arXiv subjects

B. Willems

Publications and source records attributed to B. Willems.

At least 19 recordsLinked to original sources

arXiv2010

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.

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arXiv2009

A comprehensive population synthesis study of post-common envelope binaries

We apply population synthesis techniques to calculate the present day population of post-common envelope binaries (PCEBs) for a range of theoretical models describing the common envelope (CE) phase. Adopting the canonical energy budget approach we consider models where the ejection efficiency, $α_{\rmn{CE}}$ is either a constant, or a function of the secondary mass. We obtain the envelope binding energy from detailed stellar models of the progenitor primary, with and without the thermal and ionization energy, but we also test a commonly used analytical scaling. We also employ the alternative angular momentum budget approach, known as the $γ$-algorithm. We find that a constant, global value of $α_{\rmn{CE}} \ga 0.1$ can adequately account for the observed population of PCEBs with late spectral-type secondaries. However, this prescription fails to reproduce IK Pegasi, which has a secondary with spectral type A8. We can account for IK Pegasi if we include thermal and ionization energy of the giant's envelope, or if we use the $γ$-algorithm. However, the $γ$-algorithm predicts local space densities that are 1 to 2 orders of magnitude greater than estimates from observations. In contrast, the canonical energy budget prescription with an initial mass ratio distribution that favours unequal initial mass ratios gives a local space density which is in good agreement with observations, and best reproduces the observed distribution of PCEBs. Finally, all models fail to reproduce the sharp decline for orbital periods, $P_{\rmn{orb}} \ga 1$ d in the orbital period distribution of observed PCEBs, even if we take into account selection effects against systems with long orbital periods and early spectral-type secondaries.

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arXiv2009

Interacting Binaries with Eccentric Orbits II. Secular Orbital Evolution Due To Non-Conservative Mass Transfer

We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, allowing for both mass and angular momentum loss from the system. Adopting a delta function mass transfer rate at the periastron of the binary orbit, we find that, depending on the initial binary properties at the onset of mass transfer, the orbital semi-major axis and eccentricity can either increase or decrease at a rate linearly proportional to the magnitude of the mass transfer rate at periastron. The range of initial binary mass ratios and eccentricities that leads to increasing orbital semi-major axes and eccentricities broadens with increasing degrees of mass loss from the system and narrows with increasing orbital angular momentum loss from the binary. Comparison with tidal evolution timescales shows that the usual assumption of rapid circularization at the onset of mass transfer in eccentric binaries is not justified, irrespective of the degree of systemic mass and angular momentum loss. This work extends our previous results for conservative mass transfer in eccentric binaries and can be incorporated into binary evolution and population synthesis codes to model non-conservative mass transfer in eccentric binaries.

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arXiv2009

Energy Dissipation through Quasi-Static Tides in White Dwarf Binaries

We study tidal interactions in white dwarf binaries in the limiting case of quasi-static tides. The formalism is valid for arbitrary orbital eccentricities and therefore applicable to white dwarf binaries in the Galactic disk as well as globular clusters. In the quasi-static limit, the total perturbation of the gravitational potential shows a phase shift with respect to the position of the companion, the magnitude of which is determined primarily by the efficiency of energy dissipation through convective damping. We determine rates of secular evolution of the orbital elements and white dwarf rotational angular velocity for a 0.3 solar mass helium white dwarf in binaries with orbital frequencies in the LISA gravitational wave frequency band and companion masses ranging from 0.3 to 10^5 solar masses. The resulting tidal evolution time scales for the orbital semi-major axis are longer than a Hubble time, so that convective damping of quasi-static tides need not be considered in the construction of gravitational wave templates of white dwarf binaries in the LISA band. Spin-up of the white dwarf, on the other hand, can occur on time scales of less than 10Myr, provided that the white dwarf is initially rotating with a frequency much smaller than the orbital frequency. For semi-detached white dwarf binaries spin-up can occur on time scales of less than 1Myr. Nevertheless, the time scales remain longer than the orbital inspiral time scales due to gravitational radiation, so that the degree of asynchronism in these binaries increases. As a consequence, tidal forcing eventually occurs at forcing frequencies beyond the quasi-static tide approximation. For the shortest period binaries, energy dissipation is therefore expected to take place through dynamic tides and resonantly excited g-modes.

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arXiv2009

Transient Low-Mass X-Ray Binary Populations in Elliptical Galaxies NGC 3379 and NGC 4278

We propose a physically motivated and self-consistent prescription for the modeling of transient neutron star (NS) low-mass X-ray binary (LMXB) properties, such as duty cycle (DC), outburst duration and recurrence time. We apply this prescription to the population synthesis (PS) models of field LMXBs presented by Fragos et al. (2008), and compare the transient LMXB population to the Chandra X-ray survey of the two elliptical galaxies NGC 3379 and NGC 4278, which revealed several transient sources (Brassington et al., 2008, 2009). We are able to exclude models with a constant DC for all transient systems, while models with a variable DC based on the properties of each system are consistent with the observed transient populations. We predict that the majority of the observed transient sources in these two galaxies are LMXBs with red giant donors. Our comparison suggests that LMXBs formed through evolution of primordial field binaries are dominant in globular cluster (GC) poor elliptical galaxies, while they still have a significant contribution in GC rich ones.

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arXiv2008

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.

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arXiv2008

How Many CVs are Crossing the Period Gap? A Test for the Disruption of Magnetic Braking

We apply population synthesis techniques to calculate the present day number of two types of white dwarf-main sequence star (WDMS) binaries within the cataclysmic variable period gap. The first are post-common envelope binaries with secondary stars that have masses between 0.17 and 0.36 Msun (gPCEBs), such that they will commence mass transfer within the period gap. The second type are systems that were CVs at some point in their past, but detached once they evolved down in orbital period to ~3 h as a consequence of disrupted magnetic braking, and are crossing the period gap via gravitational radiation (dCVs). Full population synthesis calculations are performed where we assume either constant, global values of the common envelope ejection efficiency, or consider the ejection efficiency as a function of secondary mass. Several forms of magnetic braking are also considered. We predict an excess of dCVs over gPCEBs within the period gap of ~4 to ~13 assuming an ejection efficiency between 0.1 and 0.6, and a flat initial mass ratio distribution. This excess is revealed as a prominent peak at the location of the period gap in the orbital period distribution of the combined gPCEB and dCV population. We suggest that if such a feature is observed in the orbital period distribution of an observed sample of short orbital period WDMS binaries, this would strongly corroborate the disruption of magnetic braking.

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arXiv2008

Eccentric double white dwarfs as LISA sources in globular clusters

We consider the formation of double white dwarfs (DWDs) through dynamical interactions in globular clusters. Such interactions can give rise to eccentric DWDs, in contrast to the exclusively circular population expected to form in the Galactic disk. We show that for a 5-year Laser Interferometer Space Antenna (LISA) mission and distances as far as the Large Magellanic Cloud, multiple harmonics from eccentric DWDs can be detected at a signal-to-noise ratio higher than 8 for at least a handful of eccentric DWDs, given their formation rate and typical lifetimes estimated from current cluster simulations. Consequently the association of eccentricity with stellar-mass LISA sources does not uniquely involve neutron stars, as is usually assumed. Due to the difficulty of detecting (eccentric) DWDs with present and planned electromagnetic observatories, LISA could provide unique dynamical identifications of these systems in globular clusters.

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arXiv2008

Probing white dwarf interiors with LISA: periastron precession in double white dwarfs

In globular clusters, dynamical interactions give rise to a population of eccentric double white dwarfs detectable by the Laser Interferometer Space Antenna (LISA) up to the Large Magellanic Cloud. In this Letter, we explore the detectability of periastron precession in these systems with LISA. Unlike previous investigations, we consider contributions due to tidal and rotational distortions of the binary components in addition to general relativistic contributions to the periastron precession. At orbital frequencies above a few mHz, we find that tides and stellar rotation dominate, opening up a possibly unique window to the study of the interior and structure of white dwarfs.

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arXiv2007

Polar kicks and the spin period - eccentricity relation in double neutron stars

We present results of a population synthesis study aimed at examining the role of spin-kick alignment in producing a correlation between the spin period of the first-born neutron star and the orbital eccentricity of observed double neutron star binaries in the Galactic disk. We find spin-kick alignment to be compatible with the observed correlation, but not to alleviate the requirements for low kick velocities suggested in previous population synthesis studies. Our results furthermore suggest low- and high-eccentricity systems may form through two distinct formation channels distinguished by the presence or absence of a stable mass transfer phase before the formation of the second neutron star. The presence of highly eccentric systems in the observed sample of double neutron stars may furthermore support the notion that neutron stars accrete matter when moving through the envelope of a giant companion.

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arXiv2007

Interacting Binaries with Eccentric Orbits. Secular Orbital Evolution Due To Conservative Mass Transfer

We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, assuming conservation of total system mass and orbital angular momentum. Assuming a delta function mass transfer rate centered at periastron, we find rates of secular change of the orbital semi-major axis and eccentricity which are linearly proportional to the magnitude of the mass transfer rate at periastron. The rates can be positive as well as negative, so that the semi-major axis and eccentricity can increase as well as decrease in time. Adopting a delta-function mass-transfer rate of $10^{-9} M_\sun {\rm yr}^{-1}$ at periastron yields orbital evolution timescales ranging from a few Myr to a Hubble time or more, depending on the binary mass ratio and orbital eccentricity. Comparison with orbital evolution timescales due to dissipative tides furthermore shows that tides cannot, in all cases, circularize the orbit rapidly enough to justify the often adopted assumption of instantaneous circularization at the onset of mass transfer. The formalism presented can be incorporated in binary evolution and population synthesis codes to create a self-consistent treatment of mass transfer in eccentric binaries.

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arXiv2007

Equipotential Surfaces and Lagrangian points in Non-synchronous, Eccentric Binary and Planetary Systems

We investigate the existence and properties of equipotential surfaces and Lagrangian points in non-synchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that accounts for non-synchronous rotation and eccentric orbits, and calculate the positions of the Lagrangian points as functions of the mass ratio, the degree of asynchronism, the orbital eccentricity, and the position of the stars or planets in their relative orbit. We find that the geometry of the equipotential surfaces may facilitate non-conservative mass transfer in non-synchronous, eccentric binary star and planetary systems, especially if the component stars or planets are rotating super-synchronously at the periastron of their relative orbit. We also calculate the volume-equivalent radius of the Roche lobe as a function of the four parameters mentioned above. Contrary to common practice, we find that replacing the radius of a circular orbit in the fitting formula of Eggleton (1983) with the instantaneous distance between the components of eccentric binary or planetary systems does not always lead to a good approximation to the volume-equivalent radius of the Roche-lobe. We therefore provide generalized analytic fitting formulae for the volume-equivalent Roche lobe radius appropriate for non-synchronous, eccentric binary star and planetary systems. These formulae are accurate to better than 1% throughout the relevant 2-dimensional parameter space that covers a dynamic range of 16 and 6 orders of magnitude in the two dimensions.

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arXiv2006

Formation of Double Compact Objects

Current observations of double neutron stars provide us with a wealth of information that we can use to investigate their evolutionary history and the physical conditions of neutron star formation. Understanding this history and formation conditions further allow us to make theoretical predictions for the formation of other double compact objects with one or two black hole components and assess the detectability of such systems by ground-based gravitational-wave interferometers. In this paper we summarize our group's body of work in the past few years and we place our conclusions and current understanding in the framework of other work in this area of astrophysical research.

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arXiv2006

Black Hole Formation in X-Ray Binaries: The Case of XTE J1118+480

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arXiv2006

Theoretical orbital period distributions of cataclysmic variables above the period gap: effects of circumbinary disks

The population of non magnetic cataclysmic variables evolving under the influence of a circumbinary disk is investigated for systems above the upper edge of the period gap at orbital periods greater than 2.75hr. For a fractional mass input rate into the disk, corresponding to 3e-4 of the mass transfer rate, the model systems exhibit a bounce at orbital periods greater than 2.75hr. The simulations reveal that (1) some systems can exist as dwarf nova type systems throughout their lifetime, (2) dwarf nova type systems can evolve into nova-like systems as their mass transfer rate increases with increasing circumbinary disk mass, and (3) nova-like systems can evolve back into dwarf nova systems during their postbounce evolution to longer orbital periods. Among these subclasses, nova-like cataclysmic variables would be the best candidates to search for circumbinary disks at wavelengths greater than 10 micron. The theoretical orbital period distribution of our population synthesis model is in reasonable accord with the combined population of dwarf novae and nova-like systems above the period gap, suggesting the possibility that systems with unevolved donors need not detach and evolve below the period gap as in the disrupted magnetic braking model. The resulting population furthermore reveals the possible presence of systems with small mass ratios (a property of systems exhibiting superhump phenomena at long orbital periods) and a preference of O/Ne/Mg white dwarfs in dwarf nova systems in comparison to nova-like systems. The importance of observational bias in accounting for the differing populations is examined, and it is shown that an understanding of these effects is necessary in order to confront the theoretical distributions with the observed ones in a meaningful manner. (abridged)

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arXiv2006

On the Formation and Progenitor of PSR J0737-3039: New Constraints on the Supernova Explosion Forming Pulsar B

We revisit the formation of PSR J0737-3039, taking into account the most recent observational constraints. We show that the most likely kick velocity and progenitor parameters depend strongly on the consideration of the full five-dimensional PDF for the magnitude and direction of the kick velocity imparted to pulsar B at birth, the mass of pulsar B's pre-supernova helium star progenitor, and the pre-supernova orbital separation, and on the adopted prior assumptions. The priors consist of the transverse systemic velocity, the age of the system, and the treatment of the unknown radial velocity. Since the latter cannot be determined from observation, we adopt a statistical approach and use theoretical radial-velocity distributions obtained from population synthesis calculations for coalescing double neutron stars. We find that the prior assumptions about the pre-supernova helium star mass affect the derived most likely parameters significantly: when the minimum helium star mass required for neutron star formation is assumed to be 2.1Msun, the most likely kick velocity ranges from 70-180km/s; when masses lower than 2.1Msun are assumed to allow neutron star formation, the most likely kick velocity can be as low as a few km/s, although the majority of the considered models still yield most likely kick velocities of 50-170km/s. We also show that the proximity of the double pulsar to the Galactic plane and the small proper motion do not pose stringent constraints on the kick velocity and progenitor mass of pulsar B. Instead, the constraints imposed by the orbital dynamics of asymmetric supernova explosions turn out to be much more restrictive. We conclude that the currently available observational constraints cannot be used to favor a specific core-collapse and neutron star formation mechanism. (abridged)

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arXiv2006

Eclipsing binaries in extrasolar planet transit surveys: the case of SuperWASP

Using a comprehensive binary population synthesis scheme, we investigate the statistical properties of a sample of eclipsing binaries that is detectable by an idealised extrasolar planet transit survey with specifications broadly similar to those of the SuperWASP (Wide Angle Search for Planets) project. In this idealised survey the total number of detectable single stars in the Galactic disc is of the order of 10^6-10^7, while, for a flat initial mass ratio distribution, the total number of detectable eclipsing binaries is of the order of 10^4-10^5. The majority of the population of detectable single stars is made up of main-sequence stars (60%), horizontal-branch stars (20%), and giant-branch stars (10%). The largest contributions to the population of detectable eclipsing binaries stem from detached double main-sequence star binaries (60%), detached giant-branch main-sequence star binaries (20%), and detached horizontal-branch main-sequence star binaries (10%). The ratio of the number of eclipsing binaries to the number of single stars detectable by the idealised SuperWASP survey varies by less than a factor of 2.5 across the sky, and decreases with increasing Galactic latitude. It is found to be largest in the direction of the Galactic longitude l=-7.5deg and the Galactic latitude b=-22.5deg. We also show that the fractions of systems in different subgroups of eclipsing binaries are sensitive to the adopted initial mass ratio distribution, which is one of the poorest constrained input parameters in present-day binary population synthesis calculations. This suggests that once statistically meaningful results from transit surveys are available, they will be able to significantly improve the predictive power of population synthesis studies of interacting binaries and related objects. (abridged)

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arXiv2005

Dynamic Tides in Close Binaries

The basic theory of dynamic tides in close binaries is reviewed. Particular attention is paid to resonances between dynamic tides and free oscillation modes and to the role of the apsidal-motion rate in probing the internal structure of binary components. The discussed effects are generally applicable to stars across the entire Hertzsprung-Russell diagram, including the binary OB-stars discussed at this meeting.

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