Cosmic-ray acceleration at stellar wind terminal shocks

Steady-state spherically symmetric analytic solutions of the cosmic-ray transport equations, applicable to the problem of acceleration of cosmic rays at the terminal shock to a stellar wind, are studied. The spectra, graidents, and flow patterns of particles modulated and accelerated by the stellar wind and shock are investigated by means of monoenergetic-source solutions at finite radius, as well as solutions with monoenergetic and power-law galactic spectra. On the basis of calculations given, early-type stars could supply a significant fraction of the 3 x 10 to the 40th ergs/sec required by galactic cosmic rays.