REEXAMINATION OF ASTROPHYSICAL RESONANCE-REACTION-RATE EQUATIONS FOR AN ISOLATED, NARROW RESONANCE

The well-known astrophysical resonant-reaction-rate (RRR) equations for an isolated narrow resonance induced by the charged particles have been reexamined. The validity of those assumptions used in deriving the classical analytic equations has been checked, and found that these analytic equations only hold for certain circumstances. It shows the customary definition of "narrow" is inappropriate or ambiguous in some sense, and it awakes us not to use those analytic equations without caution. As a suggestion, it is better to use the broad-resonance equation to calculate the RRR numerically even for a narrow resonance of a few keV width. The present conclusion may influence some work in which the classical narrow-resonant equations were used for calculating the RRRs, especially at low stellar temperatures for those previously defined "narrow" resonances.

Spatio-temporal evolution of thin Alfven resonance layer

We describe the spatio-temporal evolution of one-dimensional Alfven resonance disturbance in the presence of various factors of resonance detuning: dispersion and absorption of Alfven disturbance, nonstationarity of large-scale wave generating resonant disturbance. Using analytical solutions to the resonance equation, we determine conditions for forming qualitatively different spatial and temporal structures of resonant Alfven disturbances. We also present analytical descriptions of quasi-stationary and non-stationary spatial structures formed in the resonant layer, and their evolution over time for cases of drivers of different types corresponding to large-scale waves localized in the direction of inhomogeneity and to nonlocalized large-scale waves.