Noise storm continua: power estimates for electron acceleration

We use a generic stochastic acceleration formalism to examine the power $L_{\mathrm{i}\mathrm{n}}$ ($\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{s}}^{-1}$) 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 $L_{\mathrm{i}\mathrm{n}}$ with the power $L_{\mathrm{o}\mathrm{u}\mathrm{t}}$ observed in noise storm radiation. Using typical values for the various parameters, we find that $L_{\mathrm{i}\mathrm{n}}\sim {10}^{23-26}$ $\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{s}}^{-1}$, yielding an efficiency estimate $\eta \equiv L_{\mathrm{o}\mathrm{u}\mathrm{t}}\mathrm{/}{L}_{\mathrm{i}\mathrm{n}}$ in the range $10^{-10} \lsim \eta \lsim 10^{-6}$ 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.