Doppler velocity of m=1 high-latitude inertial mode over the last five sunspot cycles

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A variety of solar global modes of oscillation in the inertial frequency range have been identified in maps of horizontal flows derived from GONG and HMI data. Among these, the high-latitude mode with azimuthal order m=1 (HL) has the largest amplitude and plays a role in shaping the Sun's differential rotation profile. We aim to study the evolution of the HL mode parameters, utilizing Dopplergrams from the Mount Wilson Observatory (MWO), GONG, and HMI, covering together five solar cycles since 1967. We calculated the averages of line-of-sight Doppler signals over longitude, weighted by the sine of longitude with respect to the central meridian, as a proxy for zonal velocity at the surface. We measured the mode's power and frequency from these zonal velocities at high latitudes in sliding time windows of three years. The HL mode is easily observed in the maps of zonal velocity at latitudes above 50 degrees, especially during solar minima. The mode parameters measured from the three independent data sets are consistent during their overlapping periods and agree with previous findings using HMI ring-diagram analysis. We find that the amplitude of the mode undergoes very large variations, taking maximum values at the start of solar cycles 21, 22, and 25, and during the rising phases of cycles 23 and 24. The mode amplitude is anticorrelated with the sunspot number (textrm corr =-0.50) but not correlated with the polar field strength. Over the period 1983--2022 the mode amplitude is strongly anticorrelated with the rotation rate at latitude $60^∘$ (textrm corr =-0.82), that is, with the rotation rate near the mode's critical latitude. The mode frequency variations are small and display no clear solar cycle periodicity above the noise level (∼ ± 3 nHz). Since about 1990, the mode frequency follows an overall decrease of ∼ 0.25 nHz/year, consistent with the long-term decrease of the angular velocity at $60^∘$ latitude. We have shown that the amplitude and frequency of the HL mode can be measured over the last five solar cycles, together with the line-of-sight projection of the velocity eigenfunction. We expect that these very long time series of the mode properties will be key to understand the dynamical interactions between the high-latitude modes, differential rotation, and (possibly) magnetic activity.