Chris S. Hanson1, Shravan Hanasoge2,1, & Katepalli R. Sreenivasan1,3
1. Center for Space Science, New York University Abu Dhabi, UAE
2. Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai, India
3. New York University, New York, USA
For decades, theorists have suggested the existence of solar inertial waves, which are a type of hydrodynamic wave found in rotating fluid bodies. On Earth, inertial waves play an important role in weather systems, such as driving cold polar air from the arctic into North America. In the Sun, they likely play a role in transporting angular momentum to the equator, allowing the Sun’s equator to continue rotating faster than its poles. Most importantly, they are sensitive to critically important properties of the solar plasma, such as details of the stratification and the effective turbulent viscosity, that are otherwise hidden from us. The restoring mechanism of inertial modes is the Coriolis force and these waves have oscillation periods comparable to or longer than the rotation period (28 days). A distinct property of the Rossby wave, a particularly well-known inertial wave, is that it propagates in the opposite direction (retrograde) to the Sun’s rotation. Löptien et al.[1] reported the detection of equatorial Rossby waves using helioseismic techniques to measure the induced fluid motions. The dispersion relation, which relates the temporal frequency to the spatial wavenumber of the wave, was found to compare remarkably well to simple theory. Since then, a number of studies have set out to characterize the Rossby waves[2,3] and to find other inertial wave types predicted by theory such as magnetized-Rossby waves or thermal-Rossby waves.
Video 1|Animation of the equatorial Rossby waves (top) and the recently discovered high-frequency retrograde (HFR) vorticity waves (bottom). Red indicates clockwise vortical motion and blue is anti-clockwise. Both waves travel in the opposite direction to the Sun’s rotation, but the HFR waves travel three times faster than the hydrodynamical Rossby waves.
Using a new powerful helioseismic technique known as mode-coupling[4], we have detected an unexplained and distinct set of inertial waves. These waves travel retrograde at three times the speed of Rossby waves, appear as equatorially anti-symmetric vortical flows and have amplitudes one-third of the Rossby waves. We call these waves high-frequency-retrograde (HFR) vorticity waves.
What is unusual about these HFR waves is that they propagate faster than equatorial Rossby waves, which already travel at the greatest phase speeds permitted by hydrodynamics alone (see the movie and Figure 1). One possible suggestion is that HFR waves are influenced by magnetism, gravity or convection, acting to accelerate them.
Figure 1| Power spectra of the Sun’s high-frequency retrograde vorticity waves. (A to C) Normalized radial vorticity power spectra from HMI using mode coupling analysis (MCA), ring-diagram analysis (RDA) and local correlation tracking (LCT) of granulation, for the spherical harmonics l=m+1 covering { the years} 2010-2020. (D and E) Power spectra for GONG coupling (1996-2020) and ring-diagrams (2001-2020), i.e., most of solar cycles 23 and 24. Negative frequencies indicate retrograde motion. The red line shows the dispersion relation of sectoral Rossby-Haurwitz modes. The high-frequency-retrograde (HFR) modes, identified by the power along the magenta line, between the cyan arrows, appear at approximately three times the frequencies of Rossby-Haurwitz waves. (F) Measured dispersion relation of the HFR power spectra for HMI ring-diagrams (blue) and coupling (red). For reference, the measured Rossby dispersion relation, with error bars, from HMI ring-diagrams is also shown[5] (black line). (G) Ratio of the measured power amplitudes of the HFR to Rossby modes, with the colors indicating the same data from panel (F).
Theorists have suggested that coupling between the Rossby waves and toroidal magnetic field at the base of the Sun’s convection zone (at around 70% of the Sun’s radius), could modify the wave dispersion relation. Given the correct field strength and configuration, these might serve to increase the frequencies of Rossby modes to achieve the dispersion relation of HFR modes. If these HFR modes were magneto-Rossby waves, this would give us profound insight into magnetic structures of the deep solar interior. However, we use numerical studies and theoretical arguments to demonstrate that, for a range of field configurations, magnetic fields tend to induce a very different dispersion relation than that exhibited by HFR waves. Furthermore, the Sun is a magnetically active star, with a cycle of 11 years. If the HFR modes were magnetic in nature, then we expect the dispersion relation to change during the cycle, as the toroidal field amplitude winds up and down. Our observations show that the dispersion relation of the HFR modes is stable throughout the solar cycle, suggesting that magnetism ought to be excluded.
We then investigated the possible role of gravity. Internal gravity waves are thought to be trapped in the interior of the Sun, with their motions undetectable by current observational techniques. In this scenario, Rossby waves would couple with these internal gravity waves, forming a new type of wave known as the Yanai wave, which, if confirmed, would be the first incontrovertible detection of the Sun’s gravity waves. However, these waves are theoretically predicted to be symmetric across the equator, unlike HFR modes. Furthermore, we argue that this would require the transition layer from the outer convection zone to the radiative interior to be extremely thin, on the order of 0.001% of the Sun’s radius, contrary to current theoretical expectations and independent observational constraints.
The final plausible candidate is thermal Rossby waves. The outer 30% of the Sun is convective, in that thermal flux is transported by the upward motion of hot material, compensated by the descent of cold fluid. Most numerical convection simulations state that thermal Rossby waves should naturally arise in the near-surface layers as a system of anti-symmetric vorticities, like HFR waves, with diverging outflows. If HFR waves were identified as thermal Rossby waves, this would shed new light into the physics of solar convection. However, we find no evidence that HFR waves are associated with diverging outflows. Furthermore, simulations and theory state that thermal Rossby modes propagate in the direction of rotation, while HFR modes are distinctly retrograde.
Thus, we have yet to identify the source of the HFR modes, since they appear to defy explanation by simple hydrodynamics alone and also by several coupling mechanisms. The undetermined nature so far of these waves promises novel physics and fresh insight into solar and stellar dynamics.
References
[1] Löptien, B., et al. 2018, Nature Astron., 2, 568
[2] Liang, Z.-C., Gizon, L., Birch, A. C., & Duvall, T. L., 2019, A&A, 626, A3
[3] Proxauf, B., et al. 2020, A&A, 634, A44
[4] Woodard, M. F. 2016, MNRAS, 460, 3292
[5] Hanson, C., S., Gizon, L., & Liang, Z.-C. 2020, A&A, 635, A109