# Time-dependent modeling of extended thin decretion disks of critically rotating stars

### Kurfürst, P.; Feldmeier, A.; Krticka, J.

*Abstract:*
*Context.* During their evolution massive stars can reach the phase of
critical rotation when a further increase in rotational speed is no
longer possible. Direct centrifugal ejection from a critically or
near-critically rotating surface forms a gaseous equatorial decretion
disk. Anomalous viscosity provides the efficient mechanism for
transporting the angular momentum outwards. The outer part of the disk
can extend up to a very large distance from the parent star.

*Aims:* We study the evolution of density, radial and azimuthal velocity,
and angular momentum loss rate of equatorial decretion disks out to very
distant regions. We investigate how the physical characteristics of the
disk depend on the distribution of temperature and viscosity.

*Methods:* We calculated stationary models using the Newton-Raphson
method. For time-dependent hydrodynamic modeling we developed the
numerical code based on an explicit finite difference scheme on an
Eulerian grid including full Navier-Stokes shear viscosity.

*Results:* The sonic point distance and the maximum angular momentum loss
rate strongly depend on the temperature profile and are almost
independent of viscosity. The rotational velocity at large radii rapidly
drops accordingly to temperature and viscosity distribution. The total
amount of disk mass and the disk angular momentum increase with
decreasing temperature and viscosity.

*Conclusions:* The time-dependent one-dimensional models basically confirm
the results obtained in the stationary models as well as the assumptions
of the analytical approximations. Including full Navier-Stokes viscosity
we systematically avoid the rotational velocity sign change at large
radii. The unphysical drop of the rotational velocity and angular
momentum loss at large radii (present in some models) can be avoided in
the models with decreasing temperature and viscosity.

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