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
Mass and angular momentum loss via
decretion disksarXiv:1101.1732v1
Ref:arXiv:0010517v1 etc.
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
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
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 /)(
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
Numerical modelsDevelops set of equations governing structure and kinematics of the disk
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
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
~
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
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
Results of numerical models
Solves these to derive simple scaling for how thermal expansion affects the outer disk radius and disk mass loss
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
Close to the star
2)( rrvavfor rr (Okazaki 2001)
2/1 rv2/1rrvJ
constrvvr
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
)(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
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
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
x=r/R
Assuming the disk wind is not viscously coupled to the disk, then
P1(x) solid lineP1/2(x) dashed line
)(rvv K
A more detailed calculation gives:
For Rout → ∞
Maximum disk wind mass-loss rate
Maximum angular momentum loss rate
For α≈0.6, CAKdw MM 251)(
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
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
Conclusion
The disk mass loss is set by needed to keep the rotation at or below the Ωcrit
J
A
B
C
Thank you!