*Astron. Astrophys. 339, 95-112 (1998)*
## 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
4 and 5. Viewing the decay as a general
physical process and studying a 1,000 system realizations, we have
obtained precise values (within 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
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
. On the other hand, the multiplicity fractions
are sensitive to *N*, but not to .
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
Heggie Law with . 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 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
10's A.U. (DM), while collapse calculations
for reasonable initial cloud parameters give typical fragment system
sizes 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 3-4 km/s) can be attained by
single stars of all masses and that the lower speeds of the binaries
and multiples ( 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.
© European Southern Observatory (ESO) 1998
Online publication: September 30, 1998
helpdesk.link@springer.de |