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

TL;DR

This work tracks the temporal evolution of solar inertial modes, focusing on the $m=1$ high-latitude mode and equatorial Rossby modes with $3 \le m \le 16$, using near-surface flows from GONG and HMI ring-diagram analyses over 2002–2024. By dividing the data into overlapping four-year windows and extracting mode frequency and power via Lorentzian fits to mean spectra and robust estimators for time segments, the study reveals significant solar-cycle–timescale variability. Frequencies generally anti-correlate with sunspot number for ER modes, while powers tend to correlate positively with sunspot number, with a notable exception for $m=3$ where power anti-correlates strongly; HL $m=1$ shows power anti-correlation with SSN but little frequency variation. Frequencies and powers exhibit cycle-to-cycle differences and increasing sensitivity with mode order, underscoring the potential of inertial modes as diagnostics of deep interior dynamics and magnetic fields. The cross-instrument consistency between GONG and HMI reinforces the robustness of these findings as a solar-cycle–dependent probe of the Sun’s interior dynamics.

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.

Figures (11)

• Figure 1: GONG reference power spectra $\overline{P}_m(\nu)$ (blue curves) with frequency resolution $\textrm{d}\nu=8$ nHz. The top left panel shows $\overline{P}_m(\nu)$ for the $m=1$ component of $u_{\phi}^-$; the peak corresponds to the $m = 1$ high-latitude mode. All other panels show $\overline{P}_m(\nu)$ for the $u_{\theta}^+$ component of the flow and different $m$ values ranging from $3$ to $16$. The red curves show the Lorentzian fits to the power spectra (Sect. \ref{['sec:mean_spectra']}). The horizontal black segments show the frequency windows $W$ used to extract the mode parameters from consecutive 4-year power spectra (see Sect. \ref{['sec:parameter_calc']}).
• Figure 2: Square root of mode power as a function of $m$ for the GONG observations ($\overline{E}_m$ from Table \ref{['tab:parameters']}). The stochastic excitation model from Philidet2023 is overplotted.
• Figure 3: Temporal variations of the mode frequencies ($\nu_m$) obtained from the GONG (blue) and HMI (magenta) datasets. The top left panel is for the $m=1$ high-latitude mode, the other panels for the equatorial Rossby modes. The shaded regions indicate the $68\%$ confidence intervals of $\nu_m$ estimated from Monte Carlo simulations. Mode frequencies shown as open circles indicate no significant power ($<95\%$ confidence) in the corresponding time segments. The mode frequencies obtained from the reference GONG data (2002--2021) are shown as horizontal dashed lines.
• Figure 4: Temporal variations of the mode power ($E_m$) and the negative of the background power ($-B_m w$). The top left panel is for the $m=1$ high-latitude mode, the other panels for the equatorial Rossby modes. The powers computed from the GONG and HMI datasets are shown in blue and magenta, respectively. The shaded regions represent the $68\%$ confidence intervals of $E_m$ estimated from Monte Carlo simulations. The horizontal dashed lines indicate the mode powers obtained from the reference GONG data (2002--2021).
• Figure 5: Fourier (top panels) and wavelet (bottom panels) power spectra of the $m=1$ HL and $m=3$ and $9$ ER modes, as a function of time and frequency. The frequencies $\nu_m(t_n)$, calculated using Eq. \ref{['eq:frequency_calc']}, are overplotted as light blue curves with widths representing the $68\%$ confidence intervals. In the top panels, the horizontal dashed lines indicate the frequency window $W$ used in Eqs. \ref{['eq:frequency_calc']} and \ref{['eq:power_calc']}.