EDP Sciences
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Volume 395, Number 1, November III 2002
Page(s) 321 - 338
Section Physical and chemical processes
DOI http://dx.doi.org/10.1051/0004-6361:20021071

A&A 395, 321-338 (2002)
DOI: 10.1051/0004-6361:20021071

Gravitational collapse of nonsingular logatropic spheres

L. Di G. Sigalotti1, F. de Felice2 and E. Sira1

1  Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020A, Venezuela
    e-mail: lsigalot@cassini.ivic.ve
    e-mail: esira@hubble.ivic.ve
2  Dipartimento di Fisica Galileo Galilei, Università di Padova, via Marzolo n. 8, 35131 Padova, Italy
    e-mail: defelice@pd.infn.it

(Received 2 May 2002 / Accepted 19 July 2002 )

We present the results of high-resolved, hydrodynamic calculations of the spherical gravitational collapse and subsequent accretion of nonsingular subcritical and critical A=0.2 logatropes, starting with initial configurations close to hydrostatic equilibrium. Two sequences of models with varying masses and the same central temperature $T_{\rm c}=10$ K are defined, which differ only in the fiducial value of the truncation pressure ( $p_{\rm s}/k=1.3\times 10^{5}$ cm -3 K and $1.0\times 10^{7}$ cm -3 K). In all cases, we follow the calculations until the central protostar has accreted 99% of the total available mass. Thus, the models may be indicative of early evolution from the Class 0 to the Class I protostellar phase. We find that the approach to the singular density profile is never entirely subsonic. In the lower $p_{\rm s}$ sequence, about 6% of the mass collapses supersonically in a $1~M_{\odot}$ sphere, while only $\sim $0.02% behaves this way in a critical ( $\approx $92.05  $M_{\odot}$) logatrope. In the high $p_{\rm s}$ sequence the same trend is observed, with $\sim $0.7% of the mass now infalling supersonically at the time of singularity formation in a $1~M_{\odot}$ sphere. Immediately after singularity formation, the accretion rate rises steeply in all cases, reaching a maximum value when the central protostar has accreted $\sim $40% of its final mass. Thereafter, it decreases monotonically for the remainder of the evolution. Our models predict peak values of ${\dot M}_{\rm acc}$ as high as $\sim $ $5 {-} 6\times 10^{-5}~M_{\odot}$ yr -1 for logatropes close to the critical mass. In contrast, a subcritical $1~M_{\odot}$ logatrope reaches a maximum value of $\sim $ $8\times 10^{-7}~M_{\odot}$ yr -1 for the lower $p_{\rm s}$ sequence compared to ~ $ 5\times 10^{-6}~M_{\odot}$ yr -1 for the higher $p_{\rm s}$ case. The results also imply that the accretion lifetimes are longer in logatropes with lower $p_{\rm s}$, consistent with the observational evidence that star formation in clumped regions occurs on shorter timescales compared to more isolated environments.

Key words: hydrodynamics -- methods: numerical -- stars: formation -- circumstellar matter

Offprint request: L. Di G. Sigalotti, lsigalot@cassini.ivic.ve

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