Towards Multiple-Star Population Synthesis

The multiplicities of stars, and some other properties, were collected recently by Eggleton & Tokovinin, for the set of 4559 stars with Hipparcos magnitude brighter than 6.0 (4558 excluding the Sun). In this paper I give a numerical recipe for constructing, by a Monte Carlo technique, a theoretical ensemble of multiple stars that resembles the observed sample. Only multiplicities up to 8 are allowed; the observed set contains only multiplicities up to 7. In addition, recipes are suggested for dealing with the selection effects and observational uncertainties that attend the determination of multiplicity. These recipes imply, for example, that to achieve the observed average multiplicity of 1.53, it would be necessary to suppose that the real population has an average multiplicity slightly over 2.0. This numerical model may be useful for (a) comparison with the results of star and star cluster formation theory, (b) population synthesis that does not ignore multiplicity above 2, and (c) initial conditions for dynamical cluster simulations

Adiabatic Mass Loss and the Outcome of the Common Envelope Phase of Binary Evolution

We have developed a new method for calculating common envelope (CE) events based on explicit consideration of the donor star's structural response to adiabatic mass loss. In contrast to existing CE prescriptions, which specify a priori the donor's remnant mass, we determine this quantity self-consistently and find it depends on binary and CE parameters. This aspect of our model is particularly important to realistic modeling for upper main sequence star donors without strongly degenerate cores (and hence without a clear core/envelope boundary). We illustrate the central features of our method by considering CE events involving 10 solar mass donors on or before their red giant branch. For such donors, the remnant core mass can be as much as 30% larger than the star's He-core mass. Applied across a population of such binaries, our methodology results in a significantly broader remnant mass and final orbital separation distribution and a 20% increase in CE survival rates as compared to previous prescriptions for the CE phase.Comment: 4 pages, 3 figures; corrected typo in equation (1); updated reference dat

On Packing Colorings of Distance Graphs

The {\em packing chromatic number} $\chi_{\rho}(G)$ of a graph $G$ is the least integer $k$ for which there exists a mapping $f$ from $V(G)$ to $\{1,2,\ldots ,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. This paper studies the packing chromatic number of infinite distance graphs $G(\mathbb{Z},D)$, i.e. graphs with the set $\mathbb{Z}$ of integers as vertex set, with two distinct vertices $i,j\in \mathbb{Z}$ being adjacent if and only if $|i-j|\in D$. We present lower and upper bounds for $\chi_{\rho}(G(\mathbb{Z},D))$, showing that for finite $D$, the packing chromatic number is finite. Our main result concerns distance graphs with $D=\{1,t\}$ for which we prove some upper bounds on their packing chromatic numbers, the smaller ones being for $t\geq 447$: $\chi_{\rho}(G(\mathbb{Z},\{1,t\}))\leq 40$ if $t$ is odd and $\chi_{\rho}(G(\mathbb{Z},\{1,t\}))\leq 81$ if $t$ is even

Evolution of the progenitor binary of V1309 Scorpii before merger

It was recently demonstrated that the eruption of V1309 Sco was a result of a merger of the components of a cool contact binary. We computed a set of evolutionary models of the detached binaries with different initial parameters to compare it with pre-burst observations of V1309 Sco. The models are based on our recently developed evolutionary model of the formation of cool contact binaries. The best agreement with observations was obtained for binaries with initial masses of 1.8-2.0 solar masses and initial periods of 2.5-3.1 d. The evolution of these binaries consists of three phases: at first the binary is detached and both components lose mass and angular momentum through a magnetized wind. This takes almost two thirds of the total evolutionary lifetime. The remaining third is spent in a semi-detached configuration of the Algol-type, following the Roche-lobe overflow by the initially more massive component. When the other component leaves the main sequence and moves toward the giant branch, a contact configuration is formed for a short time, followed by the coalescence of both components.Comment: 5 pages, 1 figure, Astronomy and Astrophysics, in prin

Gap soliton formation by nonlinear supratransmission in Bragg media

A Bragg medium in the nonlinear Kerr regime, submitted to incident cw-radiation at a frequency in a band gap, switches from total reflection to transmission when the incident energy overcomes some threshold. We demonstrate that this is a result of nonlinear supratransmission, which allows to prove that i) the threshold incident amplitude is simply expressed in terms of the deviation from the Bragg resonance, ii) the process is not the result of a shift of the gap in the nonlinear dispersion relation, iii) the transmission does occur by means of gap soliton trains, as experimentally observed [D. Taverner et al., Opt Lett 23 (1998) 328], iv) the required energy tends to zero close to the band edge.Comment: 5 figures, submitted to EuroPhysics Letter

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.Comment: 7 pages for main text, 11 pages for appendix (table A1), 12 figure