Modeling the frequency dependence of the durations of solar radio spikes

The dependence of the durations of millisecond narrow-band solar radio spikes τ on the frequency f at which they are emitted is studied. A regression analysis of available experimental data at 0.3-3 GHz yields the relationship τ α f ^-1.29±0.08, refining the known Güdel-Benz law. This relationship differs at a statistically significant level from the intuitive expectation τ α f ^-1; this requires a physical interpretation. The frequency dependences of the pulse durations for various modes of cyclotron maser emission near the first, second, and third harmonics of the electron cyclotron frequency have been modeled. The model relationships for different cyclotron maser emission modes are different; only the results of the model for the second harmonic of the extraordinary wave are consistent with the observed behavior. Thus, this wave is a probable candidate for the dominant mode in spike bursts.