Peter P. Eggleton

Approximate input physics for stellar modelling

We present a simple and efficient, yet reasonably accurate, equation of state, which at the moderately low temperatures and high densities found in the interiors of stars less massive than the Sun is substantially more accurate than its predecessor by Eggleton, Faulkner & Flannery. Along with the most recently available values in tabular form of opacities, neutrino loss rates, and nuclear reaction rates for a selection of the most important reactions, this provides a convenient package of input physics for stellar modelling. We briefly discuss a few results obtained with the updated stellar evolution code.

The distribution of visual binaries with two bright components

Among the 4908 stellar systems which have at least one resolvable component brighter than V = 6.00 are 115 systems with two or more resolvable components both brighter than V = 6.00. These bright stellar systems, both single and double, are modeled by a distribution convolving (1) formulas from theoretical models for stellar evolution, including giants as well as main-sequence stars, (2) an initial mass function and birth rate function, (3) a density distribution of stars as a function of distance from the Galactic plane, and (4) a distribution of mass ratios and orbital separations. One reasonably firm conclusion is that masses, even in wide binaries, are correlated: there are too many doubly bright visual binaries (DBVBs), by a factor of 3-5, to agree with the hypothesis that the component masses are selected independently from the same IMF or luminosity function. Another conclusion is that the number of DBVBs per decibel of separation a (absolute, not apparent) is not constant in the range a = 10-100,000 AU, but instead decreases slowly with increasing a. 21 refs.

Evolution of close binary systems

We collected data on the masses, radii, etc. of three classes of close binary stars: low-temperature contact binaries (LTCBs), near-contact binaries (NCBs), and detached close binaries (DCBs). They restrict themselves to systems where (1) both components are, at least arguably, near the Main Sequence, (2) the periods are less than a day, and (3) there is both spectroscopic and photometric analysis leading to reasonably reliable data. They discuss the possible evolutionary connections between these three classes, emphasizing the roles played by mass loss and angular momentum loss in rapidly-rotating cool stars.

Deep Mixing of 3He: Reconciling Big Bang and Stellar Nucleosynthesis

Low-mass stars, ∼1 to 2 solar masses, near the Main Sequence are efficient at producing the helium isotope 3He, which they mix into the convective envelope on the giant branch and should distribute into the Galaxy by way of envelope loss. This process is so efficient that it is difficult to reconcile the low observed cosmic abundance of 3He with the predictions of both stellar and Big Bang nucleosynthesis. Here we find, by modeling a red giant with a fully three-dimensional hydrodynamic code and a full nucleosynthetic network, that mixing arises in the supposedly stable and radiative zone between the hydrogen-burning shell and the base of the convective envelope. This mixing is due to Rayleigh-Taylor instability within a zone just above the hydrogen-burning shell, where a nuclear reaction lowers the mean molecular weight slightly. Thus, we are able to remove the threat that 3He production in low-mass stars poses to the Big Bang nucleosynthesis of 3He.

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 M10, mass ratio q0, and period P0, designed to sample the phase-space of Case A binaries in the range -0.10 ≤ log M10 ≤ 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 to the point where contact or reverse mass transfer occurs. The resulting binary tracks show a rich variety of behavior that 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 classes III to 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, for which we expect significant dynamo-driven mass loss and angular momentum loss. We fit each observed binary to our library of tracks using a χ2-minimizing procedure. We find that the hot Algols display overall acceptable χ2, confirming the conservative assumption, while the cool Algols show much less acceptable χ2, suggesting the need for more free parameters, such as mass and angular momentum loss.

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

Using Eggletons 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.

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 {sup 3}He({sup 3}He,2p){sup 4}He 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 {sup 3}He 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 operates rapidly 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 M{sub {circle_dot}} develop {sup 12}C/{sup 13}C 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 M{sub {circle_dot}}, this mechanism also destroys 90% to 95% of the {sup 3}He produced on the main sequence.

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.

Three-dimensional 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 one-dimensional (1D) evolutionary calculation of a 1 M☉ 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.

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-1 away from the Trapezium cluster. The star iota Orionis is an eccentric (e~= 0.8) binary moving with a velocity of about 10 km s-1 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.