Solar inertial modes: Observations, identification, and diagnostic promise

Abstract

The oscillations of a slowly rotating star have long been classified into spheroidal and toroidal modes. The spheroidal modes include the well-known 5-min acoustic modes used in helioseismology. Here we report observations of the Sun's toroidal modes, for which the restoring force is the Coriolis force and whose periods are on the order of the solar rotation period. By comparing the observations with the normal modes of a differentially rotating spherical shell, we are able to identify many of the observed modes. These are the high-latitude inertial modes, the critical-latitude inertial modes, and the equatorial Rossby modes. In the model, the high-latitude and critical-latitude modes have maximum kinetic energy density at the base of the convection zone, and the high-latitude modes are baroclinically unstable due to the latitudinal entropy gradient. As a first application of inertial-mode helioseismology, we constrain the superadiabaticity and the turbulent viscosity in the deep convection zone.

Theory of solar oscillations in the inertial frequency range: Linear modes of the convection zone

“…The highest amplitude mode (∼ 10 -20 m s −1 above 50 • latitude) is the m = 1 mode with north-south antisymmetric longitudinal velocity v φ with respect to the equator. This m = 1 mode was identified by Gizon et al (2021) using linear calculations in two-dimensional model, which are further discussed in the present paper and Fournier et al (2022). It corresponds to the spiral-like velocity feature reported at high latitudes by Hathaway et al (2013), although it was there reported as giantcell convection.…”

“…Fournier et al (2022) extended this model to a spherical geometry using a realistic differential rotation model and found that some Rossby modes can be unstable for m ≤ 3. Gizon et al (2021) also report a family of modes at midlatitudes that are localized near their critical latitudes. Several tens of critical-latitude modes have been identified in the range m ≤ 10.…”

“…Because the Sun is essentially symmetric about its rotation axis, the velocity of each mode in the rotating frame has the form v(r, θ) exp [i(mφ − ωt)], where r is the radius, θ is the colatitude, φ is the longitude, m is the azimuthal order, and ω is the mode eigenfrequency. Gizon et al (2021) provide all observed eigen-frequencies ω for each m, and the eigenfunctions (v θ and v φ at the surface) for a few selected modes.…”

“…Using 10 years of observations from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), Gizon et al (2021) discovered that the Sun supports a large number of global modes of inertial oscillations. The restoring force for these inertial modes is the Coriolis force, and thus the modes have periods comparable to the solar rotation period (∼ 27 days).…”

Imaging the Sun's near-surface flows using mode-coupling analysis

“…Notable local helioseismic results include imaging of the meridional flow (Giles et al 1997;Gizon et al 2020) through time-distance helioseismology (Duvall et al 1993), and farside imaging of active regions (Braun & Lindsey 2001) and their near side emergence (Birch et al 2016), through helioseismic holography (Lindsey & Braun 2000). The recent discovery of various inertial waves (Gizon et al 2021), including the equatorial Rossby wave (Löptien et al 2018), has been achieved through local helioseismic ring-diagram analysis (Hill 1988) and the non-helioseismic local correlation tracking (LCT, November & Simon 1988) of granulation.…”