Spin angular momentum evolution of the long-period Algols

Abstract

We consider the spin angular momentum evolution of the accreting components of Algol‐type binary stars. In wider Algols the accretion is through a disc so that the accreted material can transfer enough angular momentum to the gainer that material at its equator should be spinning at breakup. We demonstrate that even a small amount of mass transfer, much less than required to produce today's mass ratios, transfers enough angular momentum to spin the gainer up to this critical rotation velocity. However the accretors in these systems have spins typically between 10 and 40 per cent of the critical rate. So some mechanism for angular momentum loss from the gainers is required. Unlike solar‐type chromospherically active stars, with enhanced magnetic activity which leads to angular momentum and mass loss, the gainers in classical Algols have radiative envelopes. We further find that normal radiative tides are far too weak to account for the necessary angular momentum loss. Thus enhanced mass loss in a stellar wind seems to be required to spin‐down the gainers in classical Algol systems. We consider generation of magnetic fields in the radiative atmospheres in a differentially rotating star and the possibility of angular momentum loss driven by strong stellar winds in the intermediate‐mass stars, such as the primaries of the Algols. Differential rotation, induced by the accretion itself, may produce such winds which carry away enough angular momentum to reduce their rotational velocities to the today's observed values. We apply this model to two systems with initial periods of 5 d, one with initial masses 5 and and the other with 3.2 and . Our calculations show that, if the mass outflow rate in the stellar wind is about 10 per cent of the accretion rate and the dipole magnetic field is stronger than about 1 kG, the spin rate of the gainer is reduced to below breakup velocity even in the fast phase of mass transfer. Larger mass loss is needed for smaller magnetic fields. The slow rotation of the gainers in the classical Algol systems is explained by a balance between the spin‐up by mass accretion and spin‐down by a stellar wind linked to a magnetic field.

Mass loss out of close binaries

“…This value is in good agreement with the mass transfer rate given in Polidan (1989). It is pointed out by Simon (1999) and Dervisoglu et al (2010) that the gainer rotates at the high equatorial velocity of ∼212 km s −1 . This is, however, far below the critical velocity of ∼612 km s −1 so that in view of the Roche model (e.g.…”

“…A refined value of T spot ≈ 30 000 K was then assigned to the hot spot by the same author who assumes that this HTAR (high temperature accretion region) radiates as a black body. It is also interesting to notice that the gainer in this binary rotates 7.8 times faster than the synodic value (Dervisoglu et al 2010). …”

Critically-rotating accretors and non-conservative evolution in Algols

“…Except for the study of Dervişoglu et al (2010), there are, however, basically no simulations that follow the angular-momentum evolution for both the stars and the orbit in detail, and that account for torques arising from tides, mass transfer, magnetic-field effects, disc accretion or direct impact, and spin-down mechanisms.…”

Efficiency of ETV diagrams as diagnostic tools for long-term period variations

“…The disk will be considered as permanent (or high viscous) provided that the fluid's material bulk viscosity is efficient enough to return the proffered angular momentum back to the orbit (once more, we adopt the notation of Kaitchuck et al 1985) or, equivalently, when it experiences a strong coupling regime with the donor (e.g., Hut & Paczynski 1984;Verbunt & Rappaport 1988). However, material at the inner edge of the disk still has angular momentum that acts to spin up the accretor at the expense of the orbital angular momentum (e.g., Packet 1981;Marsh et al 2004;Dervişoglu et al 2010;Deschamps et al 2013). The description of the period evolution of such systems does not differ at all from those systems that accommodate a transient disk, by simply replacing r r by r 2 = R 2 /A orb or r 1 = R 1 /A orb when the gainer is the less or the more massive star, respectively (Marsh et al 2004).…”

“…In Algols, for instance, tides seem incapable of spinning down the gainer during the transfer process (Dervişoglu et al 2010;Deschamps et al 2013), considering that radiative damping is the driving tidal dissipation mechanism for stars with a radiative envelope (Zahn 1977). By using the appropriate tidal torque and apsidal motion constants of Zahn (1975, see Table 1 of his work) for the gainer of IO UMa (M 1 = 2.1 M , e.g., Soydugan et al 2013), for example, a long synchronization time of 9.69 × 10 9 yr arises.…”