Evolutionary Sequences for Low‐ and Intermediate‐Mass X‐Ray Binaries

A binary in which a slightly evolved star starts mass transfer to a neutron star can evolve towards ultra-short orbital periods under the influence of magnetic braking. This is called magnetic capture. We investigate in detail for which initial orbital periods and initial donor masses binaries evolve to periods less than 30–40 min within the Hubble time. We show that only small ranges of initial periods and masses lead to ultra-short periods, and that for those only a small time interval is spent at ultra-short periods. Consequently, only a very small fraction of any population of X-ray binaries is expected to be observed at ultra-short period at any time. If 2 to 6 of the 13 bright X-ray sources in globular clusters have an ultra-short period, as suggested by recent observations, their formation cannot be explained by the magnetic capture model.

The masses of the white dwarfs in a binary carry information about previous mass-transfer phases. The core mass -- radius relation of low-mass giants gives the size of the progenitor of a helium white dwarf at the moment it last filled its Roche lobe. Previously, we used this information for a few observed systems to propose a new mass-transfer type based on an angular momentum balance. Our aim is to investigate if stable mass transfer instead of the angular-momentum prescription is consistent with the observed double-helium white-dwarf masses. We reconstructed the progenitor evolution of observed double-helium white dwarfs using the core mass -- radius relation and evaluated if the periods at the start of the second phases of mass transfer are consistent with the outcome of stable mass transfer. More generally, we calculated the mass distribution of double-helium white dwarfs for three different progenitor scenarios: double common envelope (with parameter α łambda), angular-momentum prescription (with parameter γ), and stable mass transfer. We find that the observed systems are generally not consistent with stable mass transfer. Stable mass transfer leads to a tight correlation between the two white dwarf masses in a binary that is not consistent with the observed mass distribution. Double-common-envelope evolution is a particularly poor fit to the observations. The angular-momentum prescription can populate the observed mass distribution, but not perfectly. We conclude that the first phase of mass transfer initiated on the red giant branch in low-mass systems does not generally proceed as stable mass transfer nor as a common envelope, and thus it is poorly understood. This may be related to the fact that for many observed binaries that have finished the first phase of mass transfer the orbit is eccentric, which is an unexpected outcome of mass transfer.

Evolutionary scenarios must account for Algol binaries surviving their first phase of mass transfer. The outcome of this phase is dependent upon the rapidity of the initial mass transfer, which can be estimated by calculating the radial reponse of potential progenitors to mass loss. Limits on the donor's evolutionary state, and its companion mass, can be placed on systems which would transfer mass on a thermal or dynamical timescale. Slower mass transfer rates are necessary for the successful transition to an Algol. Considering 1.5 and 5.0 M⊙ models, the former succeed in case A and Br systems, while the latter can do so only in case A systems. To evolve into an Algol binary, all systems seem to require initial mass ratios near one.

The evolution of binaries consisting of evolved main sequence stars (1 < M_d/Msun < 3.5) with white dwarf companions (0.7 < M_wd/Msun < 1.2) is investigated through the thermal mass transfer phase. Taking into account the stabilizing effect of a strong, optically thick wind from the accreting white dwarf surface, we have explored the formation of several evolutionary groups of systems for progenitors with initial orbital periods of 1 and 2 days. The numerical results show that CO white dwarfs can accrete sufficient mass to evolve to a Type Ia supernova and ONeMg white dwarfs can be built up to undergo accretion induced collapse for donors more massive than about 2 Msun. For donors less massive than ~2 Msun the system can evolve to form a He and CO or ONeMg white dwarf pair. In addition, sufficient helium can be accumulated (~0.1 Msun) in systems characterized by 1.6 < M_d/Msun < 1.9 and 0.8 < M_wd/Msun < 1 such that sub Chandrasekhar mass models for Type Ia supernovae, involving off center helium ignition, are possible for progenitor systems evolving via the Case A mass transfer phase. For systems characterized by mass ratios > 3 the system likely merges as a result of the occurrence of a delayed dynamical mass transfer instability. A semi-analytical model is developed to delineate these phases which can be easily incorporated in population synthesis studies of these systems.

Context. Wolf-Rayet (WR) and O-star binaries can be the progenitors of X-ray binaries and double black hole binaries. Their formation is not yet fully understood, however. For 21 observed WR+O systems, we aim to infer whether the mass transfer started on the main sequence (Case A) or later (Case B). We also calculated (limits on) the mass-transfer efficiency β, that is, the fraction of transferred mass that is accreted, and the parameter γ, which denotes the fraction of angular momentum of the binary that is lost per unit mass in units of the average angular momentum of the binary per unit mass. Aims. We inferred the possible values for the initial masses based on the observed WR masses and models for WR from the literature. With these initial primary masses, we created a grid of possible periods and secondary masses for which we determined the values that β and γ would have taken for either Case A or Case B mass transfer. Based on this, we also determined the case of mass transfer that is most likely for each system. Methods. Taking into account the progenitor distribution of WR+O binaries, we find that highly non-conservative Case A mass transfer seems to be the most likely scenario for the majority of systems as this can explain 14 out of 21 systems. The angular momentum loss is likely relatively high (typically γ > 1). Our finding that most systems in our sample experienced Case A mass transfer contradicts the expectation that most massive binaries go through Case B mass transfer. This suggests that post-case-B systems are significantly underrepresented in the observed WR+O binary population, either intrinsically or due to severe selection effects.

The evolution and the stability of mass transfer of CO+He white dwarf (WD) binaries are not well understood. Observationally they may emerge as AM CVn binaries and are important gravitational wave (GW) emitters. In this work, we have modeled the evolution of double WD binaries with accretor masses of 0.50–1.30 M ⊙ and donor masses of 0.17–0.45 M ⊙ using the detailed stellar evolution code mesa. We find that the evolution of binaries with same donor masses but different accretor masses is very similar and binaries with same accretor masses but larger He donor masses have larger maximum mass transfer rates and smaller minimum orbital periods. We also demonstrate that the GW signal from AM CVn binaries can be detected by spaceborne GW observatories, such as LISA and TianQin. There is a linear relation between the donor mass and gravitational wave frequency during the mass transfer phase. In our calculation, all binaries can have dynamically stable mass transfer, which is very different from previous studies. The threshold donor mass of Eddington-limited mass transfer for a given accretor WD mass is lower than previous studies. Assuming that a binary may enter a common envelope if the mass transfer rate exceeds the maximum stable burning rate of He, we provide a new criterion for double WDs surviving mass transfer, which is below the threshold of the Eddington limit. Finally, we find that some systems with oxygen–neon (ONe) WDs in our calculation may evolve into detached binaries consisting of neutron stars and extremely low-mass He WDs, and further ultracompact X-ray binaries.

Boriakoff et al.1 have reported the discovery of a 6.1-ms radio pulsar in a binary with an orbital period of 120 days, a1 sin i = 0.99 × 1012 cm, and e ≈ 0. This is the fourth binary radio pulsar, and the third to have a nearly circular orbit2. The origin of such systems has been discussed frequently3,4 and I now report that evolutionary history of the new millisecond pulsar is perhaps the simplest of them all. The rapid rotation of the pulsar, small mass function, circular orbit, and long binary period suggest that following the formation of a neutron star there had to be a phase of mass transfer from the low-mass secondary onto the neutron star primary. That mass transfer circularized the orbit and spun up the primary, and it required the secondary to be a red giant at that time. The present binary period of 120 days implies that the secondary has a mass of 0.3 M⊙. The observed mass function of 0.0027M⊙ implies that the primary must be less massive than 3.1M⊙, not an interesting mass limit for a neutron star. The secondary is probably a white dwarf at present. However, if the mass transfer terminated < 106 yr ago then the secondary may be still burning hydrogen at the rate of about 300L⊙, and it may be optically detectable.

Context.Despite 50 yr of extensive binary research, we must conclude that the Roche lobe overflow/mass transfer process that governs close binary evolution is still poorly understood.Aims.It is the scope of the present paper to lift the edge of the veil by studying the spin-up and spin-down processes of the O-type components of WR+O binaries.Methods.We critically analyzed the available observational data of rotation speeds of the O-type components in WR+O binaries. By combining a binary evolutionary code and a formalism that describes the effects of tides in massive stars with an envelope in radiative equilibrium, we computed the corresponding rotational velocities during the Roche lobe overflow of the progenitor binaries.Results.In all the WR+O binaries studied, we find that the O-type stars were affected by accretion of matter during Roche lobe overflow (RLOF) of the progenitor. This means that common envelope evolution, which excludes any accretion onto the secondary O star, has not played an important role in explaining WR+O binaries. Moreover, although it is very likely that the O-type star progenitors were spun up by mass transfer, many ended the RLOF (and mass transfer) phase with a rotational velocity that is significantly smaller than the critical rotation speed. This may indicate that during the mass transfer phase there is a spin-down process that is of the same order, although significantly less, than that of the spin-up process. We propose a Spruit–Tayler type dynamo spin-down suggested in the past to explain the rotation speeds of the mass gainers in long-period Algols.

Context. Numerous studies have established that in main-sequence binary systems, mass transfer generally proceeds from the initially more massive star to its less massive companion, thereby inducing rejuvenation in the latter. However, in certain massive close binary systems with orbital periods on the order of a few days, a reversed mass transfer scenario emerges: mass flows from the initially less massive component to the more massive one, during which the two stars simultaneously overflow their Roche lobes. This configuration potentially facilitates stellar rejuvenation in both members of the binary system. Aims. The phenomenon of reverse mass transfer in binary systems is closely linked to the efficiency of stellar rejuvenation in the mass accretor. However, the physical mechanism driving the rejuvenation of the accretor remains poorly understood. In this work, we employ the Schwarzschild criterion to define the boundaries of convective regions at the solar metallicity, as opposed to the Ledoux criterion typically used for convective conditions at low metallicities. Our study aims to investigate how mass transfer significantly influences the rejuvenation process of the mass-accreting star. Furthermore, we aim to systematically investigate how initial binary parameters (particularly the mass ratio and orbital period) regulate the initiation of reverse mass transfer from the secondary to the primary component. Methods. We constructed a new set of detailed, grid-based binary evolution models, systematically varying initial orbital periods and mass ratios, q, within a parameter space. Results. Our results show that for systems with initial primary masses of 16 M⊙ and initial mass ratios of qini= M2M1 ≥ 0.4, those with shorter initial orbital periods, Porb &lt; 1.8 days, are statistically more prone to evolving into contact binaries that exhibit reverse mass transfer. The results further demonstrate that stellar rejuvenation significantly influences the overall evolution of binary systems, notably extending the main-sequence lifetime of the mass-gaining star. Specifically, rejuvenation can induce increases in both the radius and luminosity of the accretor, potentially triggering reverse mass transfer. The transfer causes the mass of accretor’s convective core to increase, facilitating the mixing of fresh fuel from outer layers into the central nuclear-burning region. Following mass transfer, the evolutionary state of the accretor is closer to the zero age main sequence. Due to the high efficiency of rejuvenation, the mass-gaining star can even outpace the mass-losing star in terms of evolution. Meanwhile, the initially more massive star can also undergo rejuvenation via reverse mass transfer, as it must rapidly adapt to its newly increased mass.

Context.The stability of mass transfer is critical in determining pathways towards various kinds of compact binaries, such as compact main-sequence white-dwarf binaries, and transients, such as double white-dwarf mergers and luminous red novae. Despite its importance, very few systematic studies of the stability of mass transfer exist.Aims.We study the behaviour of mass-losing donor stars in binary systems in a systematic way. We focus on identifying and understanding the parameter space for stable mass transfer in low- and intermediate-mass binaries with post-main-sequence donor stars as well as the properties of ultimately unstable binary systems at the onset of the instabilities.Methods.We employed the 1D stellar evolution code MESA to simulate the mass-transfer evolution of 1404 binary systems with donor-star masses between 1 M⊙and 8 M⊙. We studied the behaviour of the binaries during mass transfer, without assuming that the donor star responds adiabatically to mass loss. We treated the accretor as a point mass, which we do not evolve, and assumed the mass transfer is conservative.Results.We considered several criteria to define when unstable mass transfer occurs. We find that the criterion that best predicts the onset of runaway mass transfer is based on the transition to an effectively adiabatic donor response to mass loss. Using this quasi-adiabatic criterion, we determine the location of the stability boundary to within a relative uncertainty of five per cent in the mass ratio at the onset of mass transfer. Defining this critical mass ratio (qqad) in terms of accretor mass over donor mass, we find thatqqad ∼ 0.25 for stars with radiative envelopes that cross the Hertzsprung gap, while for convective giantsqqaddecreases from ∼1 at the base of the red giant branch to ∼0.1 at the onset of thermal pulses on the asymptotic giant branch. Compared with recent similar studies, we find increased stability of mass transfer from convective giants. This is because an effectively adiabatic response of the donor star only occurs at a very high critical mass-transfer rate due to the short local thermal timescale in the outermost layers of a red giant. Furthermore, we find that forq &gt; qqadmass transfer is self-regulated, but that for evolved giants the resulting mass-transfer rates can be so high that the evolution becomes dynamical and/or the donor can overflow its outer lobe.Conclusions.Our results indicate that mass transfer is stable for a wider range of binary parameter space than typically assumed in rapid binary population synthesis. Moreover, we find a systematic dependence of the critical mass ratio on the donor star mass and radius, which may have significant consequences for predictions of post-mass-transfer populations.

2MASS J15274848+3536572 (J1527) is a semidetached binary system consisting of a main-sequence star and a white dwarf (WD) in an orbit of 0.2556686 day. The magnetic braking (MB) mechanism plays an important role in driving the mass transfer of binary systems with an orbital period longer than 3 hr. Based on the standard and saturated MB laws, in this work we perform a detailed stellar evolution model for the formation of J1527. The simulated results indicate that two MB laws can successfully reproduce the observed orbital period, WD mass, donor-star mass, donor-star radius, surface gravity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">log</mml:mi> <mml:mi>g</mml:mi> </mml:math> ) and effective temperature of the donor star. However, the standard and saturated MB laws predicted a current mass transfer rate of 10 −8 and 7.5 × 10 −10 M ⊙ yr −1 , respectively, which are much higher than the inferred value (≤3.9 × 10 −11 M ⊙ yr −1 ) according to the effective temperature detected in the WD. A sudden mass loss (4 × 10 −4 M ⊙ ) caused by the recent strong hydrogen shell flash on the surface of the WD could result in an instantaneous orbital expansion and a sharp decay of the mass-transfer rate. To produce inferred mean mass transfer rate, it requires a relatively low mass transfer rate prior to the hydrogen shell flash, which favors the saturated MB law.

We explore properties of Type Ib and IIb SN progenitors that are produced by stable mass transfer in binary systems using a new grid of stellar evolution models from an initial primary mass in the range of at solar and Large Magellanic Cloud metallicities. We find that blue and yellow supergiant SN IIb progenitors (e.g., of SN 2008ax, SN 2011dh, and SN 2016gkg) have a hydrogen envelope mass less than about , mostly resulting from early Case B mass transfer with relatively low initial masses and/or low metallicity. Red supergiant (RSG) SN IIb progenitors (e.g., of SN 1993J, SN 2013df) are produced via late Case B mass transfers and have a more massive hydrogen envelope ( ). SN Ib progenitors are predominantly produced by early Case B mass transfers. Our models predict that SN IIb progenitors are systematically more luminous in the optical ( ) than the majority of SN Ib progenitors ( ) for our considered initial mass range. However, the optically bright progenitor of SN Ib iPTF13bvn (i.e., ) can be well explained by a relatively low-mass progenitor with a final mass of . The event rate of blue and yellow SN IIb progenitors would increase as metallicity decreases, while the event rate of SN Ib progenitors would decrease instead. By contrast, the population of RSG SN IIb progenitors would not be significantly affected by metallicity.

The evolution of a binary star system by various analytical and numerical approximations of mass transfer rate normalized to the equilibrium rate and its stability conditions are investigated. We present results from investigations of mass transfer and stability in close binary star systems using the different orbital parameters. The stability and instability of mass transfer in binary star evolution depends on the exchange of material which the response of the binary to the initial Roche lobe overflow causes the donor to loose even more material. Our work is mainly focused on basic mathematical derivations, analytical and numerical solutions in order to explain the mass transfer system in different orbital parameters as well as the results are compared with previous studies in both cases. Mass transfer is usually stable, as long as the winds specific angular momentum does not exceed the angular momentum per reduced mass of the system. This holds for both dynamical and thermal time scales. Those systems which are not stable will usually transfer mass on the thermal time scale. The variation of Roche lobe radius with mass ratio in the binary, for various orbital parameters in the conservative and non-conservative mass transfer, as well as the evolution equations, orbital angular momentum of the binary system and the corresponding analytical and numerical solutions for different cases, under certain restrictive approximations is derived, simulated and discussed.

We examine the proposal that the subset of neutron-star and black-hole X-ray binaries that form with Ap or Bp star companions will experience systemic angular-momentum losses due to magnetic braking, not otherwise operative with intermediate-mass companion stars. We suggest that for donor stars possessing the anomalously high magnetic fields associated with Ap and Bp stars, a magnetically coupled, irradiation-driven stellar wind can lead to substantial systemic loss of angular momentum. Hence, these systems, which would otherwise not be expected to experience ‘magnetic braking’, evolve to shorter orbital periods during mass transfer. In this paper, we detail how such a magnetic braking scenario operates. We apply it to a specific astrophysics problem involving the formation of compact black-hole binaries with low-mass donor stars. At present, it is not understood how these systems form, given that lowmass companion stars are not likely to provide sufficient gravitational potential to unbind the envelope of the massive progenitor of the black hole during a prior ‘common-envelope’ phase. On the other hand, intermediate-mass companions, such as Ap and Bp stars, could more readily eject the common envelope. However, in the absence of magnetic braking, such systems tend to evolve to long orbital periods. We show that, with the proposed magnetic braking properties afforded by Ap and Bp companions, such a scenario can lead to the formation of compact black-hole binaries with orbital periods, donor masses, lifetimes and production rates that are in accord with the observations. In spite of these successes, our models reveal a significant discrepancy between the calculated effective temperatures and the observed spectral types of the donor stars. Finally, we show that this temperature discrepancy would still exist for other scenarios invoking initially intermediate-mass donor stars, and this presents a substantial unresolved mystery.

The distributions of the initial main-sequence binary parameters are one of the key ingredients in obtaining evolutionary predictions for compact binary (BH–BH/BH–NS/NS–NS) merger rates. Until now, such calculations were done under the assumption that initial binary parameter distributions were independent. For the first time, we implement empirically derived inter-correlated distributions of initial binary parameters primary mass (M1), mass ratio (q), orbital period (P), and eccentricity (e). Unexpectedly, the introduction of inter-correlated initial binary parameters leads to only a small decrease in the predicted merger rates by a factor of ≲2–3 relative to the previously used non-correlated initial distributions. The formation of compact object mergers in the isolated classical binary evolution favours initial binaries with stars of comparable masses (q ≈ 0.5–1) at intermediate orbital periods (log P (days) = 2–4). New distributions slightly shift the mass ratios towards lower values with respect to the previously used flat q distribution, which is the dominant effect decreasing the rates. New orbital periods (∼1.3 more initial systems within log P (days) = 2–4), together with new eccentricities (higher), only negligibly increase the number of progenitors of compact binary mergers. Additionally, we discuss the uncertainty of merger rate predictions associated with possible variations of the massive-star initial mass function (IMF). We argue that evolutionary calculations should be normalized to a star formation rate (SFR) that is obtained from the observed amount of UV light at wavelength 1500 Å (an SFR indicator). In this case, contrary to recent reports, the uncertainty of the IMF does not affect the rates by more than a factor of ∼2. Any change to the IMF slope for massive stars requires a change of SFR in a way that counteracts the impact of IMF variations on compact object merger rates. In contrast, we suggest that the uncertainty in cosmic SFR at low metallicity can be a significant factor at play.