Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994aas...185.8411s&link_type=abstract
American Astronomical Society, 185th AAS Meeting, #84.11; Bulletin of the American Astronomical Society, Vol. 26, p.1458
Astronomy and Astrophysics
Astronomy
Scientific paper
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: Thermal stresses are negligible compared to magnetic stresses. The cloud is spherically symmetric, and the only non-vanishing component of the Lorentz force is given by the scalar term ~ dB(2/dr) , where B=B(r), and r is the usual spherical radius. The evolution is quasi-static and the ion velocity is negligible compared to the neutral velocity. For Lagrangian inital conditions of the form rho (t=0,M) ~ 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_cloud to the magnetic critical mass M_Phi . These solutions are valid up to the time when the core of mass M_core = AM_cloud undergoes dynamical collapse, and immediately thereafter. By a judicious choice of A and M_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.
McKee Christopher F.
Safier Pedro N.
Stahler Steven W.
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