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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

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mass and angular momentum loss via decretion disks

Mass and angular momentum loss via decretion disks

arXiv:1101.1732v1

Ref:arXiv:0010517v1 etc.

outline
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
basic analytic scaling for disk mass loss
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

1 basic analytic scaling for disk mass loss
1. Basic analytic scaling for disk mass loss
  • Assuming a star that rotates as a rigid body
numerical models
Numerical models

Develops set of equations governing structure and kinematics of the disk

slide7

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 :
slide8

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
slide9

Close to the star, detailed energy-balance models show:

(Millar & Marlborough 1998)

In the outer regions: p>0

slide10

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

results of numerical models
Results of numerical models

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

stellar parameter evolved massive first star teff 30000 k m 50m r 30r
Stellar parameter evolved massive first star (Teff=30000 K, M=50M⊙,R=30R⊙)

Note does not significantly depend on the assumed viscosity parameter

close to the star
Close to the star

(Okazaki 2001)

in the supersonic region
In the supersonic region

Result in Shakura-Sunyaev viscosity prescription, not in the supersonic region

From the numerical models

In this case,

equation

slide15

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):

radiative ablation
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

slide17

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

slide18

x=r/R

Assuming the disk wind is not viscously coupled to the disk, then

slide19

P1(x) solid line

P1/2(x) dashed line

slide21

Maximum disk wind mass-loss rate

Maximum angular momentum loss rate

For α≈0.6,

mass loss of the star disk system at the critical limit
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

slide23

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

slide25

The disk mass loss is set by needed to keep the rotation at or below the Ωcrit

A

B

C