Mass and angular momentum loss via decretion disks

1. Mass and angular momentum loss via decretion disks arXiv:1101.1732v1 Ref:arXiv:0010517v1 etc.

2. 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 • Other processes that may influence the outer disk radius • conclusions

3. 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

4. 1. Basic analytic scaling for disk mass loss • Assuming a star that rotates as a rigid body

5. Mass decouples in a spherical shell, where Rout=Req : (2)/(1):

6. Numerical models Develops set of equations governing structure and kinematics of the disk

7. 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 • Equation of continuity :

8. The stationary conservation of the r component of momentum gives μ=0.62 • The equation of conservation of the φ component of momentum, viscosity term

9. Close to the star, detailed energy-balance models show: (Millar & Marlborough 1998) In the outer regions: p>0

10. 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

11. Results of numerical models Solves these to derive simple scaling for how thermal expansion affects the outerdisk radius and disk mass loss

12. Stellar parameter evolved massive first star (Teff=30000 K, M=50M⊙,R=30R⊙) Note does not significantly depend on the assumed viscosity parameter

13. Close to the star (Okazaki 2001)

14. In the supersonic region Result in Shakura-Sunyaev viscosity prescription, not in the supersonic region From the numerical models In this case, equation

15. Factor ½ comes from the fact that the disk is not rotating as a Keplerian one at large radii For given the minimum ~ (2)/(1):

16. Radiative ablation Discusses the effects of inner-disk ablation, deriving the associated abated mass loss and its effect on the net disk angular momentum and mass loss

17. Stellar outflow disk, disk wind(~r) • Viscous doubling is not maintained in the supersonic wind • Mass-loss rate of such disk wind: - the classical Castor, Abbott & Klein (1975, CAK) stellar wind mass-loss rate

18. x=r/R Assuming the disk wind is not viscously coupled to the disk, then

19. P1(x) solid line P1/2(x) dashed line

20. A more detailed calculation gives: For Rout → ∞

21. Maximum disk wind mass-loss rate Maximum angular momentum loss rate For α≈0.6,

22. 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

23. The structure of disk and radiatively driven wind , radiative force Rout→∞ If net is carried away by disk outflow < > (p=0) Stellar wind disk wind disk itself

24. Conclusion

25. The disk mass loss is set by needed to keep the rotation at or below the Ωcrit A B C

26. Thank you!