This work aims to present our current best physical understanding of common-envelope evolution (CEE). We highlight areas of consensus and disagree- ment, and stress ideas which should point the way forward for progress in this important but long-standing and largely unconquered problem. Unusually for CEE-related work, we mostly try to avoid relying on results from population synthesis or observations, in order to avoid potentially being misled by previous misunderstandings. As far as possible we debate all the relevant issues starting from physics alone, all the way from the evolution of the binary system immediately before CEE begins to the processes which might occur just after the ejection of the envelope. In particular, we include extensive discussion about the energy sources and sinks operating in CEE, and hence examine the foundations of the standard energy formalism. Special attention is also given to comparing the results of hydrodynamic simulations from different groups and to discussing the potential effect of initial conditions on the differences in the outcomes. We compare current numerical techniques for the problem of CEE and also whether more appropriate tools could and should be produced (including new formulations of computational hydrodynamics, and attempts to include 3D processes within 1D codes). Finally we explore new ways to link CEE with observations. We compare previous simulations of CEE to the recent outburst from V1309 Sco, and discuss to what extent post-common-envelope binaries and nebulae can provide information, e.g. from binary eccentricities, which is not currently being fully exploited.

The carbon-enhanced metal-poor (CEMP) stars constitute approximately one fifth of the metal-poor ([Fe/H] < ∼ −2) population but their origin is not well understood. The most widely accepted formation scenario, at least for the majority of CEMP stars which are also enriched in s-process elements, invokes mass-transfer of carbon-rich material from a thermally-pulsing asymptotic giant branch (TPAGB) primary star to a less massive main-sequence companion which is seen today. Recent studies explore the possibility that an initial mass function biased toward intermediate-mass stars is required to reproduce the observed CEMP fraction in stars with metallicity [Fe/H] < −2.5. These models also implicitly predict a large number of nitrogen-enhanced metal-poor (NEMP) stars which is not seen. In this paper we investigate whether the observed CEMP and NEMP to extremely metal-poor (EMP) ratios can be explained without invoking a change in the initial mass function. We construct binary-star populations in an attempt to reproduce the observed number and chemical abundance patterns of CEMP stars at a metallicity [Fe/H] ∼ −2.3. Our binary-population models include synthetic nucleosynthesis in TPAGB stars and account for mass transfer and other forms of binary interaction. This approach allows us to explore uncertainties in the CEMP-star formation scenario by parameterization of uncertain input physics. In particular, we consider the uncertainty in the physics of third dredge up in the TPAGB primary, binary mass transfer and mixing in the secondary star. We confirm earlier findings that with current detailed TPAGB models, in which third dredge up is limited to stars more massive than about 1.25 M , the large observed CEMP fraction cannot be accounted for. We find that efficient third dredge up in low-mass (less than 1.25 M ), low-metallicity stars may offer at least a partial explanation for the large observed CEMP fraction while remaining consistent with the small observed NEMP fraction.

In the cores of young dense star clusters, repeated stellar collisions involving the same object can occur. It has been suggested that this leads to the formation of an intermediate-mass black hole. To verify this scenario we compute the detailed evolution of the merger remnant of three sequences, then follow the evolution until the onset of carbon burning, and estimate the final remnant mass to determine the ultimate fate of a runaway merger sequence. We use a detailed stellar evolution code to follow the evolution of the collision product. At each collision we mix the two colliding stars, accounting for the mass loss during the collision. During the stellar evolution we apply mass-loss rates from the literature, as appropriate for the evolutionary stage of the merger remnant. We computed models for high (Z = 0.02) and low (Z = 0.001) metallicity to quantify metallicity effects. We find that the merger remnant becomes a Wolf-Rayet star before the end of core hydrogen burning. Mass loss from stellar winds dominates the mass increase due to repeated mergers for all three merger sequences that we consider. In none of our high-metallicity models an intermediate-mass black hole is formed, instead our models have a mass of 10-14 M at the onset of carbon burning. For low metallicity the final remnant is more massive and may explode as a pair-creation supernova. We find that our metal-rich models become inflated as a result of developing an extended low-density envelope. This may increase the probability of further collisions, but self-consistent N-body calculations with detailed evolution of runaway mergers are required to verify this.

One possible scenario for the formation of carbon-enhanced metal-poor stars is the accretion of carbon-rich material from a binary companion which may no longer visible. It is generally assumed that the accreted material remains on the surface of the star and does not mix with the interior until first dredge-up. However, thermohaline mixing should mix the accreted material with the original stellar material as it has a higher mean molecular weight. We investigate the effect that this has on the surface abundances by modelling a binary system of metallicity Z = 10 −4 with a 2 M primary star and a 0.74 M secondary star in an initial orbit of 4000 days. The accretion of material from the wind of the primary leads to the formation of a carbon-rich secondary. We find that the accreted material mixes fairly rapidly throughout 90% of the star, with important consequences for the surface composition. Models with thermohaline mixing predict very different surface abundances after first dredge-up compared to canonical models of stellar evolution.

We investigate the formation of carbon-enhanced metal-poor (CEMP) stars via the scenario of mass transfer from a carbon-rich asymptotic giant branch primary to a low-mass companion in a binary system. We explore the extent to which material accreted from a companion star mixes with that of the recipient, focusing on the effects of thermohaline mixing and gravitational settling. We have created a new set of asymptotic giant branch models to determine what the composition of material being accreted in these systems will be. We then model a range of CEMP systems by evolving a grid of models of low-mass stars, varying the amount of material accreted by the star (to mimic systems with different separations), and also the composition of the accreted material (to mimic accretion from primaries of different mass). We find that with thermohaline mixing alone, the accreted material can mix with 16-88 per cent of the pristine stellar material of the accretor, depending on the mass accreted and the composition of the material. If we include the effects of gravitational settling, we find that thermohaline mixing can be inhibited and, in the case that only a small quantity of material is accreted, can be suppressed almost completely.

Subdwarf B (sdB) stars show chemical peculiarities that cannot be explained by diffusion theory alone. Both mass loss and turbulence have been invoked to slow down atomic diffusion in order to match observed abundances. The fact that some sdB stars show pulsations give upper limits on the amount of mass loss and turbulent mixing allowed. Consequently, nonadiabatic asteroseismology has the potential to decide which process is responsible for the abundance anomalies. We compute for the first time seismic properties of sdB models with atomic diffusion included consistently during the stellar evolution. The diffusion equations with radiative forces are solved for H, He, C, N, O, Ne, Mg, Fe and Ni. We examine the effects of various mass-loss rates and mixed surface masses on the abundances and mode stability. It is shown that the mass-loss rates needed to simulate the observed He abundances (10 −14 Ṁ /M yr −1 10 −13 ) are not consistent with observed pulsations. We find that for pulsations to be driven the rates should beṀ 10 −15 M yr −1 . On the other hand, weak turbulent mixing of the outer 10 −6 M can explain the He abundance anomalies while still allowing pulsations to be driven. The origin of the turbulence remains unknown but the presence of pulsations gives tight constraints on the underlying turbulence model.

In young dense clusters repeated collisions between massive stars may lead to the formation of a very massive star (above 100 M ⊙ ). In the past the study of the longterm evolution of merger remnants has mostly focussed on collisions between low-mass stars (up to about 2 M ⊙ ) in the context of blue-straggler formation. The evolution of collision products of more massive stars has not been as thoroughly investigated. In this paper we study the long-term evolution of a number of stellar mergers formed by the head-on collision of a primary star with a mass of 5-40 M ⊙ with a lower mass star at three points in its evolution in order to better understand their evolution.We use smooth particle hydrodynamics (SPH) calculations to model the collision between the stars. The outcome of this calculation is reduced to one dimension and imported into a stellar evolution code. We follow the subsequent evolution of the collision product through the main sequence at least until the onset of helium burning.We find that little hydrogen is mixed into the core of the collision products, in agreement with previous studies of collisions between low-mass stars. For collisions involving evolved stars we find that during the merger the surface nitrogen abundance can be strongly enhanced. The evolution of most of the collision products proceeds analogously to that of normal stars with the same mass, but with a larger radius and luminosity. However, the evolution of collision products that form with a hydrogen depleted core is markedly different from that of normal stars with the same mass. They undergo a long-lived period of hydrogen shell burning close to the main-sequence band in the Hertzsprung-Russell diagram and spend the initial part of core helium burning as compact blue supergiants.

In recent years, accurate observational constraints become available for an increasing number of Galactic X-ray binaries. Together with proper motion measurements, we could reconstruct the full evolutionary history of X-ray binaries back to the time of compact object formation. In this paper, we present the first study of the persistent X-ray source Cygnus X-1 that takes into account of all available observational constraints. Our analysis accounts for three evolutionary phases: orbital evolution and motion through the Galactic potential after the formation of black hole (BH), and binary orbital dynamics at the time of core collapse. We find that the mass of the BH immediate progenitor is 15.0 − 20.0 M ⊙ , and at the time of core collapse, the BH has potentially received a small kick velocity of ≤ 77 km s −1 at 95% confidence. If the BH progenitor mass is less than ∼ 17 M ⊙ , a non zero natal kick velocity is required to explain the currently observed properties of Cygnus X-1. Since the BH has only accreted mass from its companion's stellar wind, the negligible amount of accreted mass is impossible to explain the observationally inferred BH spin of a * > 0.95, and the origin of this extreme BH spin must be connected to the BH formation itself. Right after the BH formation, we find that the BH companion is a 19.8 − 22.6 M ⊙ main sequence star, orbiting the BH at a period of 4.7 − 5.2 days. Furthermore, recent observations show that the BH companion is currently super-synchronized. This supersynchronism indicates that the strength of tides exerted on the BH companion should be weaker by a factor of at least two compared to the usually adopted strength.