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Astron. Astrophys. 339, 95-112 (1998)

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5. Conclusions

We have performed a statistical study of complete few-body decay for N = 3, 4, and 5 using direct orbit integrations and a novel analysis technique. For N = 4 and 5, these are the first such results available from a modern few-body code that we are aware of. Our main conclusions divide naturally into contributions to few-body stellar dynamics theory and applications to star formation.

Stellar Dynamics. The combination of long integrations and our hierarchical virtual-particle analysis has permitted us to characterize the complete decay, i.e., to identify the independent, long-lived, bound remnants and their kinematics. These results completely supercede those of Harrington (1974, 1975) for [FORMULA] 4 and 5. Viewing the decay as a general physical process and studying a 1,000 system realizations, we have obtained precise values (within [FORMULA] 0.02 or less) for the "branching ratios" between possible decay channels. Many overall results are in accord with classic expections, although there are significant refinements. Decays are dominated by the production of a single hard binary, but the binary plus [FORMULA] singles decay channel is not the only important mode of decay, especially as N increases. Branching ratios are sensitive to N and somewhat more weakly to the mass spectrum [FORMULA]. On the other hand, the multiplicity fractions are sensitive to N, but not to [FORMULA]. Dynamical biasing is only violated at the 10-20% level.

For the zero angular momentum initial system conditions considered in this paper, we find that the distribution of binding energies for the hard remnant binaries is extremely well-matched by an [FORMULA] Heggie Law with [FORMULA]. This is distinctly different from the 9/2 suggested by Heggie himself (1975) for bound three-body systems and the 5/2 advocated by Monaghan (1976a). The law is sufficiently precise and the hard binary sufficiently dominates the energetics of decay that analytic expressions for the escape speeds of single and multiple remnants can be derived which accurately reproduce the computational results for all N and f. The same is true for the distribution of binary semi-major axes. In general, for unequal mass systems, the binaries formed have semi-major axes [FORMULA] 5 times smaller than the original virial system size with a full width at half maximum of about a factor of 3 to 4.

Star Formation. If cloud collapse and multiple fragmentation, followed by dynamic decay of the fragment system, is a common mode of star formation, then our results imply several observational consequences. A two-step IMF, like our clump mass spectrum, where fragment mass choices are constrained by the mass distribution of collapsing clouds, shows considerable promise for reproducing observed trends in binary fractions and binary mass ratio distributions along the main sequence, even for gas-free decay. Although the lowest-mass objects in the overall IMF always end up being ejected as singles, even stars only a few times more massive than the lower cut-off can have a significant binary fraction. At the same time, quite massive stars can have a nonnegligible fraction of singles.

The generic reduction of a factor of five in the semi-major axes of our binaries compared with the initial system size may help explain why binary separation distribution for solar-type stars peaks at [FORMULA] 10's A.U. (DM), while collapse calculations for reasonable initial cloud parameters give typical fragment system sizes [FORMULA] 100's A.U. It is difficult to be as definitive about the kinematic consequences of few-body decay during star formation, because more needs to known about the initial few-body system properties. However, some plausible examples discussed in this paper show that significant escape speeds (one-dimensional velocity dispersions [FORMULA] 3-4 km/s) can be attained by single stars of all masses and that the lower speeds of the binaries and multiples ([FORMULA] 1 km/s) would result in spatial segregation of remnant types over time. The latter sounds a cautionary note regarding the completeness of SFR binary frequency surveys. The speed distributions are distinctly nonGaussian and have a power-law high-speed tail.

Future papers in this series will consider initial few-body conditions with nonzero velocities and nonspherical geometries and will include at least some effects of background and/or accreting gas. We also plan to make simple kinematic models of SFR's hypothetically dominated by this mode of star formation.

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© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998
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