An alternative to common envelope evolution

ABSTRACT We investigate the evolution of interacting binaries where the donor star is a low-mass giant more massive than its companion. It is usual to assume that such systems undergo common envelope (CE) evolution, where the orbital energy is used to eject the donor envelope, thus producing a closer binary or a merger. We suggest instead that because mass transfer is superEddington even for non-compact companions, a wide range of systems avoid this type of CE phase. The accretion energy released in the rapid mass-transfer phase unbinds a significant fraction of the giant's envelope, reducing the tendency to dynamical instability and merging. We show that our physical picture accounts for the success of empirical parametrizations of the outcomes of assumed CE phases. Key words: binaries: close -stars: evolution. I N T RO D U C T I O N Binary systems tend to shrink when they transfer mass from the more massive to the less massive star. The consequent contraction of the donor's Roche lobe leads to high transfer rates, proceeding on a thermal or near-dynamical time-scale depending on whether this star is predominantly radiative or convective. There is evidently a tendency for such systems to enter common envelope (CE) evolution, where the donor star engulfs the system Despite this early promise, several decades of strenuous effort have failed to provide convincing evidence that the process works as originally hoped (see Taam & Sandquist 2000, and references therein). Technically the problem is difficult, requiring full 3D hydrodynamics and a careful treatment of the dissipation processes. However, there appear to be problems at a more basic level, which are manifest when we consider the most popular parametrization of CE (e.g. Webbink 1984). This compares the envelope binding energy with the change in orbital energy as E-mail: martin.beer@astro.le.ac.uk Here M g is the giant mass, R g its radius, M c its core mass, M e its envelope mass, M 2 is the accretor mass (assumed fixed during CE evolution) and a i , a f are the initial and final binary separations. Stellar structure calculations specify the dimensionless parameter λ < 1, which is often taken as a constant, for example, λ = 0.5, and α < 1 is a dimensionless efficiency parameter. Clearly only the combination αλ is important. The problem which emerges is that in many cases the post-CE orbital separation a f is too large, that is, there was too little orbital energy release to unbind the giant envelope. Formally, this problem appears in the requirement αλ > 1 (values αλ ∼ 6 are not unknown). Nelemans & Tout (2005) show that these problems are still worse when considering the formation of double white dwarf binaries, where it is possible to reconstruct the state of the progenitor binaries. The required values of αλ are actually negative in most cases. All these difficulties point to the need for an extra source of energy to unbind the giant envelope. A clue to this energy source comes from an observed case which CE evolution clearly cannot produce. The low-mass X-ray binary Cyg X-2 consists of a neutron star accreting from a low-mass donor ( 0.5-0.7 M ) in a 9.8-d orbit (see King & Ritter 1999, and references therein). The donor has radius 7 R , and its effective temperature implies luminosity 150 L . Evidently this star was considerably more massive in the recent past and we are now seeing its luminous inner layers before they cool. But the current binary period of 9.8 d makes the binary so wide that far too little orbital energy was available to unbind the envelope, regardless of how wide the pre-CE separation a i was. However, in this case the required extra energy source is clear. Assuming that mass transfer began when the donor was the more massive star and still predominantly radiative, mass flowed towards the neutron star on a therma