Stellar winds and breezes

Abstract

Steady stellar winds are generally divided into two classes: (i) the winds proper, for which the energy flux per unit solid angle, E ∞ , is non-zero, and (ii) the breezes, for which E oo = 0. The breezes may be distinguished from one another by the value of the ratio, g , of kinetic to thermal energy of the particles in the limit of large distance, r , from the stellar centre, or more precisely by g=lim mv 2 r->∞ — kT ' where v ( r ) is breeze velocity, T ( r ) is temperature, m is mean particle mass, and k is the Boltzmann constant. Solutions have previously been obtained for values of g in the range 0 < g < 1, in which the breezes are subsonic everywhere with respect to the isothermal speed of sound. It is demonstrated here that two distinct solutions exist as g -> 5/3, namely (in an obvious notation) the g = 5/3 — and the g = 5/3 + possibilities. It is shown that, if g > 5/3 ( g < 5/3) the solutions are everywhere supersonic (subsonic) with respect to the adiabatic speed of sound. If 1 < g < 5/3, they possess a critical point, at which the isothermal speed of sound and the flow speed coincide. The winds are examined in the limit E ∞ -> 0, and the relation with the breezes is studied. In particular, it is shown that, for r < 0 ( E ∞ -2/5 ), the winds satisfy the stellar breeze equations to leading order, and possess a critical point at r = 0 (1). For r > 0 ( E ∞ -2/5 ), the solutions do not obey the breeze equations. They ultimately follow the Durney asymptotic law [T = 0 ( r -4/3 ), for r -> ∞] for the winds. This demonstration of how the winds merge continuously into the breezes as E ∞ -> 0 is new. The question of how the particle density ( N 0 ) and temperature ( T 0 ) at the base of the stellar corona determine the type of solution realized outside the star is examined. Even when the flow speed, v 0 , at the base of the corona is subsonic, non-uniqueness can occur. In one domain of the ( N 0 , T 0 ) plane, two distinct types of breeze are possible; in another these, together with a wind (E∞ =f= 0), are permissible. Elsewhere (large N 0 , moderate T 0 ) only a unique breeze exists or (small N 0 and/or T 0 ) a unique wind. In some domains (large T 0 ) no steady solution exists, unless the requirement that the corona is subsonic is relaxed. In this case, however, the problems of non-uniqueness are severely aggravated.