Mass loss in evolved massive stars is one of the outstanding questions in stellar evolution theory. During the Luminous Blue Variable (LBV) phase, stars can lose several solar masses during so-called S Doradus outbursts and giant eruptions. There is no established physical mechanism yet to explain this phenomenon, but numerous hypotheses have been proposed. In general, the evolution of the majority of massive stars is affected by binary interactions. It should therefore be considered that LBVs could be formed through binary channels or that the LBV instability itself may be triggered or assisted by a close companion.

It is now clear that a binary evolutionary pathway is responsible for a significant fraction of all planetary nebulae, with some authors even going so far as to claim that binarity may be a near-requirement for the formation of an observable nebula. This chapter discusses the theoretical and observational support for the importance of binarity in the formation of planetary nebulae, initially focusing on common envelope evolution but also covering wider binaries. Furthermore, the chapter highlights the impact that these results have on our understanding of other astrophysical phenomena, includingType Ia supernovae, chemically peculiar stars and circumbinary exoplanets. Finally,the latest results will be presented with regard to the relationship between post–common-envelope central stars and the abundance discrepancy problem in planetary nebulae, and what further clues this may hold in forwarding our understanding of the common-envelope phase itself.

Any white dwarf or neutron star that accretes enough material from a red giant companion, such that this interaction can be detected at some wavelength, is currently termed asymbiotic star (orbital period ∼2–3 years). In the majority of ∼400 known systems, the white dwarf burns nuclearly at its surface the accreted material, and the resulting high temperatureand luminosity allow ionisation of a large fraction of the cool giant’s wind. X-ray observations are revealing the existence of a parallel (and large ?) population of optically quiet, accreting-only symbiotic stars. Accretion flows and disks, ionisation fronts and shock, complex 3D geometries and new evolution channels are gaining relevance and are reshaping our understanding of symbiotic stars. The chapter reviews the different types of symbiotic stars currently in the family and their variegated outburst behaviours.

Stars are mostly found in binary and multiple systems, as at least 50% of all solarlike stars have companions – a fraction that goes up to 100% for the most massive stars. Moreover, a large fraction of them will interact in some way or another: at least half of the binary systems containing solarlike stars, in particular when the primary will evolve on the Asymptotic Giant Branch and at least 70% of all massive stars. Such interactions can, and often will, alter the structure and evolution of both components in the system. This will, in turn, lead to the production of exotic objects whose existence cannot be explained by standard stellar evolution models. Moreover, the chapter explores one of the most luminous stars in our Galaxy, Eta Carinae. The year 2016 saw the first ever announcement of the detection of gravitational waves, coming from the merging of a binary black hole. In this chapter, the author leads the reader through a walk in the zoo of binary stars, highlighting some specific examples.

This chapter discusses the problem of modelling mixing and chemical element transport in low- and intermediate-mass stellar evolution calculations. In particular, emphasis is given to the uncertainties and parametrisations involved, and hopes of future developments based on asteroseismic data and hydrodynamics simulations.

Binary stars are of course more than two stars, but they are also at least two stars. This chapter will review some aspects of the physics governing the evolution of single massive stars. It will also review the uncertainties of key physical ingredients: mass loss, rotation and convection.

The stellar Initial Mass Function (IMF) can be conveniently represented as a canonical two-part power law function and is largely invariant for star formation regions evident in the Local Group of galaxies. The lack of massive stars in regions of low star formation density and other evidence imply that the IMF is not a probability density distribution function, but is instead closer to an optimal density distribution function. Binary stars and stellar dynamics have a very significant influence on the counts of low-mass stars and need to be corrected for. This chapter offers a review of how recent advancements in the measurement of the IMF from detailed star counts in different environments (e.g., young massive clusters, globular clusters, elliptical galaxies and ultrafaint dwarf galaxies), properly interpreted via detailed numerical models, indicate that the environmental conditions and metallicity both have an impact on the shape of the IMF.

The so-called blue straggler Ssars (BSSs) represent the most striking (and certainly the most famous) evidence of binary stars in Galactic Globular Clusters (GCs). In this chapter, the most intriguing properties of BSSs are discussed and two innovative tools based on the physical properties of these fascinating objects are presented: (1) the dynamical clock, and (2) the stellar scale. The former uses the level of central segregation of BSSs to empirically measure the level of dynamical evolution suffered by the parent cluster. The the stellar scale is a spectroscopic tool that allows differential measures of stellar mass able to efficiently distinguish massive objects (as the elusive evolved BSS progeny) from normal low-mass cluster stars.

We still do not have an end-to-end theory of binary star formation that both satisfies observational constraints and also includes all necessary physical ingredients. Large-scale star formation simulations do an excellent job of replicating binary statistics under severely simplified physical conditions (neglect of thermal feedback and magnetic fields). Simulations that include these processes, however, tend to suppress binary formation, and their extra computational expense makes it hard to generate statistical samples of binaries for observational comparison. In addition to reviewing the literature on binary formation simulations, this chapter also examines the insights into the process that are provided by observations of the youngest protomultiple systems.

The binary fraction of metal-poor stars provides important constraints on star formation in the early Galaxy, and is a key piece of information in the understanding the origin of the observed high frequency of C enhanced metal-poor stars. It is now widely accepted that a majority of solar metallicity stars are in binaries; it is not clear, however, if this is the case for metal-poor stars. While state-of-the-art models agree in predicting an increase in the binary fraction and a shift towards lower values for the orbital period distribution at extremely low metallicities, the observational findings paint a patchier picture. This chapter summarises the key motivations for the study of binaries in the very metal-poor regime and reviews the current state of the field and the plans for the future.

In this chapter, the focus is on the properties of post–Asymptotic Giant Branch (post-AGB) stars in binary systems. Their spectral energy distributions (SEDs) are very characteristic: they show a near-infrared excess, indicative of the presence of warm dust, while the central stars are too hot to be in a dust-production evolutionary phase. This allows for an efficient detection of binary post-AGB candidates. It is now well established that the near-infrared excess is produced by the inner rim of a stable dusty disc that surrounds the binary system. These discs are scaled-up versions of protoplanetary discs and form a second generation of stable Keplerian discs. They are likely formed during a binary interaction process when the primary was on ascending the AGB. The chapter summarises what has been learnt so far from the observational properties of these post-AGB binaries. The impact of the creation, lifetime and evolution of the circumbinary discs on the evolution of the system is yet to be fully understood.

Short-duration gamma-ray bursts (short-GRBs) are thought to be produced during the merger ofcompact binary stars involving at least one neutron star. The recent detection of a gravitational wave signal coincident with a short-GRB (170817), albeit one with unusually low intrinsic luminosity, has cemented this link and opened a new era of multimessenger astrophysics. Long-duration gamma-ray bursts are produced by the core collapse of envelope-stripped massive stars, which may also be the end product of binary evolution. Establishing the nature of the long-GRB progenitor more definitely is important not only for our understanding of GRBs, but also for their use as probes of the distant Universe, many of which depend on how representative GRBs are of the general population of massive stars.

The observational parameter space that allows us to detect and describe nonsingle stars is enormous. It comes from the fact that binary stars are very numerous, present themselves with a huge variety of physical properties and have signatures in all astronomical fundamental techniques (astrometry, photometry, spectroscopy). It is, therefore, not a surprise that any significant improvement in observational astronomical facilities has an important impact on our knowledge of binaries. We are currently in an era where the development of various large-scale surveys is impressive. Among them, Gaia and LSST are exceptional surveys that have and likely will have a profound and long-lasting impact on the astronomical landscape. This chapter reviews the status of these two projects, and considers how they improve our knowledge of binary stars.

The chapter presents a summary of the present-day understanding of Type Ia supernova progenitors, mostly discussing the observational approach. This chapter is to provide the nonspecialist with a sufficiently comprehensive view of where we stand.

The statistical distributions of main-sequence multiple-star properties reveal invaluable insights into the processes of binary star formation, and they provide initial conditions for population synthesis studies of binary star evolution. Binary stars are discovered and characterised through a variety of techniques. Correcting for their respective selection effects and combining the bias-corrected results is not a trivial process. This is partially because the intrinsic distributions of companion frequency, primary mass M1, orbital period P, mass ratio q and eccentricity e are all interrelated , i.e., f(M1,P,q,e)/= f(M1)f(P)f(q)f(e). In particular, the binary fraction increases with primary mass, especially across short orbital periods, and binaries become weighted towards larger eccentricities and more extreme mass ratios with increasing separation, especially for more massive primaries. Moreover, binary star statistics vary with age, environment and metallicity. This chapter summarises the strengths and limitations of the various observational techniques, and reviews the statistical correlations in the intrinsic (bias-corrected) multiple-star properties.

With the discovery of both binary black hole mergers and a binary neutron star merger, the field of gravitational wave astrophysics has really begun. The LIGO and Virgo detectors will soon improve their sensitivity allowing for the detection of thousands new sources. All these measurements will provide new answers to open questions in binary evolution related to mass transfer, out-of-equilibrium stars and the role of metallicity. The data will give new constraints on uncertainties in the evolution of (massive) stars, such as stellar winds, the role of rotation and the final collapse to a neutron star or black hole. In the long run, the thousands of detections by the Einstein Telescope will enable us to probe their population in great detail over the history of the Universe. For neutron stars, the first question is whether the first detection GW170817 is a typical source or not. In any case, it has spectacularly shown the promise of complementary electromagnetic follow-up. For white dwarfs, we have to wait for LISA (around 2034), but new detections by, e.g., Gaia and LSST will prepare for the astrophysical exploitation of the LISA measurements.