Mathematics – Probability
Scientific paper
Mar 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...424..292o&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 424, no. 1, p. 292-318
Mathematics
Probability
58
Accretion Disks, Binary Stars, Interstellar Matter, Perturbation Theory, Pre-Main Sequence Stars, Stellar Envelopes, Angular Momentum, Celestial Mechanics, Stellar Mass Accretion, Stellar Orbits
Scientific paper
Young stars display evidence of moderately massive, centrifugally supported, gaseous, and dusty circumstellar disks. These disks are highly susceptible to compressional and transverse disturbances. Such density and bending waves may be excited by tidal forces from external gravitational perturbers, including passing, initially unbound stars. The energy and angular momentum exchange between the two-body orbit and the disk permits capture of passing stars on near-parabolic orbits, and can cause disk accretion. We compute energy and angular momentum transfer for near-parabolic orbits with periastron xmin beyond two disk radii rD, as a function of relative disk-orbit angles, using linear perturbation theory. We present both numerical evaluation of the integrations and asymptotic analytic results. These are used to compute capture rates and induced accretion rates in stellar clusters. We find that for encounters with xmin near 2rD, the disk angular momentum is reduced by a few to several percent (angle-averaged), with prograde, coplanar orientations yielding reductions by more than 10%. For typical open cluster parameters, the capture probability is less than 0.1% at xmin approximately 2rD; for most orientations energy is actually given to the perturber, rather than the reverse. Capture is permitted only for polar and retrograde encounters, and even then is unlikely. In particular, the asymptotic analytic results (large xmin/rD limit) for resonant transfer predict that the disk's energy change will be positive for inclinations greater than 101.5 deg, with the maximum, positive value at inclination 117 deg only 1% of the (negative) disk energy change at zero inclination. Both the angular momentum transfer and the capture probability drop off with increasing xmin/rD, first as an exponential and then as a power law. We explain this behavior in terms of the ratio of perturbed angular velocity to disk angular velocities, and the spectrum of allowed resonances. We compare our results on star/disk-star encounters with other capture calculations, and find that many of the same considerations also apply to star-star encounters and galaxy-galaxy encounters.
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