1. Spin angular momentum evolution of the long-period Algols Dervişoğlu, A.; Tout, Christopher A.; Ibanoğlu, C. arXiv:1003.4392

2. Introduction Evolution of single stars is well modelled - mass loss, rotation, convection - appropriate, successful empirical treatments Evolution of a binary star - interaction between the components Mystery of Algol systems (Crawford 1955; Hoyle 1955) Prototype of semi-detached Algol-type binary stars - one evolved and one main-sequence component - unavoidable stages of evolution: mass transfer, mass loss A.M. and magnetic interaction

3. Over the last few decades, mass transfer well modelled - episodes: accretion discs, disc-like structures A.M. transfer during mass exchange not well understood Current approximation of binary star evolution, not adequately explain spin A.M. of accreting star - high A.M. disc material → breakup rotational velocity - less than time needed to reverse mass ratio, enter Algol phase Discuss formation of discs, consider spin A.M. evolution - discs, tides, magnetic stellar wind We demonstrate: remove excess A.M. from the gainer, tidal effects play a minor role, magnetic stellar wind do most

4. Observations and motivation

5. 61 Algols Primary component with mass M 1 : brighter, hotter and currently more massive ● Secondary with mass M 2 : redder, mass lossing ○ ZAMS,continuous TAMS,dashed BGB,dotted Locations of components in the HRD

6. Observations concerning J orb and mass Semidetached binaries (SDBs) with q=M 2 /M 1 >0.3: P>5d: J orb ≈ detached binaries (DBs)’ P<5d: J orb < DBs’ II.For J orb of DBs with total mass of 3 M ⊙ J orb of SDBs with P<5d: 45% smaller with P>5d: 25% smaller III.J 2 with P>5d twice one with P<5d IV.J 1 with P>5d about 24% larger than those with P<5d more extremely, J 2 with P>5d 65% larger than those with P<5d For SDBs, mechanism govern angular momentum evolution for short and long period are different

8. U Cep: transient disc←eclipse duration vary, P orb 、 L consistent with mass transfer and convective activity, q, transfer dynamically

9. The above results let us to reconsider tidal interaction and angular momentum transfer in system in which mass transfer is still ocurring Evolutions of Algols, angular momentum loss mechanisms (Packet 1981; Eggleton 2000; Chen, Li & Qian 2006) none is entirely satisfactory In any case, accretion discs can be formed when relative R of mass-accreting star is small enough

10. Accretion discs Classical Algols: semidetached interacting eclipsing binary stars M 2 : less massive, evolved, Spectral type F or later G, Luminosity class of giant or subgiant For P>5d R 1 small enough relative to a, mass transfer, accretion disc Condition for formation of disc: Stream, ballistic flow from the inner L 1

11. aω min <R 1 : formation of variable accretion structures aω min >R 1 : form a permanent accretion disc of radius aω d aω min <R 1 < aω d : form a transient disc R 1 >aω d : stream can impact the star directly

12. The radii below which a disc must form ω min The radii below which a disc may form ω d Solid dots: gainers with permanent accretion discs among the long- period Algols ω

13. Models

14. Keplerian disc, angular velocity Ω k of material at radius R is given by The specific angular momentum of accreted material at the surface of the star, of radius R, is The rate of angular momentum transferred from the disc to the star is

15. Let the radiusof gyration of the star be kR so that its total angular momentum is when spinning rigidly at Ω then For MS k 2 ≈ 0.1 and varies little. Thus when 0.1<Ω 0 /Ω k <0.4 we find 0.1> △ M/M 0 >0.06 Despite having high spin velocities observations show that the detached components in most of the Algols do not actually attain their critical rotational velocity The shaded area, material from the disc to spin the star up to Ω k

16. Tidal forces and energy dissipation mechanisms Tidal interaction act to synchronize stellar spins with the orbital period t diss is the time-scale for the most effective dissipation mechanism - convective envelope: convective eddies - radiative envelope: gravity wave dissipation energy dissipation in convective envelopes is much more effective than in radiative envelopes

17. Intially the angular momentum of the gainer is Initial mass 5+3M ⊙,P=5d Tides incapable of synchronizing the star with the orbit No physical basis for stand tides ×10 7-8 Hope convective core’s ability (dissipate energy by tidal forces) may have effect,but…

18. Magnetic winds The total A.M. lost from a star in a wind coupled to a magnetic field = A.M. carried away by the wind material corotating up to R A Rate of change of A.M. of the star owing to the wind is R A at which outflow speed = local magnetic Alfven speed For a spherical outflow The A.M. loss rate depends on the field structure and flow velocity assume where n describles the geometry of the stellar field n=3 → dipole field

19. It is assumed thermal wind velocity is of the order of the escape velocity Some of the stellar magnetic dipole flux connects to the accretion disc and transports A.M. between star and disc where μ =B s R 3 —— magnetic moment of stellar magnetic wind

20. We assume B s remains constant because the mass of the accreting star increases at a substantial rate (10-5 M ⊙ /yr) All observed Agols show reversed mass ratio so much of the material lost by the donor must be accreted by the gainer. we may write and 0<β<1

21. initial mass 5+3M ⊙,P=5d, B s =1.5kG

23. B s =1, 2, 3, 4 and 5 kG, from top to bottom

24. initial mass 3.2+2M ⊙,P=5d, B s =1.5kG

26. Bs=0.5, 1,2, 3 and 4 from top to bottom

27. Initial mass 5+3M ⊙ P=5d β=0.9

29. Thank you!