Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation

Abstract

Context. Several types of inertial modes have been detected on the Sun. Properties of these inertial modes have been studied in the linear regime but have not been studied in nonlinear simulations of solar rotating convection. Comparing the nonlinear simulations, the linear theory, and the solar observations is important to better understand the differences between the models and the real Sun. Aims. We wish to detect and characterize the modes present in a nonlinear numerical simulation of solar convection, in particular to understand the amplitudes and lifetimes of the modes. Methods. We developed a code with a Yin-Yang grid to carry out fully-nonlinear numerical simulations of rotating convection in a spherical shell. The stratification is solar-like up to the top of the computational domain at 0.96 R . The simulations cover a duration of about 15 solar years, which is more than the observational length of the Solar Dynamics Observatory (SDO). Various large-scale modes at low frequencies (comparable to the solar rotation frequency) are extracted from the simulation. Their characteristics are compared to those from the linear model and to the observations. Results. Among other modes, both the equatorial Rossby modes and the columnar convective modes are seen in the simulation. The columnar convective modes, with north-south symmetric longitudinal velocity v φ , contain most of the large-scale velocity power outside the tangential cylinder and substantially contribute to the heat and angular momentum transport near the equator. Equatorial Rossby modes with no radial node (n = 0) are also found: They have the same spatial structures as the linear eigenfunctions. They are stochastically excited by convection and have the amplitudes of a few m s −1 and mode linewidths of about 20-30 nHz, which are comparable to those observed on the Sun. We also confirm the existence of the "mixed Rossby modes" between the equatorial Rossby modes with one radial node (n = 1) and the columnar convective modes with north-south antisymmetric v φ in our nonlinear simulation, as predicted by the linear eigenmode analysis. We also see the high-latitude mode with m = 1 in our nonlinear simulation but its amplitude is much weaker than that observed on the Sun.

Three-dimensional non-kinematic simulation of the post-emergence evolution of bipolar magnetic regions and the Babcock-Leighton dynamo of the Sun

“…We can clearly see the existence of the equatorial Rossby modes as represented by a clear power ridge along the expected dispersion relations (red points) for 3 ≤ m ≤ 12. In our simulation, these Rossby modes are excited both by the non-axisymmetric random fluctuations in the Λ-effect and by the non-axisymmetric Lorentz-force; this is different from the rotating convection simulation of Bekki et al (2022b), where they are stochastically excited by turbulent convective motions alone. It is implied that our code can be used to study the magnetic cycle dependence of the Rossby modes (or inertial modes in general) in the future.…”

“…In order to avoid the singularities in a spherical coordinate at the poles, we used the Yin-Yang grid (Kageyama & Sato 2004). For more details about the implementation of the Yin-Yang grid, refer Bekki et al (2022b).…”

Nonlinear tidal interactions in the convective envelopes of low-mass stars and giant gaseous planets

“…Therefore, an accurate theoretical estimation of tidal dissipation is needed to interpret the orbital decay rate of the planet/accelerating spin of star. In the WASP-12 system, non-linear wave breaking of gravity waves (restored by buoyancy) in the radiative central portions of the host star is believed to be responsible for the inward spiralling of the planet (Chernov et al, 2017;Weinberg et al, 2017;Barker, 2020). In other systems where this mechanism probably cannot apply, tidal dissipation of inertial waves (restored by the Coriolis acceleration) in stellar convective envelopes could be another avenue to explain any inferred orbital decay, as in the KELT-1 Hot Jupiter/brown dwarf system (Maciejewski et al, 2022) or for the Hot Jupiter Kepler-1658b (Vissapragada et al, 2022.…”

“…We fixed the Ekman number E = ν/(ΩR 2 ) to 10 −5 (e.g. Bekki et al, 2022) for an envelope as thick as the core (α = 0.5), where R is the outer radius. The nonlinear self-interaction of inertial waves along their shear layers triggers cylindrical differ-3 These can be shown to be small in our problem (Astoul & Barker, 2022), but they can lead to unrealistic evolution of the total angular momentum in a spherical model, as observed in Favier et al (2014) and demonstrated in Astoul & Barker (2022).…”

Theory of solar oscillations in the inertial frequency range

“…The same analysis method as § 3.2 is used for the Fourier transform in time and longitude. Note, however, that unlike the rotating convection simulation of Bekki et al (2022a), Rossby modes are excited by the non-axisymmetric random fluctuations in the Λ-effect and by the non-axisymmetric Lorentz-force in our non-convecting model. For comparison, we also compute the same power spectrum for the hydrodynamic (non-magnetic) simulation data, in which the non-axisymmetric flows are purely driven by the random fluctuations in the Λ-effect.…”