An upper bound to the periods of radial pulsation of the Sun

It is demonstrated that the periods of linear adiabatic radial pulsation of any stably stratified star with given mass M and radius R, and constant adiabatic exponent #betta#, are bounded above by the period of the fundamental radial mode of the adiabatically stratified model. Thus when #betta# = 5/3, the greatest period is that of the polytrope of index 1.5. If M and R have the solar values, that period is 101.5 min. Our analysis does not generalize to the case when #betta# is permitted to vary in a realistic way, but we argue that in that case the period of the adiabatically stratified model is likely to be a good estimate of the upper bound. This period depends weakly on composition, its greatest value being 101.9 min when the heavy-element abundance is taken to be 2 per cent. (author)