Temporal variations of solar inertial mode parameters from GONG (2002--2024) and HMI (2010--2024): Rossby modes ($3 \leq m \leq 16 $) and $m=1$ high-latitude mode

Abstract

We study the temporal evolution of solar inertial modes over the solar cycle using observations from GONG and SDO/HMI. We focus on the high-latitude mode with azimuthal wavenumber $m=1$ and the equatorial Rossby modes with $3 \le m \le 16$. We use maps of horizontal flows near the solar surface from the GONG and HMI ring-diagram pipelines at a cadence of approximately one day, covering the period 2002--2024. The data are divided into overlapping four-year windows, with central times separated by six months. Within each time window and for each inertial mode, we measure the frequency and the power of the mode from the GONG and HMI data. We find good agreement between the GONG and HMI measurements throughout their overlapping period from 2010 to 2024. In general, the magnitude of the frequency variations increases with increasing $m$, while relative changes in mode power typically exceed 100\%. For the $m=1$ high-latitude mode, the measured power is anti-correlated with the sunspot number, while its frequency shows no significant temporal variation. For the equatorial Rossby modes, the frequencies are generally anti-correlated with the sunspot number, whereas the mode powers tend to correlate positively with the sunspot number. An exception is the $m=3$ equatorial Rossby mode, whose mode power is strongly anti-correlated with the sunspot number, in contrast to the other equatorial Rossby modes, highlighting its distinct behavior. We find that the frequencies and power of the Sun's inertial modes exhibit significant variability on solar-cycle timescales over the past 23 years. The mode parameters are however not uniformly synchronized with the sunspot number; clear differences are observed both from mode to mode and from one solar cycle to the next. The sensitivity of inertial modes to solar-cycle changes indicates their potential as a diagnostic of solar interior dynamics and magnetism.