Spin angular momentum evolution of the long-period Algols

Dervişoğlu, A.; Tout, Christopher A.; Ibanoğlu, C. arXiv:1003.4392

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

• 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

Observations and motivation

61 Algols

Primary component with mass M1: brighter, hotter and currently more massive ●

Secondary with mass M2: redder, mass lossing ○

ZAMS,continuous TAMS,dashed BGB,dotted

Locations of components in the HRD

Observations concerning Jorb and mass

Semidetached binaries (SDBs) with q=M2/M1>0.3: • P>5d: Jorb ≈ detached binaries (DBs)’

P<5d: Jorb < DBs’

II. For Jorb of DBs with total mass of 3 M⊙

Jorb of SDBs with P<5d: 45% smaller

with P>5d: 25% smaller III. J2 with P>5d twice one with P<5d

IV. J1 with P>5d about 24% larger than those with P<5d

more extremely, J2 with P>5d 65% larger than those with P<5d

For SDBs, mechanism govern angular momentum

evolution for short and long period are different

U Cep: transient disc←eclipse duration vary, Porb 、 L consistent

with mass transfer and convective activity, q , transfer dynamically

• 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

Accretion discs

Classical Algols: semidetached interacting eclipsing binary stars

M2: less massive, evolved, Spectral type F or later G, Luminosity class of giant or subgiant

• For P>5d

• R1 small enough relative to a , mass transfer , accretion disc

• Condition for formation of disc: Stream, ballistic flow from the inner L1

• aωmin<R1: formation of variable accretion structures

• aωmin>R1: form a permanent accretion disc of radius aωd

• aωmin<R1< aωd: form a transient disc

• R1>aωd: stream can impact the star directly

• The radii below which a disc must form ωmin

• The radii below which a disc may form ωd

• Solid dots: gainers with permanent accretion discs among the long-period Algols

ω

Models

• Keplerian disc, angular velocity Ωk 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

3

2

R

GMk

GMRhd

GMRMdt

dJacc

acc

• Let the radiusof gyration of the star be kR so that its total angular momentum is when spinning rigidly at Ω then

• For MS k2 ≈ 0.1 and varies little.

• Thus when 0.1<Ω0/Ωk<0.4 we

find 0.1>△M/M0>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 Ωk

22MRk

00

2

2

11

Mk

kM

k

Tidal forces and energy dissipation mechanisms• Tidal interaction act to synchronize stellar spins with

the orbital period

• tdiss 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

622111

a

R

I

MRq

tt disssync

• Intially the angular momentum of the gainer is

022

0 MRkJ s

022

MRkdt

dJ

tid

Initial mass 5+3M⊙,P=5d

Tides incapable of synchronizing the star with the orbit

No physical basis for stand tides ×107-8

Hope convective core’s ability (dissipate energy by tidal forces) may have effect,but…

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 RA

• Rate of change of A.M. of the star owing to the wind is

• RA 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

• 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 =BsR3 —— magnetic moment of stellar magnetic wind

• We assume Bs 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

initial mass 5+3M⊙,P=5d, Bs=1.5kG

Bs=1, 2, 3, 4 and 5 kG, from top to bottom

initial mass 3.2+2M⊙,P=5d, Bs=1.5kG

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

Initial mass 5+3M⊙

P=5d

β=0.9

Thank you!