arXiv subjects

Peter P. Eggleton

Publications and source records attributed to Peter P. Eggleton.

12 recordsLinked to original sources

arXiv2018

Numerical Modelling of Tertiary Tides

Stellar systems consisting of multiple stars tend to undergo tidal interactions when the separations between the stars are short. While tidal phenomena have been extensively studied, a certain tidal effect exclusive to hierarchical triples (triples in which one component star has a much wider orbit than the others) has hardly received any attention, mainly due to its complexity and consequent resistance to being modelled. This tidal effect is the tidal perturbation of the tertiary by the inner binary, which in turn depletes orbital energy from the inner binary, causing the inner binary separation to shrink. In this paper, we develop a fully numerical simulation of these "tertiary tides" by modifying established tidal models. We also provide general insight as to how close a hierarchical triple needs to be in order for such an effect to take place, and demonstrate that our simulations can effectively retrieve the orbital evolution for such systems. We conclude that tertiary tides are a significant factor in the evolution of close hierarchical triples, and strongly influence at least ~ 1% of all multiple star systems.

astro-ph.SR↗

arXiv2016

Models for Sixty Double-Lined Binaries containing Giants

The observed masses, radii and temperatures of 60 medium- to long-period binaries, most of which contain a cool, evolved star and a hotter less-evolved one, are compared with theoretical models which include (a) core convective overshooting, (b)mass loss, possibly driven by dynamo action as in RS CVn binaries, and (c) tidal friction, including its effect on orbital period through magnetic braking. A reasonable fit is found in about 42 cases, but in 11 other cases the primaries appear to have lost either more mass or less mass than the models predict, and in 4 others the orbit is predicted to be either more or less circular than observed. Of the remaining 3 systems, two ($γ$ Per and HR 8242) have a markedly `over-evolved' secondary, our explanation being that the primary component is the merged remnant of a former short-period sub-binary in a former triple system. The last system (V695 Cyg) defies any agreement at present. Mention is also made of three other systems (V643 Ori, OW Gem and V453 Cep), which are relevant to our discussion.

astro-ph.SR↗

arXiv2011

Adiabatic Evolution of Mass-losing Stars

We have calculated the equilibrium properties of a star in a circular, equatorial orbit about a Super-Massive Black Hole (SMBH), when the star fills and overflows its Roche lobe. The mass transfer time scale is anticipated to be long compared with the dynamical time and short compared with the thermal time of the star, so that the entropy as a function of the interior mass is conserved. We have studied how the stellar entropy, pressure, radius, mean density, and orbital angular momentum vary when the star is evolved adiabatically, for a representative set of stars. We have shown that the stellar orbits change with the stellar mean density. Therefore, sun-like stars, upper main sequence stars and red giants will spiral inward and then outward with respect to the hole in this stable mass transfer process, while lower main sequence stars, brown dwarfs and white dwarfs will always spiral outward.

astro-ph.HE↗

arXiv2007

Compulsory Deep Mixing of 3He and CNO Isotopes in the Envelopes of low-mass Red Giants

Three-dimensional stellar modeling has enabled us to identify a deep-mixing mechanism that must operate in all low mass giants. This mixing process is not optional, and is driven by a molecular weight inversion created by the 3He(3He,2p)4He reaction. In this paper we characterize the behavior of this mixing, and study its impact on the envelope abundances. It not only eliminates the problem of 3He overproduction, reconciling stellar and big bang nucleosynthesis with observations, but solves the discrepancy between observed and calculated CNO isotope ratios in low mass giants, a problem of more than 3 decades' standing. This mixing mechanism, which we call `$δμ$-mixing', operates rapidly (relative to the nuclear timescale of overall evolution, ~ 10^8 yrs) once the hydrogen burning shell approaches the material homogenized by the surface convection zone. In agreement with observations, Pop I stars between 0.8 and 2.0$\Msun$ develop 12C/13C ratios of 14.5 +/- 1.5, while Pop II stars process the carbon to ratios of 4.0 +/- 0.5. In stars less than 1.25$\Msun$, this mechanism also destroys 90% to 95% of the 3He produced on the main sequence.

astro-ph↗

arXiv2005

3D Numerical Experimentation on the Core Helium Flash of low-mass Red Giants

We model the core helium flash in a low-mass red giant using Djehuty, a fully three-dimensional (3D) code. The 3D structures were generated from converged models obtained during the 1D evolutionary calculation of a 1$\Msun$ star. Independently of which starting point we adopted, we found that after some transient relaxation the 3D model settled down with a briskly convecting He-burning shell that was not very different from what the 1D model predicted.

astro-ph↗

arXiv2004

N-body simulations of stars escaping from the Orion nebula

We study the dynamical interaction in which the two single runaway stars AE Aurigae and mu Columbae and the binary iota Orionis acquired their unusually high space velocity. The two single runaways move in almost opposite directions with a velocity greater than 100 km/s away from the Trapezium cluster. The star iota Ori is an eccentric (e=0.8) binary moving with a velocity of about 10 km/s at almost right angles with respect to the two single stars. The kinematic properties of the system suggest that a strong dynamical encounter occurred in the Trapezium cluster about 2.5 Myr ago. Curiously enough, the two binary components have similar spectral type but very different masses, indicating that their ages must be quite different. This observation leads to the hypothesis that an exchange interaction occurred in which an older star was swapped into the original iota Orionis binary. We test this hypothesis by a combination of numerical and theoretical techniques, using N-body simulations to constrain the dynamical encounter, binary evolution calculations to constrain the high orbital eccentricity of iota Orionis and stellar evolution calculations to constrain the age discrepancy of the two binary components. We find that an encounter between two low eccentricity (0.4<e<0.6) binaries with comparable binding energy, leading to an exchange and the ionization of the wider binary, provides a reasonable solution to this problem.

astro-ph↗

arXiv2002

The Evolution of Cool Algols

We apply a model of dynamo-driven mass loss, magnetic braking and tidal friction to the evolution of stars with cool convective envelopes; in particular we apply it to binary stars where the combination of magnetic braking and tidal friction can cause angular-momentum loss from the {\it orbit}. For the present we consider the simplification that only one component of a binary is subject to these non-conservative effects, but we emphasise the need in some circumstances to permit such effects in {\it both} components. The model is applied to examples of (i) the Sun, (ii) BY Dra binaries, (iii) Am binaries, (iv) RS CVn binaries, (v) Algols, (vi) post-Algols. A number of problems regarding some of these systems appear to find a natural explanation in our model. There are indications from other systems that some coefficients in our model may vary by a factor of 2 or so from system to system; this may be a result of the chaotic nature of dynamo activity.

astro-ph↗

arXiv2002

Envelope Ejection: an Alternative Process for some Early Case B Binaries

We discuss the evolution of binaries with moderately high masses (about 10 - 30 solar masses), and with periods of about 3 - 300d, corresponding mostly to early Case B. These are usually thought to evolve either by reasonably conservative Roche-lobe overflow, if the initial mass ratio is fairly mild, or else by highly non-conservative common-envelope evolution, with spiral-in to short periods (hours, typically), if the initial mass ratio is rather extreme. We discuss here a handful of binaries from part of this period range (about 50 - 250d), which appear to have followed a different path: we argue that they must have lost a large proportion of initial mass (about 70 - 80%), but without shortening their periods at all. We suggest that their behaviour may be due to the fact that stars of such masses, when evolved also to rather large radii, are not far from the Humphreys-Davidson limit where single stars lose their envelopes spontaneously in P Cygni winds, and so have envelopes which are only lightly bound to the core. These envelopes therefore may be relatively easily dissipated by the perturbing effect of a companion. In addition, some or all of the stars considered here may have been close to the Cepheid instability strip when they filled their Roche lobes. One or other, or both, of high luminosity and Cepheid instability, in combination with an appropriately close binary companion, may be implicated.

astro-ph↗

arXiv2001

Evolution in Binary and Triple Stars, with an application to SS Lac

We present equations governing the way in which both the orbit and the intrinsic spins of stars in a close binary should evolve subject to a number of perturbing forces, including the effect of a third body in a possibly inclined wider orbit. We illustrate the solutions in some binary-star and triple-star situations: tidal friction in a wide but eccentric orbit of a radio pulsar about a B star, the Darwin and eccentricity instabilities in a more massive but shorter-period massive X-ray binary, and the interaction of tidal friction with Kozai cycles in a triple such as Algol (beta-Per), at an early stage in that star's life when all 3 components were ZAMS stars. We also attempt to model in some detail the interesting triple system SS Lac, which stopped eclipsing in about 1950. We find that our model of SS Lac is quite constrained by the relatively good observational data of this system, and leads to a specific inclination (29 deg) of the outer orbit relative to the inner orbit at epoch zero (1912). Although the intrinsic spins of the stars have little effect on the orbit, the converse is not true: the spin axes can vary their orientation relative to the close binary by up to 120 deg on a timescale of about a century.

astro-ph↗

arXiv2000

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 Pop I binary evolution calculations, with the initial primary mass between 1 and 8 solar masses the initial mass ratio 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 RLOF 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 of the primary, the initial mass ratio, 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 solar masses may be formed if the primary's initial mass is around 2.5 solar masses.

astro-ph↗

arXiv2000

A Complete Survey of Case A Binary Evolution with Comparison to Observed Algol-Type Systems

We undertake a comparison of observed Algol-type binaries with a library of computed Case A binary evolution tracks. The library consists of 5500 binary tracks with various values of initial primary mass M_{10}, mass ratio q_0, and period P_0, designed to sample the phase-space of Case A binaries in the range -0.10 < log M_{10} < 1.7. Each binary is evolved using a standard code with the assumption that both total mass and orbital angular momentum are conserved. This code follows the evolution of both stars until the point where contact or reverse mass transfer occurs. The resulting binary tracks show a rich variety of behavior which we sort into several subclasses of Case A and Case B. We present the results of this classification, the final mass ratio and the fraction of time spent in Roche Lobe overflow for each binary system. The conservative assumption under which we created this library is expected to hold for a broad range of binaries, where both components have spectra in the range G0 to B1 and luminosity class III - V. We gather a list of relatively well-determined observed hot Algol-type binaries meeting this criterion, as well as a list of cooler Algol-type binaries where we expect significant dynamo-driven mass loss and angular momentum loss. We fit each observed binary to our library of tracks using a chi^2-minimizing procedure. We find that the hot Algols display overall acceptable chi^2, confirming the conservative assumption, while the cool Algols show much less acceptable chi^2 suggesting the need for more free parameters, such as mass and angular momentum loss.

astro-ph↗

arXiv1998

The Equilibrium-Tide Model for Tidal Friction

We derive from first principles equations governing (a) the quadrupole tensor of a star distorted by both rotation and the presence of a companion in a possibly eccentric orbit, (b) a functional form for the dissipative force of tidal friction, based on the concept that the rate of energy loss from a time-dependent tide should be a positive-definite function of the rate of change of the quadrupole tensor as seen in the frame which rotates with the star, and (c) the equations governing the rates of change of the magnitude and direction of the stellar rotation, and the orbital period and eccentricity, based on the concept of the Laplace-Runge-Lenz vector. Our analysis leads relatively simply to a closed set of equations, valid for arbitrary inclination of the stellar spin to the orbit. The results are equivalent to classical results based on the rather less clear principle that the tidal bulge lags behind the line of centres by some time determined by the rate of dissipation; our analysis gives the effective lag time as a function of the dissipation rate and the quadrupole moment. We discuss briefly some possible applications of the formulation.

astro-ph↗