Common-envelope events (CEEs), during which two stars temporarily orbit within a shared envelope, are believed to be vital for the formation of a wide range of close binaries. For decades, the only evidence that CEEs actually occur has been indirect, based on the existence of systems that could not be otherwise explained. Here we propose a direct observational signature of CEE arising from a physical model where emission from matter ejected in a CEE is controlled by a recombination front as the matter cools. The natural range of timescales and energies from this model, as well the expected colors, lightcurve shapes, ejection velocities and event rate, match those of a recentlyrecognized class of red transient outbursts.Many binary star systems, including X-ray binaries, cataclysmic variables, close doubleneutron stars, and the potential progenitors of Type Ia supernovae and short-duration γ-ray bursts, are thought to be formed by CEEs. Because most stellar-mass binary merger sources for gravitational waves have experienced a CEE in their past, improved knowledge of CEEs should decrease the large uncertainty in theoretically-predicted merger rates. However, the short timescale expected for CEEs suggested that we would never directly observe them, allowing us only to draw inferences from the systems produced.A CEE begins when a binary orbit becomes unstable and decays. This might, for example, be driven purely by tidal forces (i.e. the Darwin instability), although CEEs are more commonly imagined as following a period of rapid mass transfer from one star to the other (1). In some cases the rate of transfer is so high that the receiving star is unable to accrete all the matter without forming a shared common envelope (CE) around the binary. This CE causes drag on one or both stars and hence orbital decay, with orbital energy and angular momentum 1

One of the two outcomes of a common envelope event is a merger of the two stars. To date, the best known case of a binary merger is the V1309 Sco outburst, where the orbital period was known and observed to decay up to the outburst. Using the hydrodynamical code StarSmasher, we study in detail which characteristics of the progenitor binary affect the outburst and produce the best match with observations. We have developed a set of tools in order to quantify any common envelope event. We consider binaries consisting of a 1.52M giant and a 0.16M companion with P orb ∼ 1.4 days, varying the nature of the companion and its synchronization. We show that all considered progenitor binaries evolve towards the merger primarily due to the Darwin instability. The merger is accompanied by mass ejection that proceeds in several separate mass outbursts and takes away a few percent of the donor mass. This very small mass, nonetheless, is important as it is not only sufficient to explain the observed light-curve, but it also carries away up to 1/3 of the both initial total angular momentum and initial orbital energy. We find that all synchronized systems experience L 2 mass loss that operates during just a few days prior to merger and produces ring-shaped ejecta. The formed star is always a strongly heated radiative star that differentially rotates. We conclude that the case of a synchronized binary with a main-sequence companion gives the best match with observations of V1309 Sco.

In this Letter, we investigate the role of recombination energy during a common envelope event. We confirm that taking this energy into account helps to avoid the formation of the circumbinary envelope commonly found in previous studies. For the first time, we can model a complete common envelope event, with a clean compact double white dwarf binary system formed at the end. The resulting binary orbit is almost perfectly circular. In addition to considering recombination energy, we also show that between 1/4 and 1/2 of the released orbital energy is taken away by the ejected material. We apply this new method to the case of the double white dwarf system WD 1101+364, and we find that the progenitor system at the start of the common envelope event consisted of an ∼1.5 M⊙ red giant star in an ∼30 d orbit with a white dwarf companion.

Common envelope events are important interactions between two binary stars that lead to the formation of close binary systems. We present here a systematic three-dimensional study in which we model common envelope events with low-mass giant donors. The results allow us to revise the energy formalism that is usually used to determine common envelope event outcomes. We show that the energy budget for this type of system should include the recombination energy, and that it also must take into account that a significant fraction of the released orbital energy is taken away by the ejecta. We provide three ways in which our results can be used by binary population synthesis studies: a relation that links the observed post-common envelope binary with the initial binary parameters, a fitting formula for the α ce λ parameter of the standard energy formalism, and a revised energy formalism that takes into account both the recombination energy and the energy that is taken away by the ejecta.

We present a three-dimensional (3D) study of common envelope events (CEEs) to provide a foundation for future one-dimensional (1D) methods to model the self-regulated phase of a CEE. The considered CEEs with a low-mass red giant end with one of three different outcomes -merger, slow spiral-in, or prompt formation of a binary. To understand which physical processes determine different outcomes, and to evaluate how well 1D simulations model the self-regulated phase of a CEE, we introduce tools that map our 3D models to 1D profiles. We discuss the differences in the angular momentum and energy redistribution in 1D and 3D codes. We identified four types of ejection processes: the pre-plunge-in ejection, the outflow during the plunge-in, the outflow driven by recombination, and the ejection triggered by a contraction of the circumbinary envelope. Significant mass is lost in all cases, including the mergers. Therefore a self-regulated spiral-in can start only with a strongly reduced envelope mass. We derive the condition to start a recombination outflow, which can proceed either as a runaway or a stationary outflow. We show that the way the energy of the inspiraling companion is added to the envelope in 1D studies intensifies the envelope's entropy increase, alters the start of the recombination outflow, and leads to different outcomes in 1D and 3D studies. The steady recombination outflow may dispel most of the envelope in all slow spiral-in cases, making the existence of a long-term self-regulated phase debatable, at least for low-mass giant donors.