Kazuya Saigo's paper98 Abstract page
Saigo98 Abstract
Similarity Solution for Formation of
Circumstellar Disk through the Collapse
of a Flattened Rotating Cloud
ABSTRACT
We present similarity solutions which describe the runaway
collapse of a rotating isothermal disk and its subsequent
inside-out collapse.
The similarity solutions contain
the sound speed, $ c _s $, and the ratio of the specific
angular momentum to the mass, $ \omega $, as model parameters.
During the runaway collapse, the surface density of the
disk is nearly constant in the central part and inversely
proportional to the radius in the tail.
As the central surface density increases by collapse,
the central high surface density part shrinks its radius.
Thus the surface density becomes a $1/r$ power-law at
the end of runaway collapse.
In the subsequent inside-out collapse phase,
the disk has two parts: an
inner rotating disk in quasi-equilibrium and an outer
dynamically infalling envelope. The inner disk and outer
envelope are bounded by a shock wave. The mass and outer
edge of the inner disk grow at a constant rate.
The accretion rate is proportional to the cubic of the
sound speed, i.e., $ \dot M \, \propto \, c _s {}^3 /G $,
where $ G $ denotes and gravitational constant.
The similarity solution
of the runaway collapse can reproduce numerical simulations
of dynamical collapse of either rotating or magnetized disks.
The similarity solution of the inside-out collapse
denotes growth of a centrifugally supported
circumstellar disks.
This solution can apply to a proto star which accretes
gas substantially through disk.