mass and angular momentum loss via decretion disks
DESCRIPTION
Mass and angular momentum loss via decretion disks. arXiv:1101.1732v1 Ref:arXiv:0010517v1 etc. Outline . Basic analytic scaling for disk mass loss Numerical models Results of numerical models Radiative ablation Mass loss of the star-disk system at the critical limit - PowerPoint PPT PresentationTRANSCRIPT
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Mass and angular momentum loss via
decretion disksarXiv:1101.1732v1
Ref:arXiv:0010517v1 etc.
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Basic analytic scaling for disk mass loss Numerical models Results of numerical models Radiative ablation Mass loss of the star-disk system at the
critical limit Other processes that may influence the
outer disk radius conclusions
Outline
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Basic analytic scaling for disk mass loss
Presents simple analytical relations for how the presence of a disk affects the mass loss at the critical limit
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Assuming a star that rotates as a rigid body
1. Basic analytic scaling for disk mass loss
criteqcrit IJRGM
IIJ
IIJ
IJ
0,/
0
3
rGMrvK /)(
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MR
RR
RIM
RRRMIJ
out
out
eq
eq
eq
outeqcritcrit
)1(2
2
Mass decouples in a spherical shell, where Rout=Req :
)2(23
2eqRIM
(2)/(1):
eqout RR /23
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Numerical modelsDevelops set of equations governing structure and kinematics of the disk
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obtain a detailed disc structure, stationary hydrodynamic equations, cylindrical coordinates (Okazaki 2001, Lightman1974 etc.)
vr, vΦ, and the integrated disk density , depend only on radius r
1. Equation of continuity :
dz
0)()(1)(1
zr vz
vr
vrrrt
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2. The stationary conservation of the r component of momentum gives
μ=0.623. The equation of conservation of the φ
component of momentum, viscosity term
peqH rRTTmkTarGMg )/(),/(,/ 0
22
~
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Hdz
rvaH
Hz
K
0
2
2
0
2
),21exp(
0,21
0 pTT eff (Millar & Marlborough 1998)
Close to the star, detailed energy-balance models show:
In the outer regions: p>0p
eq rRTT )/(0
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The system of hydrodynamic equations appropriate boundary conditions For obtaining vr at r=Req we use:
We have vr(Rcrit)=a to ensure the finiteness of the derivatives at this point
At the surface: vφ=vK
rrvM 2
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Results of numerical models
Solves these to derive simple scaling for how thermal expansion affects the outer disk radius and disk mass loss
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Stellar parameter evolved massive first star (Teff=30000 K, M=50M⊙,R=30R⊙)
Note does not significantly depend on the assumed viscosity parameter
J~ )(
21)( critKcrit RvRv
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Close to the star
2)( rrvavfor rr (Okazaki 2001)
2/1 rv2/1rrvJ
constrvvr
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In the supersonic region
rvr ln2
?0~ 2
rvvra
r
Result in Shakura-Sunyaev viscosity prescription, not in the supersonic regionFrom the numerical modelsIn this case,
equation
)(21)( critKcrit RvRv
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)(21)(
)()(
4103
21)(
)()(
4103
221
2
~
11
2
critKeqeqK
p
eq
eqK
p
eq
eqK
eq
crit
RJRRvMRaRv
pMJ
RaRv
pRR
Factor ½ comes from the fact that the disk is not rotating as a Keplerian one at large radii
p
eq
eqK
RaRv
M
11
)()(
)2(23
2eqRIM
)1(2out
eq
eq RR
RIM
eqout RR /23
(2)/(1):
For given the minimum
~
I
JRRpeq
crit
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Radiative ablationDiscusses the effects of inner-disk ablation, deriving the associated abated mass loss and its effect on the net disk angular momentum and mass loss
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Stellar outflow disk, disk wind(~r)Viscous doubling is not maintained in the
supersonic windMass-loss rate of such disk wind: - the classical Castor, Abbott & Klein (1975, CAK) stellar wind mass-loss rate
GMcLe
4
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x=r/R
Assuming the disk wind is not viscously coupled to the disk, then
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P1(x) solid lineP1/2(x) dashed line
)(rvv K
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A more detailed calculation gives:
For Rout → ∞
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Maximum disk wind mass-loss rate
Maximum angular momentum loss rate
For α≈0.6, CAKdw MM 251)(
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Mass loss of the star-disk system at the critical limit
Offers a specific recipe for incorporating disk mass loss rates into stellar evolution codes
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The structure of disk and radiatively driven wind , radiative force
Rout→∞If net is carried away by disk outflow < > (p=0)
J
Stellar wind disk wind disk itself
J
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Conclusion
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The disk mass loss is set by needed to keep the rotation at or below the Ωcrit
J
A
B
C
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Thank you!