Noise storm continua: power estimates for electron acceleration

Abstract

We use a generic stochastic acceleration formalism to examine the power $L_{\rm in}$ (${\rm erg s^{-1}}$) input to nonthermal electrons that cause noise storm continuum emission. The analytical approach includes the derivation of the Green's function for a general second-order Fermi process, and its application to obtain the particular solution for the nonthermal electron distribution resulting from the acceleration of a Maxwellian source in the corona. We compare $L_{\rm in}$ with the power $L_{\rm out}$ observed in noise storm radiation. Using typical values for the various parameters, we find that $L_{\rm in} \sim 10^{23-26}$ ${\rm erg s^{-1}}$, yielding an efficiency estimate $η\equiv L_{\rm out}/L_{\rm in}$ in the range $10^{-10} \lsim η\lsim 10^{-6}$ for this nonthermal acceleration/radiation process. These results reflect the efficiency of the overall process, starting from electron acceleration and culminating in the observed noise storm emission.