Statistics – Computation
Scientific paper
May 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993aas...182.6801o&link_type=abstract
American Astronomical Society, 182nd AAS Meeting, #68.01D; Bulletin of the American Astronomical Society, Vol. 25, p.915
Statistics
Computation
Scientific paper
Using linear perturbation theory, I investigate the torques between a centrifugally-supported gas/dust disk surrounding a young star and a second star. I consider both the cases of a binary companion orbiting beyond the disk, and a passing member of a stellar cluster. Extending the Goldreich-Tremaine theory of resonant wave excitation, I develop a theory for excitation of one-armed disturbances in the broad near-inner resonance of a Keplerian potential. These waves can be important when excitation of m>= 2-armed waves is impossible (or much reduced). This occurs in a bound system when an annulus is cleared in the disk around the binary companion, like the gaps seen near moons in Saturn's rings. The external torque on the disk is negative, encouraging accretion. I compute numerically and analytically accretion timescales t_acc in the disk due to near-resonantly driven waves. For the example of a 0.5 M_&sun; disk in a solar-mass scale binary with separation 100 AU, t_acc ~ 10(7) yrs, with t_acc proportional to the binary period. For unbound systems, I investigate the angular momentum L and energy transferred during parabolic perturber passages, which are most common for typical disk sizes and cluster velocity dispersions. I compute the torques for arbitrary inclination angle and longitude of the pertuber's orbit by integrating over all horizontal and vertical resonances. I present both numerical computations and analytic formulae for cases with closest perturber approach x_min beyond two disk radii R_D. I find that Delta L transferred to the disk is negative, inducing accretion. The fractional angular momentum removed from a disk is ~ 10% at x_min/R_D=2, averaged over orbit orientations. But the applied torque drops off exponentially with increasing x_min/R_D, due to the mismatch of high disk rotation frequency and low perturber orbital frequency. When the incoming perturber's orbit is polar or retrograde, energy is removed from the orbit and given to the disk, permitting capture. The probability of capture is quite small, however, because the positive energy transferred to the disk in an encounter is a tiny fraction of the typical kinetic energy of a star in a cluster.
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