  We develop Bayesian statistical methods for discovering and assigning
probabilities to non-random (e.g., physical) stellar companions. These
companions are either presently bound or were previously bound. The
probabilities depend on similarities in corrected proper motion parallel and
perpendicular to the brighter component's motion, parallax, and the local
phase-space density of field stars. Control experiments are conducted to
understand the behavior of false positives. The technique is applied to the
Hipparcos Catalogue within 100 pc. This is the first all-sky survey to locate
escaped companions still drifting along with each other. In the <100 pc
distance range, ~220 high probability companions with separations between 0.01
- 1 pc are found. The first evidence for a population (~300) of companions
separated by 1 - 8 pc is found. We find these previously unnoticed naked-eye
companions (both with V<6th mag): Capella & 50 Per, delta Vel & HIP 43797,
Alioth (epsilon UMa), Megrez (delta UMa) & Alcor (80 UMA), gamma & tau Cen, phi
Eri & eta Hor, 62 & 63 Cnc, gamma & tau Per, zeta & delta Hya, beta01, beta02 &
beta03 Tuc, N Vel & HIP 47479, HIP 98174 & HIP 97646, 44 & 58 Oph, s Eri & HIP
14913, and pi & rho Cep. High probability fainter companions (V > 6th mag) of
primaries with V < 4th mag are found for: Fomalhaut (alpha PsA), gamma UMa,
alpha Lib, Alvahet (iota Cephi), delta Ara, beta Ser, iota Peg, beta Pic, kappa
Phe and gamma Tuc.

Astrophysics of Galaxies;Solar and Stellar Astrophysics