Oscillations of the solar photospheric magnetic field caused by the m = 1 high-latitude inertial mode

TL;DR

This study demonstrates a photospheric magnetic-field counterpart to the solar $m=1$ high-latitude inertial mode by analyzing long-term LOS magnetograms from HMI and GONG. It identifies a robust Earth-frame frequency of $\nu \approx 338~\mathrm{nHz}$ in the high-latitude magnetic field, with amplitudes up to $\sim 0.2$ G and a predominantly equator-symmetric pattern, consistent with a simple model in which the radial field is advected by the mode's horizontal flow. The temporal evolution shows cycle-dependent visibility, strongest around solar minimum and rising phases, with cross-instrument agreement and a time lag relative to velocity signals. A minimal induction-model links the magnetic perturbations to passive advection by HL1 velocities, reproducing the observed amplitude and spatial structure and connecting near-surface magnetism to global inertial oscillations.

Abstract

Periodic oscillations at 338 nHz in the Earth frame are observed at high latitudes in direct Doppler velocity measurements. These oscillations correspond to the $m=1$ high-latitude global mode of inertial oscillation. In this study, we investigate the signature of this mode in the photospheric magnetic field using long-term series of line-of-sight magnetograms from the Helioseismic and Magnetic Imager (HMI) and the Global Oscillation Network Group (GONG). Through direct observations and spectral analysis, we detect periodic magnetic field oscillations at high latitudes ($65^\circ$--$70^\circ$) with a frequency of 338 nHz in the Earth frame, matching the known frequency of the $m = 1$ high-latitude inertial mode. The observed line-of-sight magnetic field oscillations are predominantly symmetric across the equator. We find a peak magnetic oscillation amplitude of up to $0.2$~gauss and a distinct spatial pattern, both consistent with simplified model calculations in which the radial component of the magnetic field is advected by the mode's horizontal flow field.

Figures (8)

• Figure 1: Supersynoptic maps in the Earth frame of $B_{\rm avg}^+$ and $V_{\rm zonal}^-$ at high latitudes, computed from HMI data for the period 2019--2020. The $m=1$ mode manifests itself as a series of stripes in both observables. A 180-day running average was subtracted, and for clarity, the maps were smoothed using a Gaussian kernel with a width of two pixels in both latitude and time.
• Figure 2: Oscillations of $\langle B_{\rm avg}^+ \rangle$ and $\langle V_{\rm zonal}^- \rangle$ in the time series from HMI and GONG data in 2019. A 180-day average was removed, and for clarity, the maps were smoothed with a Gaussian kernel with $\sigma=1$ day. Vertical lines are spaced at intervals of 34 days.
• Figure 3: Power spectra of magnetic fluctuations $\langle B_{\rm avg}^+ \rangle$ over three-year intervals with a frequency resolution of $10.5$ nHz for GONG (left) and HMI (right) data, stacked vertically and spanning from 2007 to 2024. The crosses mark the reference frequency of 338 nHz. The right-hand-side panel for 2007--2009 contains no data because the HMI dataset starts in 2010. The bottom spectra are computed using the entire available time span for each respective dataset.
• Figure 4: Temporal variations of the $m=1$ mode amplitude extracted from $B_{\rm los}$ and $V_{\rm los}$ data. The red, orange, green, and blue curves correspond to results from the HMI $\langle B_{\rm avg}^+ \rangle$, HMI $\langle V_{\rm zonal}^- \rangle$, GONG $\langle B_{\rm avg}^+ \rangle$, and GONG $\langle V_{\rm zonal}^- \rangle$ datasets, respectively. Shaded regions indicate the $68\%$ confidence interval, estimated using 10,000 Monte Carlo simulations. Open circles denote instances where the excess power near the mode frequency falls below the $90\%$ confidence level. We note that $\langle V_{\rm zonal}^- \rangle$ is derived directly from the LOS Doppler velocity (Eqs. \ref{['eq:vzonal']}--\ref{['eq:vband']}); unlike 2024Liang_vlosm1, we did not apply a multiplicative factor in the present work to scale the $\langle V_{\rm zonal}^- \rangle$ amplitudes to match the horizontal velocities from the ring-diagram maps. The numerical values used in these plots are available in a supplementary file. Vertical lines denote key phases of the solar cycle, with solid lines representing solar minima and dashed lines indicating solar maxima. The bottom panel shows the average sunspot number (Source: WDC-SILSO, Royal Observatory of Belgium, Brussels, https://doi.org/10.24414/qnza-ac80).
• Figure 5: Bandpass-filtered images of the LOS Doppler velocity, $V_{\rm los}$, and LOS magnetic field, $B_{\rm los}$, derived from HMI data. The top-left panel shows a filtered $V_{\rm los}$ image from 14 June 2020, while the bottom-left panel displays the central-meridian $V_{\rm los}$ values stacked over time and plotted as a function of time and latitude. The right panels display the corresponding $B_{\rm los}$ data, with low-latitude regions ($<45^{\circ}$) shaded out. The filtering was performed using a bandpass filter centered at $\nu_{\rm HL1}^{\rm synodic} = 338$ nHz with a full width of 30 nHz, applied over the entire available HMI time period from 2010 to 2024. For clarity, the images were smoothed with a Gaussian kernel with a width of $2$ pixel---in longitude and latitude for the top panels, and in time and latitude for the bottom panels. A movie is available as online ( link to A&A) supplementary material.