We use three-dimensional hydrodynamical simulations to study the rapid infall phase of the common envelope interaction of a red giant branch star of mass equal to 0.88 M and a companion star of mass ranging from 0.9 down to 0.1 M . We first compare the results obtained using two different numerical techniques with different resolutions, and find overall very good agreement. We then compare the outcomes of those simulations with observed systems thought to have gone through a common envelope. The simulations fail to reproduce those systems in the sense that most of the envelope of the donor remains bound at the end of the simulations and the final orbital separations between the donor's remnant and the companion, ranging from 26.8 down to 5.9 R , are larger than the ones observed. We suggest that this discrepancy vouches for recombination playing an essential role in the ejection of the envelope and/or significant shrinkage of the orbit happening in the subsequent phase.

The α formalism is a common way to parametrize the common envelope interaction between a giant star and a more compact companion. The α parameter describes the fraction of orbital energy released by the companion that is available to eject the giant star's envelope. By using new, detailed stellar evolutionary calculations, we derive a user-friendly prescription for the λ parameter and an improved approximation for the envelope binding energy, thus revising the α equation. We then determine α both from simulations and from observations in a self-consistent manner. By using our own stellar structure models as well as population considerations to reconstruct the primary's 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 companion's mass to the mass of the primary at the time of the common envelope interaction) have higher values of α. 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 into the giant's 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.

Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability in the astrophysical community. This discussion relies largely on how the KHI test is posed and analyzed. We pose a stringent test of the initial growth of the instability. The goal is to provide a rigorous methodology for verifying a code on two dimensional Kelvin-Helmholtz instability. We ran the problem in the Pencil Code, Athena, Enzo, NDSPMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, though this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of Smoothed Particle Hydrodynamics. We then comment on the connection between this behavior to the underlying lack of zeroth-order consistency in Smoothed Particle Hydrodynamics interpolation. We comment on the tendency of some methods, particularly those with very low numerical diffusion, to produce secondary Kelvin-Helmholtz billows on similar tests. Though the lack of a fixed, physical diffusive scale in the Euler equations lies at the root of the issue, we suggest that in some methods an extra diffusion operator should be used to damp the growth of instabilities arising from grid noise. This statement applies particularly to moving-mesh tessellation codes, but also to fixed-grid Godunov schemes.

We present hydrodynamic simulations of the common envelope binary interaction between a giant star and a compact companion carried out with the adaptive mesh refinement code enzo and the smooth particle hydrodynamics code phantom. These simulations mimic the parameters of one of the simulations by Passy et al., but assess the impact of a larger, more realistic initial orbital separation on the simulation outcome. We conclude that for both codes the post-common envelope separation is somewhat larger and the amount of unbound mass slightly greater when the initial separation is wide enough that the giant does not yet overflow or just overflows its Roche lobe. phantom has been adapted to the common envelope problem here for the first time and a full comparison with enzo is presented, including an investigation of convergence as well as energy and angular momentum conservation. We also set our simulations in the context of past simulations. This comparison reveals that it is the expansion of the giant before rapid in-spiral and not spinning up of the star that causes a larger final separation. We also suggest that the large range in unbound mass for different simulations is difficult to explain and may have something to do with simulations that are not fully converged.

We present the results of hydrodynamic simulations of the interaction between a 10 Jupiter mass planet and a red or asymptotic giant branch stars, both with a zeroage main sequence mass of 3.5 M ⊙ . Dynamic in-spiral timescales are of the order of few years and a few decades for the red and asymptotic giant branch stars, respectively. The planets will eventually be destroyed at a separation from the core of the giants smaller than the resolution of our simulations, either through evaporation or tidal disruption. As the planets in-spiral, the giant stars' envelopes are somewhat puffed up. Based on relatively long timescales and even considering the fact that further inspiral should take place before the planets are destroyed, we predict that the merger would be difficult to observe, with only a relatively small, slow brightening. Very little mass is unbound in the process. These conclusions may change if the planet's orbit enhances the star's main pulsation modes. Based on the angular momentum transfer, we also suspect that this star-planet interaction may be unable to lead to large scale outflows via the rotation-mediated dynamo effect of Nordhaus and Blackman. Detectable pollution from the destroyed planets would only result for the lightest, lowest metallicity stars. We furthermore find that in both simulations the planets move through the outer stellar envelopes at Mach-3 to Mach-5, reaching Mach-1 towards the end of the simulations. The gravitational drag force decreases and the in-spiral slows down at the sonic transition, as predicted analytically.

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 M , 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. 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.

The Rotten Egg Nebula has at its core a binary composed of a Mira star and an A-type companion at a separation >10 au. It has been hypothesized to have formed by strong binary interactions between the Mira and a companion in an eccentric orbit during periastron passage ∼800 years ago. We have performed hydrodynamic simulations of an asymptotic giant branch star interacting with companions with a range of masses in orbits with a range of initial eccentricities and periastron separations. For reasonable values of the eccentricity, we find that Roche lobe overflow can take place only if the periods are ≪ 100 yr. Moreover, mass transfer causes the system to enter a common envelope phase within several orbits. Since the central star of the Rotten Egg nebula is an AGB star, we conclude that such a common envelope phase must have lead to a merger, so the observed companion must have been a tertiary companion of a binary that merged at the time of nebula ejection. Based on the mass and timescale of the simulated disc formed around the companion before the common envelope phase, we analytically estimate the properties of jets that could be launched. Allowing for super-Eddington accretion rates, we find that jets similar to those observed are plausible, provided that the putative lost companion was relatively massive.

We still do not know what causes aspherical planetary nebula morphologies. A plausible hypothesis is that they are due to the presence of a close stellar or substellar companion. So far, only ∼40 binary central stars of planetary nebula have been detected, almost all of them with such short periods that their binarity is revealed by photometric variability. Here we have endeavoured to discover binary central stars at any separation, thus determining the unbiased binary fraction of central stars of planetary nebula. 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 the central stars in the I band we have searched for cool companions. We have found that 30% of our sample have an I band excess detected between one and a few σ, possibly denoting companions brighter than M3-4V and with separations smaller than ∼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 today's PN central star population is indeed the F6V-G2V stars. The error on our estimate cannot be constrained tightly, but we determine it to be between 10 and 30%. We conclude that the central star binary fraction may be larger than expected from the putative parent population. However, this result is based on a sample of 27 bona fide central stars and should be considered preliminary. The success of the I band method rests critically on high precision photometry and a reasonably large sample. From a similar analysis, using the more sensitive J band of a subset of 11 central stars, the binary fraction is 54% for companions brighter than ∼M5-6V and with separations smaller than about 900 AU. De-biassing this number in the same way as was done for the I band 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. Finally, we note how the previously-derived short period PN binary fraction of 15-20% is far larger than expected based on the main sequence binary fraction and period distribution.As a byproduct of our analysis we 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.