Onset Of Roche-lobe Overflow Research Articles

X-ray luminosity function of high-mass X-ray binaries: Studying the signatures of different physical processes using detailed binary evolution calculations

Context. Many physical processes taking place during the evolution of binary stellar systems remain poorly understood. The ever-expanding observational sample of X-ray binaries (XRBs) makes them excellent laboratories for constraining binary evolution theory. Such constraints and useful insights can be obtained by studying the effects of various physical assumptions on synthetic X-ray luminosity functions (XLFs) and comparing them with observed XLFs. Aims. In this work we focus on high-mass X-ray binaries (HMXBs) and study the effects on the XLF of various, poorly constrained assumptions regarding physical processes, such as the common-envelope phase, core collapse, and wind-fed accretion. Methods. We used the new binary population synthesis code POSYDON, which employs extensive precomputed grids of detailed stellar structure and binary evolution models, to simulate the entire evolution of binaries. We generated 96 synthetic XRB populations corresponding to different combinations of model assumptions, including different prescriptions for supernova kicks, supernova remnant masses, common-envelope evolution, circularization at the onset of Roche-lobe overflow, and observable wind-fed accretion. Results. The generated HMXB XLFs are feature-rich, deviating from the commonly assumed single power law. We find a break in our synthetic XLF at luminosity ∼1038 erg s−1, similar to observed XLFs. However, we also find a general overabundance of XRBs (up to a factor of ∼10 for certain model parameter combinations) driven primarily by XRBs with black hole accretors. Assumptions about the transient behavior of Be XRBs, asymmetric supernova kicks, and common-envelope physics can significantly affect the shape and normalization of our synthetic XLFs. We find that less well-studied assumptions regarding the circularization of the orbit at the onset of Roche-lobe overflow and criteria for the formation of an X-ray-emitting accretion disk around wind-accreting black holes can also impact our synthetic XLFs and reduce the discrepancy with observations. Conclusions. Our synthetic XLFs do not always agree well with observations, especially at intermediate X-ray luminosities, which is likely due to uncertainties in the adopted physical assumptions. While some model parameters leave distinct imprints on the shape of the synthetic XLFs and can reduce this deviation, others do not have a significant effect overall. Our study reveals the importance of large-scale parameter studies, highlighting the power of XRBs in constraining binary evolution theory.

An Analytic Model for Mass Transfer in Binaries with Arbitrary Eccentricity, with Applications to Triple-star Systems

Abstract Most studies of mass transfer in binary systems assume circular orbits at the onset of Roche lobe overflow. However, there are theoretical and observational indications that mass transfer could occur in eccentric orbits. In particular, eccentricity could be produced via sudden mass loss and velocity kicks during supernova explosions, or Lidov–Kozai (LK) oscillations in hierarchical triple systems, or, more generally, secular evolution in multiple-star systems. However, current analytic models of eccentric mass transfer are faced with the problem that they are only well defined in the limit of very high eccentricities and break down for less eccentric and circular orbits. This provides a major obstacle to implementing such models in binary and higher-order population synthesis codes, which are useful tools for studying the long-term evolution of a large number of systems. Here we present a new analytic model to describe the secular orbital evolution of binaries undergoing conservative mass transfer. The main improvement of our model is that the mass transfer rate is a smoothly varying function of orbital phase, rather than a delta function centered at periapsis. Consequently, our model is in principle valid for any eccentricity, thereby overcoming the main limitation of previous works. We implement our model in an easy-to-use and publicly available code that can be used as a basis for implementations of our model into population synthesis codes. We investigate the implications of our model in a number of applications with circular and eccentric binaries and triples undergoing LK oscillations.

Composite hot subdwarf binaries – I. The spectroscopically confirmed sdB sample

Hot subdwarf-B (sdB) stars in long-period binaries are found to be on eccentric orbits, even though current binary-evolution theory predicts that these objects are circularized before the onset of Roche lobe overflow (RLOF). To increase our understanding of binary interaction processes during the RLOF phase, we started a long-term observing campaign to study wide sdB binaries. In this paper, we present a sample of composite binary sdBs, and the results of the spectral analysis of nine such systems. The grid search in stellar parameters (gssp) code is used to derive atmospheric parameters for the cool companions. To cross-check our results and also to characterize the hot subdwarfs, we used the independent XTgrid code, which employs Tlusty non-local thermodynamic equilibrium models to derive atmospheric parameters for the sdB component and phoenix synthetic spectra for the cool companions. The independent gssp and XTgrid codes are found to show good agreement for three test systems that have atmospheric parameters available in the literature. Based on the rotational velocity of the companions, we make an estimate for the mass accreted during the RLOF phase and the minimum duration of that phase. We find that the mass transfer to the companion is minimal during the subdwarf formation.

TIDALLY DRIVEN ROCHE-LOBE OVERFLOW OF HOT JUPITERS WITH MESA

Many exoplanets have now been detected in orbits with ultra-short periods, very close to the Roche limit. Building upon our previous work, we study the possibility that mass loss through Roche lobe overflow (RLO) may affect the evolution of these planets, and could possibly transform a hot Jupiter into a lower-mass planet (hot Neptune or super-Earth). We focus here on systems in which the mass loss occurs slowly ("stable mass transfer" in the language of binary star evolution) and we compute their evolution in detail with the binary evolution code MESA. We include the effects of tides, RLO, irradiation and photo-evaporation of the planet, as well as the stellar wind and magnetic braking. Our calculations all start with a hot Jupiter close to its Roche limit, in orbit around a sun-like star. The initial orbital decay and onset of RLO are driven by tidal dissipation in the star. We confirm that such a system can indeed evolve to produce lower-mass planets in orbits of a few days. The RLO phase eventually ends and, depending on the details of the mass transfer and on the planetary core mass, the orbital period can remain around a few days for several Gyr. The remnant planets have a rocky core and some amount of envelope material, which is slowly removed via photo-evaporation at nearly constant orbital period; these have properties resembling many of the observed super-Earths and sub-Neptunes. For these remnant planets we also predict an anti-correlation between mass and orbital period; very low-mass planets ($M_{\rm pl}\,\lesssim\,5\,M_{\oplus}$) in ultra-short periods ($P_{\rm orb}$<1d) cannot be produced through this type of evolution.

Testing eccentricity pumping mechanisms to model eccentric long-period sdB binaries with MESA

Hot subdwarf-B stars in long-period binaries are found to be on eccentric orbits, even though current binary-evolution theory predicts those objects to be circularised before the onset of Roche-lobe overflow (RLOF). We aim to find binary-evolution mechanisms that can explain these eccentric long-period orbits, and reproduce the currently observed period-eccentricity diagram. Three different processes are considered; tidally-enhanced wind mass-loss, phase-dependent RLOF on eccentric orbits and the interaction between a circumbinary disk and the binary. The binary module of the stellar-evolution code MESA (Modules for Experiments in Stellar Astrophysics) is extended to include the eccentricity-pumping processes. The effects of different input parameters on the final period and eccentricity of a binary-evolution model are tested with MESA. The end products of models with only tidally-enhanced wind mass-loss can indeed be eccentric, but these models need to lose too much mass, and invariably end up with a helium white dwarf that is too light to ignite helium. Within the tested parameter space, no sdBs in eccentric systems are formed. Phase-dependent RLOF can reintroduce eccentricity during RLOF, and could help to populate the short-period part of the period-eccentricity diagram. When phase-dependent RLOF is combined with eccentricity pumping via a circumbinary disk, the higher eccentricities can be reached as well. A remaining problem is that these models favour a distribution of higher eccentricities at lower periods, while the observed systems show the opposite. The models presented here are potentially capable of explaining the period-eccentricity distribution of long-period sdB binaries, but further theoretical work on the physical mechanisms is necessary.

THE ORIGIN OF BLACK HOLE SPIN IN GALACTIC LOW-MASS X-RAY BINARIES

Galactic field black hole (BH) low-mass X-ray binaries (LMXBs) are believed to form in situ via the evolution of isolated binaries. In the standard formation channel, these systems survived a common envelope phase, after which the remaining helium core of the primary star and the subsequently formed BH are not expected to be highly spinning. However, the measured spins of BHs in LMXBs cover the whole range of spin parameters. We propose here that the BH spin in LMXBs is acquired through accretion onto the BH after its formation. In order to test this hypothesis, we calculated extensive grids of detailed binary mass-transfer sequences. For each sequence, we examined whether, at any point in time, the calculated binary properties are in agreement with their observationally inferred counterparts of 16 Galactic LMXBs. The "successful" sequences give estimates of the mass that the BH has accreted since the onset of Roche-Lobe overflow. We find that in all Galactic LMXBs with measured BH spin, the origin of the spin can be accounted for by the accreted matter, and we make predictions about the maximum BH spin in LMXBs where no measurement is yet available. Furthermore, we derive limits on the maximum spin that any BH can have depending on current properties of the binary it resides in. Finally we discuss the implication that our findings have on the BH birth-mass distribution, which is shifted by ~1.5 Msolar towards lower masses, compared to the currently observed one.

The coupled effect of tides and stellar winds on the evolution of compact binaries

We follow the evolution of compact binaries under the coupled effect of tides and stellar winds until the onset of Roche-lobe overflow. These binaries contain a compact object (either a black-hole, a neutron-star, or a planet) and a stellar component. We integrate the full set of tidal equations, which are based on Hut's model for tidal evolution, and we couple them with the angular momentum loss in a stellar wind. Our aim is twofold. Firstly, we wish to highlight some interesting evolutionary outcomes of the coupling. When tides are coupled with a non-massive stellar wind, one interesting outcome is that in certain types of binaries, the stellar spin tends to reach a quasi-equilibrium state, where the effect of tides and wind are counteracting each other. When tides are coupled with a massive wind, we parametrize the evolution in terms of the decoupling radius, at which the wind decouples from the star. Even for small decoupling radii this \emph{wind braking} can drive systems on the main sequence to Roche-lobe overflow that otherwise would fail to do so. Our second aim is to inspect whether simple timescale considerations are a good description of the evolution of the systems. We find that simple timescale considerations, which rely on neglecting the coupling between tides and stellar winds, do not accurately represent the true evolution of compact binaries. The outcome of the coupled evolution of the rotational and orbital elements can strongly differ from simple timescale considerations, as already pointed out by Barker & Ogilvie 2009 in the case of short-period planetary systems.

INTERACTING BINARIES WITH ECCENTRIC ORBITS. III. ORBITAL EVOLUTION DUE TO DIRECT IMPACT AND SELF-ACCRETION

The rapid circularization and synchronization of the stellar components in an eccentric binary system at the onset of Roche lobe overflow (RLO) is a fundamental assumption common to all binary stellar evolution and population synthesis codes, even though the validity of this assumption is questionable both theoretically and observationally. Here we calculate the evolution of the orbital elements of an eccentric binary through the direct three-body integration of a massive particle ejected through the inner Lagrangian point of the donor star at periastron. The trajectory of this particle leads to three possible outcomes: direct accretion (DA) onto the companion star within a single orbit, self-accretion (SA) back onto the donor star within a single orbit, or a quasi-periodic orbit around the companion star. We calculate the secular evolution of the binary orbit in the first two cases and conclude that DA can increase or decrease the orbital semi-major axis and eccentricity, while SA always decreases the orbital both orbital elements. In cases where mass overflow contributes to circularizing the orbit, circularization can set in on timescales as short as a few per cent of the mass transfer timescale. In cases where mass overflow increases the eccentricity, the orbital evolution is governed by competition between mass overflow and tidal torques. In the absence of tidal torques, mass overflow resulting in DI can lead to substantially subsynchronously rotating donor stars. Contrary to common assumptions, DI furthermore does not always provide a strong sink of orbital angular momentum in close mass-transferring binaries; in fact we instead find that a significant part can be returned to the orbit during the particle orbit. The formulation presented here can be combined with stellar and binary evolution codes to generate a better picture of the evolution of eccentric, RLO binary star systems.

UNDERSTANDING COMPACT OBJECT FORMATION AND NATAL KICKS. II. THE CASE OF XTE J1118 + 480

In recent years, an increasing number of proper motions have been measured for Galactic X-ray binaries. When supplemented with accurate determinations of the component masses, orbital period, and donor effective temperature, these kinematical constraints harbor a wealth of information on the system's past evolution. Here, we consider all this available information to reconstruct the full evolutionary history of the black hole X-ray binary XTE J1118+480, assuming that the system originated in the Galactic disk and the donor has solar metallicity. This analysis accounts for four evolutionary phases: mass transfer through the ongoing X-ray phase, tidal evolution before the onset of Roche-lobe overflow, motion through the Galactic potential after the formation of the black hole, and binary orbital dynamics due to explosive mass loss and possibly a black hole natal kick at the time of core collapse. We find that right after black hole formation, the system consists of a ~6.0-10.0 solar masses black hole and a ~1.0-1.6 solar masses main-sequence star. We also find that that an asymmetric natal kick is not only plausible but required for the formation of this system, and derive a lower and upper limit on the black hole natal kick velocity magnitude of 80 km/s and 310 km/s, respectively.

Mass transfer from a giant star to a main-sequence companion and its contribution to long-orbital-period blue stragglers

Binary population synthesis shows that mass transfer from a giant star to a main-sequence (MS) companion may account for some observed long-orbital period blue stragglers. However, little attention {\bf is paid to this blue straggler formation scenario} as dynamical instability often happens when the mass donor is a giant star. In this paper, we have studied the critical mass ratio, $q_{\rm c}$, for dynamically stable mass transfer from a giant star to a MS companion using detailed evolution calculations. The results show that a more evolved star is generally less stable for Roche lobe overflow. Meanwhile, $q_{\rm c}$ almost linearly increases with the amount of the mass and angular momentum {\bf lost} during mass transfer, but has little dependance on stellar wind. To conveniently use the result, we give a fit of $q_{\rm c}$ as a function of the stellar radius at the onset of Roche lobe overflow and of the mass transfer efficiency during the Roche lobe overflow. To examine the formation of blue stragglers from mass transfer between giants and MS stars, we have performed Monte Carlo simulations with various $q_{\rm c}$. {\bf The simulations show that some binaries with the mass donor on the first giant branch may contribute to blue stragglers with $q_{\rm c}$ obtained in this paper but will not from previous $q_{\rm c}$. Meanwhile, from our $q_{\rm c}$, blue stragglers from the mass transfer between an AGB star and a MS companion may be more numerous and have a wider range of orbital periods than those from the other $q_{\rm c}$.

Understanding Compact Object Formation and Natal Kicks. I. Calculation Methods and the Case of GRO J1655−40

In recent years proper-motion measurements have been added to the set of observational constraints on the current properties of Galactic X-ray binaries. We develop an analysis that allows us to consider all this available information and reconstruct the full evolutionary history of X-ray binaries back to the time of core collapse and compact object formation. This analysis accounts for five evolutionary phases: mass transfer through the ongoing X-ray phase, tidal circularization before the onset of Roche lobe overflow, motion through the Galactic potential after the formation of the compact object, binary orbital dynamics at the time of core collapse, and hydrodynamic modeling of the core collapse that connects the compact object to its progenitor and any nucleosynthetic constraints available. In this first paper we present this analysis in a comprehensive manner and apply it to the soft X-ray transient GRO J1655-40. This is the first analysis that incorporates all observational constraints on the current system properties and uses the full three-dimensional peculiar velocity constraints right after core collapse instead of lower limits on the current space velocity given by the present-day radial velocity. We find that the system has remained within 200 pc from the Galactic plane throughout its entire lifetime and that the mass loss and a kick possibly associated with the black hole formation imparted a kick velocity of ≃45-115 km s-1 to the binary's center of mass. Right after black hole formation, the system consists of a ≃3.5-6.3 M☉ black hole and a ≃2.3-4 M☉ main-sequence star. At the onset of the X-ray phase the donor is still on the main sequence. We find that a symmetric black hole formation event cannot be formally excluded but that the associated system parameters are only marginally consistent with the currently observed binary properties. Black hole formation mechanisms involving an asymmetric supernova explosion with associated black hole kick velocities of a few tens of km s-1, on the other hand, satisfy the constraints much more comfortably. We also derive an upper limit on the black hole kick magnitude of ≃210 km s-1.

Low- and intermediate-mass close binary evolution and the initial-final mass relation - III. Conservative case with convective overshooting and non-conservative case without overshooting

We have completed our series of calculation of case B evolution of Population I close binaries by including a conservative case with convective overshooting and a non-conservative case without convective overshooting in this paper. To apply the results easily to binary population synthesis, we fit two formulae for the remnant mass as a function of the initial mass of the primary, the radius of the primary at the onset of Roche lobe overflow (RLOF) and the initial mass ratio, with errors less than 1.9 per cent and 3.6 per cent for the conservative and non-conservative cases, respectively. We have also made comparisons between the results in this paper and those of previous studies in this series to examine the effects of our assumptions. We find that the remnant mass depends on when RLOF begins in the Hertzsprung gap and the dependence increases with the mass of the primary. Helium-carbon-oxygen white dwarfs are formed in this series of calculation. Both the non-conservative assumption and convective overshooting make RLOF more stable: some binaries with initial mass ratios q (i) = 4.0 are dynamically stable during RLOF in all cases except for the conservative case without overshooting. From these models, we have discussed potential electron-degenerate oxygen-neon cores. Finally, we show the conditions under which one evolution scenario may be more likely than the others according to the results of previous authors.

Low- and intermediate-mass close binary evolution and the initial-final mass relation - II. Non-conservative case with convective overshooting

Employing Eggleton's stellar evolution code, we carry out 150 runs of non-conservative population I binary evolution calculations with the initial primary mass between 1 and 8 M⊙, the initial mass ratio q=M1/M2 between 1.1 and 4 and the onset of Roche lobe overflow (RLOF) at early, middle or late Hertzsprung gap. Convective overshooting is included in our models and we assume that 50 per cent of the mass lost from the primary during the RLOF is accreted on to the secondary. The other 50 per cent is lost from the system, carrying away the same specific angular momentum as the centre of mass of the primary. We find that the remnant mass depends on when the RLOF begins in the Hertzsprung gap and the dependence increases with the primary mass. The remnant mass, however, does not depend much on the initial mass ratio, as in conservative cases. For qi= 1.1, we fit a formula for the remnant mass as a function of the initial mass M1i of the primary and the radius of the primary at the onset of RLOF with an error of less than 2.61 per cent. We have also discussed the influences of the convective overshooting that makes the helium burning and carbon burning earlier and the final mass of the primary larger (for M1i greater than 1.6 M⊙). The convective overshooting has no effect for low-mass binaries, consistent with the results of previous studies.

Low- and intermediate-mass close binary evolution and the initial-final mass relation

Using Eggleton's stellar evolution code, we carry out 150 runs of Population I binary evolution calculations with the initial primary mass between 1 and 8 M-circle dot, the initial mass ratio q = M-1/M-2 between 1.1 and 4, and the onset of Roche lobe overflow (RLOF) at an early, middle or late Hertzsprung-gap stage. We assume that PLOP is conservative in the calculations, and find that the remnant mass of the primary may change by more than 40 per cent over the range of initial mass ratio or orbital period, for a given primary mass. This is contrary to the often-held belief that the remnant mass depends only on the progenitor mass if mass transfer begins in the Hertzsprung gap. We fit a formula, with an error less than 3.6 per cent, for the remnant (white dwarf) mass as a function of the initial mass M-li of the primary, the initial mass ratio q(i) and the radius of the primary at the onset of RLOF We also find that a carbon-oxygen white dwarf with mass as low as 0.33 M-circle dot may be formed if the initial mass of the primary is around 2.5 M-circle dot.

The Initial–Final Mass Relation for Close Low–Intermediate-Mass Binaries (Non-conservative Case)

AbstractEmploying Eggleton’s stellar evolution code, we carry out 150 runs of non-conservative Population I binary evolution calculations with the initial primary mass between 1 and 8 M⊙, the initial mass ratio q = M1/M2 between 1.1 and 4 and the onset of Roche lobe overflow (RLOF) at the early, middle or late Hertzsprung gap. We assume that 50 per cent of the mass lost from the primary during the RLOF is accreted on to the secondary, the other 50 per cent is lost from the system, carrying away the same specific angular momentum as the centre of mass of the primary. We find that the remnant mass depends on when the RLOF begins in the Hertzsprung-gap and the dependency increases with the primary mass. The remnant mass, however, does not depend much on the initial mass ratio, as compared to conservative cases. For qi = 1.1, we fit a formula for the remnant mass as a function of the initial mass M1i of the primary and the radius of the primary at the onset of RLOF with an error less than 2.61 per cent.

White Dwarfs in Cataclysmic Variables

ABSTRACTPrior to the last 15 years, the literature on cataclysmic variables (CVs) contained little on the properties of the underlying white dwarf accreter other than estimates of their masses. They were regarded simply as nondescript potential wells for studies of accretion disk structure and stability. Estimates of their masses and associated core compositions were discussed, but only in the context of thermonuclear runaway theory. With the advent of space spectroscopy, especially HST, IUE, EUVE, and HUT, direct spectroscopic observations of exposed white dwarfs in CVs were carried out during dwarf nova quiescence or low brightness states of nova‐like variables and magnetic CVs when accretion rates were very low. This review covers new insights and physical properties of white dwarfs in nonmagnetic and magnetic CVs, including surface temperatures, heating and cooling measurements, rotational velocities, CV white dwarf masses (including Einstein redshift masses), photospheric chemical abundances (including composition relics of ancient novae), accretion belts, the physics of accretion heating, and long‐term CV evolution. For an ensemble of 37 CV degenerates with secure temperatures, the average Teff=20,800 K, for nonmagnetic CV degenerates Teff=24,100 K, and for magnetic CV degenerates Teff=16,400 K. The lowest Teff values are associated with magnetic CVs and with systems whose orbital periods are less than 2 hr. Thermal e‐folding times of the white dwarf envelope in response to accretion heating are in the range 6–600 days, photospheric chemical abundances range from moderately subsolar to greatly above solar, and rotational velocities lie within the range 50 km s−1<Vsin i<1200 km s−1. If pre‐CV white dwarfs had time to cool to 10-3L⊙ prior to the onset of Roche lobe overflow, then their average lower limit lifetime is 2.5 × 108 yr, and they have been accretion heated to an average luminosity log (L/L⊙) = 1.90 or, on average, by ∼11,000 K since the end of their pre‐CV evolution phase.