Question

How can find radial and azimuthal periods using functions?

Answer 1

We present the first observational detection of radial and azimuthal oscillations in full halo coronal mass ejections (HCMEs). We analyze nine HCMEs well-observed by the Large Angle and Spectrometric Coronagraph (LASCO) from 2011 February to June. Using the LASCO C3 running difference images, we estimated the instantaneous apparent speeds of the HCMEs in different radial directions from the solar disk center. We find that the development of all these HCMEs is accompanied by quasi-periodic variations of the instantaneous radial velocity with the periods ranging from 24 to 48 minutes. The amplitudes of the instant speed variations reach about a half of the projected speeds. The amplitudes are found to anti-correlate with the periods and correlate with the HCME speed, indicating the nonlinear nature of the process. The oscillations have a clear azimuthal structure in the heliocentric polar coordinate system. The oscillations in seven events are found to be associated with distinct azimuthal wave modes with the azimuthal wave number m = 1 for six events and m = 2 for one event. The polarization of the oscillations in these seven HCMEs is broadly consistent with those of their position angles with the mean difference of 43°. The oscillations may be connected with natural oscillations of the plasmoids around a dynamical equilibrium, or self-oscillatory processes, e.g., the periodic shedding of Alfvénic vortices. Our results indicate the need for an advanced theory of oscillatory processes in coronal mass ejections.