Critically rotating stars in binaries - an unsolved problem - In close binaries mass and angular momentum can be transferred from one star to the other during Roche-lobe overflow. The efficiency of this process is not well understood and constitutes one of the largest uncertainties in binary evolution. One of the problems lies in the transfer of angular momentum, which will spin up the accreting star. In very tight systems tidal friction can prevent reaching critical rotation, by locking the spin period to the orbital period. Accreting stars in systems with orbital periods larger than a few days reach critical rotation after accreting only a fraction of their mass, unless there is an effective mechanism to get rid of angular momentum. In low mass stars magnetic field might help. In more massive stars angular momentum loss will be accompanied by strong mass loss. This would imply that most interacting binaries with initial orbital periods larger than a few days evolve very non-conservatively. In this contribution we wish to draw attention to the unsolved problems related to mass and angular momentum transfer in binary systems. [0709.2285] Critically rotating stars in binaries - an unsolved problem - Critically rotating stars in binaries - an unsolved problem - S. E. de Mink O. R. Pols E. Glebbeek Abstract In close binaries mass and angular momentum can be transferred from one star to the other during Roche-lobe overflow. The efficiency of this process is not well understood and constitutes one of the largest uncertainties in binary evolution. One of the problems lies in the transfer of angular momentum, which will spin up the accreting star. In very tight systems tidal friction can prevent reaching critical rotation, by locking the spin period to the orbital period. Accreting stars in systems with orbital periods larger than a few days reach critical rotation after accreting only a fraction of their mass, unless there is an effective mechanism to get rid of angular momentum. In low mass stars magnetic field might help. In more massive stars angular momentum loss will be accompanied by strong mass loss. This would imply that most interacting binaries with initial orbital periods larger than a few days evolve very non-conservatively. In this contribution we wish to draw attention to the unsolved problems related to mass and angular momentum transfer in binary systems. We do this by presenting the first results of an implementation of spin up by accretion into the TWIN version of the Eggleton stellar evolution code. Keywords: Binaries, rotation, mass loss, angular momentum loss : 97.10.Pg, 97.20.Tr, 97.80.-d 1 Introduction The majority of stars are found in binary systems and a large fraction of them are so close that the two stars interact during their lifetime by exchanging mass. This completely alters the evolution of both stars compared to that of isolated stars. Mass is accreted untill the star reaches critical rotation. We recently implemented a model of spin up by mass transfer in the TWIN code, a detailed binary evolution code suitable for calculating large grids of binary models if used on a computer cluster. In this contribution we present the first results. 2 Implementation of Spin up in the Evolution Code The TWIN code (Eggleton et al., 1998 ; Eggleton & Kiseleva-Eggleton, 2002 ) is a binary evolution code based on the STARS code (Eggleton, 1971 , 1972 ; Pols et al., 1995 ) . It solves the structure and composition equations for the two stars in a binary simultaneously with equations for the orbit assuming rigid rotation. For the mass losing star we assume that the material is lost from the inner Lagrangian point with specific angular momentum h = ω D ​ R L 1 2 , ℎ subscript 𝜔 D superscript subscript 𝑅 subscript 𝐿 1 2 h=\omega_{\rm D}R_{L_{1}}^{2}, where ω D subscript 𝜔 D \omega_{\rm D} is the angular speed of rotation of the donor star and R L 1 subscript 𝑅 subscript 𝐿 1 R_{L_{1}} is the distance of the center of mass of the donor star to the inner Lagrangian point. We hope to solve this in the near future. Figure 1: Example of the evolution of the orbital period P orbit subscript 𝑃 orbit P_{\rm orbit} and the spin periods P spin , ∗ 1 , 2 subscript 𝑃 spin absent 1 2 P_{\rm spin,*1,2} of a binary consisting of a 20 M ⊙ subscript M direct-product \mathrm{M}_{\odot}   and a 16 M ⊙ subscript M direct-product \mathrm{M}_{\odot}   star. The labels are explained in the main text. 3 First Results As an example we show the evolution of a massive binary, consisting of a 20 M ⊙ subscript M direct-product \mathrm{M}_{\odot}   and a 16 M ⊙ subscript M direct-product \mathrm{M}_{\odot}   star, with an initial orbital period of 3 days, in such a close orbit that the tidal forces can prevent the accreting star from reaching critical rotation in the first phases of mass transfer. Figure  1 shows the orbital period and the spin periods of both stars against the number of the computed model, which is essentially a non-linear time axis stretching rapid phases of the evolution. We start the evolution with the spin periods of both stars synchronized and aligned with the orbit (A). The primary star expands as it evolves on the main sequence and fills its Roche lobe (B). It starts to transfer mass and angular momentum We briefly discuss several such mechanisms below, noting that how effective most of these mechanisms are is very uncertain. Tidal interaction tends to keep the spin period of the accreting star synchronized with the orbit. However, tides are not efficient enough during rapid mass transfer or in systems wider than a few days, as shown in the example above. Rotation-enhanced wind mass loss and the associated angular momentum loss in massive binaries with strong intrinsic winds can slow down the star when mass is lost preferentially in the equatorial plane or spin up the star when it is lost preferentially at the poles. In both cases it leads to highly non-conservative evolution.