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

232 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
where the isothermal collapse yields a thin filament. Thus, fragmentation
of the Gaussian cloud model appears to depend sensitively on both
the numerical resolution and the detailed thermodynamical treatment.
4. CONCLUSIONS
Here we have presented a further intercode comparison with high spatial
resolution for the same Gaussian cloud model of Refs. [10] and [17].
The calculation was made using a variant of the spherical code described
in Ref. [18], which employs zooming coordinates to achieve sufficiently
high spatial resolution. With the zooming coordinates, the computational
cells shrink adaptively in accordance with the cloud collapse so
that the resolution increases in proportion to the Jeans length as the
density enhances. In this framework, we are able to follow the collapse
of the Gaussian cloud model through 7 orders of magnitude increase in
central density without violating the Jeans condition and reproduce the
filamentary solution obtained in Refs. [10] and [17] using a completely
independent numerical method. The present approach can compete with
the AMR methodology and other grid refinement techniques to provide
unprecedentedly high resolution in collapse calculations.
The isothermal collapse of the Gaussian cloud model is an excellent
test case for any gravitational hydrodynamics code and should then be
used to check the reliability of the results for the isothermal phase of collapse
calculations. This paper represents a further step in this direction
and provides extra evidence that the outcome of the isothermal collapse
of the Gaussian cloud is the formation of a singular filament rather than
the fragmentation into two or more clumps as found in previous lowresolution
calculations.
Acknowledgments
The calculation of this paper was performed on the Origin 2000 supercomputer
of the Instituto Mexicano del Petroleo (IMP). This work was
partially supported by the Consejo Nacional de Investigaciones Científicas
y Tecnológicas (CONICIT) of Venezuela and by the Consejo Nacional
de Ciencia y Tecnología (CONACyT) of México.
References
[1]
[2]
[3]
R. Mathieu, ARA&A 32 (1994) 465.
A. Duquennoy and M. Mayor, A&A 248 (1991) 485.
O.P. Lay, J.E. Carlstrom and R.E. Hills, Astrophys. J. 452 (1995) L73.
[4] L.W. Looney, L.G. Mundy and W.J. Welch, Astrophys. J. 484 (1997) L157.