arXiv: v1 Ref:arXiv: v1 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

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

Mass decouples in a spherical shell, where R out =R eq : (2)/(1):

Develops set of equations governing structure and kinematics of the disk

obtain a detailed disc structure, stationary hydrodynamic equations, cylindrical coordinates (Okazaki 2001, Lightman1974 etc.) v r, v Φ, and the integrated disk density, depend only on radius r 1. Equation of continuity :

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

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

The system of hydrodynamic equations appropriate boundary conditions For obtaining v r at r=R eq we use: We have v r (R crit )=a to ensure the finiteness of the derivatives at this point At the surface: v φ =v K

Solves these to derive simple scaling for how thermal expansion affects the outer disk radius and disk mass loss

Note does not significantly depend on the assumed viscosity parameter

(Okazaki 2001)

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

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

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

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

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

P 1 (x) solid line P 1/2 (x) dashed line

A more detailed calculation gives: For R out → ∞

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

Offers a specific recipe for incorporating disk mass loss rates into stellar evolution codes

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

The disk mass loss is set by needed to keep the rotation at or below the Ω crit ABCABC