Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

Adaptive Calculation of a Collapsing Molecular Cloud Core 231
the collapse of the filament upon itself are clarified in Figure 3, which
depicts the velocity field in the equatorial plane at the same time of
Figure 2.
By the first radial point is at cm from the
origin This radial resolution is equivalent to having started the
calculation with roughly 1700 equidistant radial points in the ordinary
space. Figure 4 describes the evolution of the four grid sizes and the
Jeans length during the cloud collapse. Evidently, satisfaction of the
Jeans conditions combined with sufficiently high spatial resolution allows
us to follow the isothermal collapse up to the point where filament
formation is expected. The present solution is in very good agreement
with the results of the AMR code calculation in Ref. [10] and the refined
spherical code calculation [17]. The agreement between these three independent
codes, each working at very high spatial resolution, implies
that the filamentary solution is the correct one. Although the outcome
of the isothermal collapse of the Gaussian cloud is shown to be a singular
filament, a physically realistic solution would require the inclusion of
non-isothermal heating. In particular, in Ref. [17] it was showed that
thermal retardation of the collapse may allow the Gaussian cloud to fragment
into a binary protostellar system at the same maximum density