spin angular momentum evolution of the long-period algols dervişoğlu, a.; tout, christopher a.;...
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Spin angular momentum evolution of the long-period Algols
Dervişoğlu, A.; Tout, Christopher A.; Ibanoğlu, C. arXiv:1003.4392
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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
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• 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
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Observations and motivation
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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
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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
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U Cep: transient disc←eclipse duration vary, Porb 、 L consistent
with mass transfer and convective activity, q , transfer dynamically
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• 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
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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
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• 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
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• 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
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Models
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• 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
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• 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
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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
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• 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…
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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
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• 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
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• 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
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initial mass 5+3M⊙,P=5d, Bs=1.5kG
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Bs=1, 2, 3, 4 and 5 kG, from top to bottom
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initial mass 3.2+2M⊙,P=5d, Bs=1.5kG
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Bs=0.5, 1,2, 3 and 4 from top to bottom
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Initial mass 5+3M⊙
P=5d
β=0.9
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Thank you!