## Abstract

Steady stellar winds are generally divided into two classes: (i) the winds proper, for which the energy flux per unit solid angle, $E_{\infty}$, is non-zero, and (ii) the breezes, for which $E_{\infty}=0$. 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 $g=\underset r\rightarrow \infty \to{\lim}\frac{mv^{2}}{kT}$, 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 $0\leq g\leq 1$, 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 $g\rightarrow \frac{5}{3}$, namely (in an obvious notation) the $g=\frac{5}{3}-$ and the $g=\frac{5}{3}+$ possibilities. It is shown that, if $g>\frac{5}{3}$ $(g<\frac{5}{3})$ the solutions are everywhere supersonic (subsonic) with respect to the adiabatic speed of sound. If $1<g<\frac{5}{3}$, they possess a critical point, at which the isothermal speed of sound and the flow speed coincide. The winds are examined in the limit $E_{\infty}\rightarrow 0$, and the relation with the breezes is studied. In particular, it is shown that, for $r\leq O(E_{\infty}^{-2/5})$, the winds satisfy the stellar breeze equations to leading order, and possess a critical point at r = O(1). For $r>O(E_{\infty}^{-2/5})$, the solutions do not obey the breeze equations. They ultimately follow the Durney asymptotic law $[T=O(r^{-4/3})$, for $r\rightarrow \infty]$ for the winds. This demonstration of how the winds merge continuously into the breezes as $E_{\infty}\rightarrow 0$ 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 $(E_{\infty}\neq 0)$, 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.

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