As part of a larger program aimed at better quantifying the uncertainties in stellar computations, we attempt to calibrate the extent of convective overshooting in low to intermediate mass stars by means of eclipsing binary systems. We model 12 such
systems, with component masses between 1.3 and 6.2 solar masses, using the detailed binary stellar evolution code STARS, producing grids of models in both metallicity and overshooting parameter. From these, we determine the best fit parameters for each of our systems. For three systems, none of our models produce a satisfactory fit. For the remaining systems, no single value for the convective overshooting parameter fits all the systems, but most of our systems can be well described with an overshooting parameter between 0.09 and 0.15, corresponding to an extension of the mixed region above the core of about 0.1-0.3 pressure scale heights. Of the nine systems where we are able to obtain a good fit, seven can be reasonably well fit with a single parameter of 0.15. We find no evidence for a trend of the extent of overshooting with either mass or metallicity, though the data set is of limited size. We repeat our calculations with a second evolution code, MESA, and we find general agreement between the two codes. For the extension of the mixed region above the convective core required by the MESA models is about 0.15-0.4 pressure scale heights. For the system EI Cep, we find that MESA gives an overshooting region that is larger than the STARS one by about 0.1 pressure scale heights for the primary, while for the secondary the difference is only 0.05 pressure scale heights.
In an attempt to determine how many planetary nebulae derive from binary interactions, we have started a project to measure their unbiased binary fraction. This number, when compared to the binary fraction of the presumed parent population can give a
first handle on the origin of planetary nebulae. By detecting 27 bona fide central stars in the I band we have found that 30% of our sample have an I band excess between one and a few sigmas, possibly denoting companions brighter than M3-4V and with separations smaller than approximately 1000 AU. By accounting for the undetectable companions, we determine a de-biased binary fraction of 67-78% for all companions at all separations. We compare this number to a main sequence binary fraction of (50+/-4)% determined for spectral types F6V-G2V, appropriate if the progenitors of todays PN central star population is indeed the F6V-G2V stars. The error on our estimate could be between 10 and 30%. We conclude that the central star binary fraction may be larger than expected from the putative parent population. Using the more sensitive J band of a subset of 11 central stars, the binary fraction is 54% for companions brighter than approximately M5-6V and with separations smaller than about 900 AU. De-biassing this number we obtain a binary fraction of 100-107%. The two numbers should be the same and the discrepancy is likely due to small number statistics. We also present an accurately vetted compilation of observed main sequence star magnitudes, colours and masses, which can serve as a reference for future studies. We also present synthetic colours of hot stars as a function of temperature (20-170kK) and gravity (log g= 6-8) for Solar and PG1159 compositions.
The recent discovery of two Earth-mass planets in close orbits around an evolved star has raised questions as to whether substellar companions can survive encounters with their host stars. We consider whether these companions could have been stripped
of significant amounts of mass during the phase when they orbited through the dense inner envelopes of the giant. We apply the criterion derived by Murray et al. for disruption of gravitationally bound objects by ram pressure, to determine whether mass loss may have played a role in the histories of these and other recently discovered low-mass companions to evolved stars. We find that the brown dwarf and Jovian mass objects circling WD 0137-349, SDSS J08205+0008, and HIP 13044 are most unlikely to have lost significant mass during the common envelope phase. However, the Earth-mass planets found around KIC 05807616 could well be the remnant of one or two Jovian mass planets that lost extensive mass during the common envelope phase.
The {alpha}-formalism is a common way to parametrize the common envelope interaction between a giant star and a more compact companion. The {alpha} parameter describes the fraction of orbital energy released by the companion that is available to ejec
t the giant stars envelope. By using new, detailed stellar evolutionary calculations we derive a user-friendly prescription for the {lambda} parameter and an improved approximation for the envelope binding energy, thus revising the {alpha} equation. We then determine {alpha} both from simulations and observations in a self consistent manner. By using our own stellar structure models as well as population considerations to reconstruct the primarys parameters at the time of the common envelope interaction, we gain a deeper understanding of the uncertainties. We find that systems with very low values of q (the ratio of the companions mass to the mass of the primary at the time of the common envelope interaction) have higher values of {alpha}. A fit to the data suggests that lower mass companions are left at comparable or larger orbital separations to more massive companions. We conjecture that lower mass companions take longer than a stellar dynamical time to spiral in to the giants core, and that this is key to allowing the giant to use its own thermal energy to help unbind its envelope. As a result, although systems with light companions might not have enough orbital energy to unbind the common envelope, they might stimulate a stellar reaction that results in the common envelope ejection.
