ROTATIONAL EFFECTS ON STELLAR STRUCTURE AND STABILITY

We present a non-linear analysis of rotational effects (i.e. effects o f changes in the angular momentum distribution) in slightly distorted stars. The discussion is universal, i.e. approximately valid for any r otation law. The quantities involved (energies, moment of inertia, fun damental frequency etc.) are integral quantities. The discussion is ba sed on universal relations between integral quantities. The law of ene rgy conservation and the virial theorem are linear universal relations . Ledoux's formula is a non-linear universal relation. Two further non -linear universal relations are derived in this paper. The resulting s et of equations is sufficient for a discussion of rotational effects. In case of constant gamma the rotational effects on integral quantitie s can be described by simple analytic expressions. A special case are polytropes in differential rotation. Linear rotational effects are sho wn to be destabilizing. This extends results of Sidorov. Non-linear ef fects in stable configurations are also destabilizing. In unstable sys tems however nonlinear effects can be stabilizing. This explains the s tabilizing influence of rotation which is seen from Ledoux's formula.I n marginally unstable systems an increase of angular momentum is impos sible, i.e. incompatible with hydrostatic equilibrium. In systems with gamma < 4/3 there is an upper limit for the angular momentum. Loss of stability occurs when the angular momentum distribution prevents hydr ostatic equilibrium. As a result a rotating system will expand. This c onfirms a result of Tassoul & Tassoul.