Star Formation in Cold, Magnetized Molecular Clouds: A Semi-Analytic Model
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**Session 84 -- Star Forming Clouds**
*Display presentation, Wednesday, 11, 1995, 9:20am - 6:30pm*

## [84.11] Star Formation in Cold, Magnetized Molecular Clouds: A Semi-Analytic Model

*P.N. Safier, C. F. McKee, S. W. Stahler (UC Berkeley)*
We present an idealized, *semi-analytic*
model of the evolution of
a magnetized molecular cloud due to ambipolar diffusion.
This model allows us to
follow the quasi-static evolution of
a core up to its collapse, and the subsequent
evolution of the remaining envelope. Our main simplifying assumptions are:
\begin{enumerate}
\item Thermal stresses are negligible compared to magnetic
stresses.
\item The cloud is spherically symmetric, and the only non-vanishing
component of the Lorentz force is given by the scalar term $\propto
dB^2/dr$, where $B=B(r)$, and $r$ is the usual spherical radius.
\item The evolution is quasi-static and the ion velocity is
negligible compared to the neutral velocity.
\end{enumerate}

For Lagrangian inital conditions of the form $\rho(t=0,M) \propto
1/(A+M)^2$, where $A$ is a free parameter, we are able to find *exact,
analytic\/*
solutions of the MHD equations for $\rho(t,M)$, $v(t,M)$,
and $r(t,M)$, and numerical solutions for $B(t,M)$ and $v_i(t,M)$
that involve only simple quadratures. The non-dimensional solutions
depend on two parameters, the initial degree of concentration,
which depends on $A$,
and the initial ratio of the cloud's mass $M_{\rm cloud}$ to the magnetic
critical mass $M_\Phi$. These solutions are valid
up to the time when the core of mass $M_{\rm core} =
A\,M_{\rm cloud}$ undergoes dynamical collapse, and
inmediately thereafter.

By a judicious choice of $A$ and $M_{\rm cloud}/M_\Phi$ we reproduce within
factors of order unity the numerical results of Fiedler \& Mouschovias
(1992; ApJ 415, 680)
for the physical quantities in the midplane of a collapsing, magnetized,
axisymmetric cloud. In addition, we can follow the evolution of the
remnant, magnetized envelope after the collapse of the core.

**Wednesday
program listing**