor star of mass 1.0-6.0M⊙. In our calculations we take into account physical processes such as unstable disk accretion, radio ejection, bump-induced detachment, and outflow from the L2 point. Comparing the calculated results with the observations of binary radio pulsars, we report the following results. (1) The allowed parameter space for forming binary pulsars in the initial orbital period-donor mass plane increases with increasing neutron star mass. This may help explain why some millisecond pulsars with orbital periods longer than ～60 days seem to have less massive white dwarfs than expected. Alternatively, some of these wide binary pulsars may be formed through mass transfer driven by planet/brown dwarf-involved common envelope evolution. (2) Some of the pulsars in compact binaries might have evolved from intermediate-mass X-ray binaries with anomalous magnetic braking. (3) The equilibrium spin periods of neutron stars in low-mass X-ray binaries are in general shorter than the observed spin periods of binary pulsars by more than one order of magnitude, suggesting that either the simple equi-librium spin model does not apply, or there are other mechanisms/processes spinning down the neutron stars.In Chapter 4, angular momentum loss mechanisms in cataclysmic variables below the period gap is presented. Mass transfer in cataclysmic variables is usually considered to be caused by angular momentum loss driven by magnetic braking and gravitational radiation above the period gap, and solely by gravitational radiation below the period gap. The best-fit revised model of cataclysmic variable evolution recently by Knigge et al. (2011), however, indicates that angular momentum loss rate below the period gap is 2.47(±0.22) times the gravitational radiation rate, suggesting the existence of some other angular momentum loss mechanisms. We consider several kinds of consequential angular momentum loss mechanisms often invoked in the literature:isotropic wind from the accreting white dwarfs, outflows from the Langrangian points, and the formation of a circumbinary disk. We found that neither isotropic wind from the white dwarf nor outflow from the L1 point can explain the extra angular momentum loss rate, while ouflow from the L2 point or a circumbinary disk can effectively extract the angular momentum provided that ～(15-45)% of the transferred mass is lost from the binary. A more promising mechanism is a circumbinary disk exerting gravitational torque on the binary. In this case the mass loss fraction can be as low as (?)10-3.In Chapter 5 we present a study on a population of ultraluminous X-ray sources (ULXs) with an accreting neutron star. Most ULXs are believed to be X-ray binary systems, but previ- ous observational and theoretical studies tend to prefer a black hole rather than a neutron star accretor. The recent discovery of 1.37 s pulsations from the ULX M82 X-2 has established its nature as a magnetized neutron star. In this Chapter we model the formation history of neutron star ULXs in an M82- or Milky Way-like galaxy, by use of both binary population synthesis and detailed binary evolution calculations. We find that the birthrate is around 10-4 yr-1 for the incipient X-ray binaries in both cases. We demonstrate the distribution of the ULX popu-lation in the donor mass-orbital period plane. Our results suggest that, compared with black hole X-ray binaries, neutron star X-ray binaries may significantly contribute to the ULX pop-ulation, and high/intermediate-mass X-ray binaries dominate the neutron star ULX population in M82/Milky Way-like galaxies, respectively.In Chapter 6, the population of intermediate- and low-mass X-ray binaries in the Galaxy is explored. We investigate the formation and evolutionary sequences of Galactic intermediate-and low-mass X-ray binaries (I/LMXBs) by combining binary population synthesis (BPS) and detailed stellar evolutionary calculations. Using an updated BPS code we compute the evolution of massive binaries that leads to the formation of incipient I/LMXBs, and present their distribu-tion in the initial donor mass vs. initial orbital period diagram. We then follow the evolution of I/LMXBs until the formation of binary millisecond pulsars (BMSPs). We find that the birthrates of I/LMXB population are in the range of 9×10-6-3.4×10-5 yr-1, compatible with those of BMSPs, which are thought to descend from I/LMXBs. We show that during the evolution of I/LMXBs they are likely to be observed as relatively compact binaries with the orbital periods (?)1 day and the donor masses (?)0.3M⊙. The resultant BMSPs have orbital periods ranging from less than 1 day to a few hundred days. These features are consistent with observations of LMXBs and BMSPs. We also confirm the discrepancies between theoretical predications and observations mentioned in the literature, that is, the theoretical average mass transfer rates (～10-10M⊙ yr-1) of LMXBs are considerably lower than observed, and the number of BM-SPs with orbital periods ～0.1-1 day is severely underestimated. Both imply that something is missing in the modeling of LMXBs, which is likely to be related to the mechanisms of the orbital angular momentum loss.Finally in Chapter 7 we summarize our results and give the prospects for future work.