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Astron. Astrophys. 354, L6-L8 (2000)

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3. Hydrodynamic considerations

We use simple molecular cloud model with generic initial conditions: initial size of the molecular cloud [FORMULA]cm, average temperature of the cloud [FORMULA]K, and angular velocity of the cloud [FORMULA] rad s-1. The sound speed becomes [FORMULA]cm s-1 and corresponding initial density (Shu, Adams & Lizano 1987) is [FORMULA]g cm-3 and accretion rate is [FORMULA]g s-1. Here, [FORMULA] mean molecular weight, [FORMULA] is the mass of the hydrogen atom, and k is the Boltzmann constant. In the isothermal phase of the cloud collapse, density [FORMULA] (Chandrasekhar 1939) and the velocity is constant. When opacity becomes high enough to trap radiations (say, at [FORMULA]), the cloud collapses adiabatically with [FORMULA]. In presence of rotation, centrifugal barrier forms at [FORMULA], where centrifugal force balances gravity. Density falls off as [FORMULA] in this region (Hartmann, 1998). Following Shu, Adams & Lizano (1987), we compute the density, temperature and velocity distribution inside the cloud and follow the chemical evolution at the same time. With density chosen as above, the initial constant velocity of infall becomes 8900cm s-1 and below [FORMULA] velocity [FORMULA] to preserve the accretion rate in a disk like structure of constant height. Since for the parameters chosen (generic as they are) [FORMULA], we chose [FORMULA] inside the centrifugal barrier ([FORMULA]) as in an adiabatic flow. We follow the collapse till a radius of [FORMULA]cm is reached. Fig. 1 shows the temperature and mass density (in units of [FORMULA]) distribution in a log-log scale. Our choice of [FORMULA] is small by at least an order of magnitude from that of the observed value in some of the clouds. This was done to obtain atmosphere at a distance of around 1AU from the proto-star to be as close to reducing ([FORMULA]).

[FIGURE] Fig. 1. Log-log plot of temperature (dotted) and mass density (in units of [FORMULA]) as functions of the radial distance. Vertical dashed line is drawn at 1AU.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000