arXiv subjects

Yuto Bekki

Publications and source records attributed to Yuto Bekki.

15 recordsLinked to original sources

arXiv2026

Towards inertial-mode helioseismology: Direct sensing of solar rotation at 75 deg latitude and 0.8 Rsun

Solar internal rotation at high latitudes is poorly constrained by acoustic-mode helioseismology. Global inertial modes observed on the Sun are highly sensitive to solar differential rotation and may provide new diagnostics of rotation in these regions. We aim to constrain solar rotation with the measured frequency of the $m=1$ high-latitude inertial mode, starting from the HMI/SDO reference rotation profile given by p-mode helioseismology for 2010-2024. Using a validated and accurate eigenvalue solver, we compute the perturbation to the mode frequency resulting from localised changes in the differential rotation rate throughout the solar interior. We find that the linear sensitivity kernel of the $m=1$ high-latitude mode peaks at latitude 75 deg and radius $0.8 R_\odot$, with full widths of 7 deg and $0.13 R_\odot$. From the observed mode frequency in the Carrington frame, $-87.9 \pm 1.9$ nHz (retrograde, averaged over 2010-2024), we infer that the solar rotation rate near this location is $365.3\pm 2.0$ nHz, which exceeds the reference p-mode estimate by $8.1$ nHz. Additionally, we propose a latitudinally smooth, radially independent modification to the rotation rate at high latitudes beyond the linear (small-perturbation) regime. This work demonstrates that individual inertial modes can provide direct constraints on rotation in the bulk of the solar convection zone, well below the surface, representing the first example of spatially resolved inertial-mode helioseismology.

astro-ph.SR↗

arXiv2025

Effects of the radiative interior on solar inertial modes

Solar inertial modes are believed to play important diagnostic and dynamical roles in the Sun's differentially rotating convection zone. However, the coupling of these modes to the radiative interior has not yet been discussed. We aim to understand the dependence of the modes on the uniformly rotating sub-adiabatic region below the convection zone and determine whether this leads to measurable changes at the surface. We used the Dedalus code to compute linear eigenmodes in the inertial frequency range in a setup that includes both the convection zone and the radiative interior down to $0.5R_\odot$. We imposed free-surface boundary conditions at both radial boundaries. For comparison, we also computed the eigenmodes in a setup restricted to the convection zone. We find that including the radiative zone only slightly modifies the frequencies and surface eigenfunctions, except for some modes with significant radial motion (high-frequency retrograde and prograde columnar modes). On the other hand, most modes penetrate significantly into the overshooting layer below the convection zone. This reduces their growth rates and distorts their eigenfunctions near the base of the convection zone. Furthermore, the uniformly rotating sub-adiabatic radiative zone supports oscillations due to Rossby modes of all possible spherical harmonics and radial nodes. In particular, when the nearest inertial mode in frequency space lies within around 10 nHz and shares the same north-south symmetry, these Rossby modes evolve into mixed modes characterized by significant motions within both the radiative and convection zones. However, such mixed modes have a high mode mass in the radiative interior and thus will be difficult to excite stochastically via convection.

astro-ph.SR↗

arXiv2025

Impacts of small-scale dynamo on rotating columnar convection in stellar convection zones

Understanding the complex interactions between convection, magnetic fields, and rotation is key to modeling the internal dynamics of the Sun and stars. Under rotational influence, compressible convection forms prograde-propagating convective columns near the equator. The interaction between such rotating columnar convection and the small-scale dynamo (SSD) remains largely unexplored. We investigate the influence of the SSD on the properties of rotating convection in the equatorial regions of solar and stellar convection zones. A series of rotating compressible magnetoconvection simulations is performed using a local f-plane box model at the equator. The flux-based Coriolis number Co is varied systematically. To isolate the effects of the SSD, we compare results from hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations. The SSD affects both convective heat and angular momentum transport. In MHD cases, convective velocity decreases more rapidly with increasing Co than in HD cases. This reduction is compensated by enhanced entropy fluctuations, maintaining overall heat transport efficiency. Furthermore, a weakly subadiabatic layer is maintained near the base of the convection zone even under strong rotational influence when the SSD is present. These behaviors reflect a change in the dominant force balance: the SSD introduces a magnetostrophic balance at small scales, while geostrophic balance persists at larger scales. The inclusion of the SSD also reduces the dominant horizontal scale of columnar convective modes by enhancing the effective rotational influence. Regarding angular momentum transport, the SSD generates Maxwell stresses that counteract the Reynolds stresses, thereby quenching the generation of mean shear flows. These SSD effects should be accounted for in models of solar and stellar convection.

astro-ph.SR↗

arXiv2025

Structure and Dynamics of the Sun's Interior Revealed by Helioseismic and Magnetic Imager

High-resolution helioseismology observations with the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) provide a unique three-dimensional view of the solar interior structure and dynamics, revealing a tremendous complexity of the physical processes inside the Sun. We present an overview of the results of the HMI helioseismology program and discuss their implications for modern theoretical models and simulations of the solar interior.

astro-ph.SR↗

arXiv2025

Assessing the validity of the anelastic and Boussinesq approximations to model solar inertial modes

Global-scale inertial modes of oscillations have been recently observed on the Sun. They might play an important dynamic and diagnostic role for the Sun. This work aims to assess the validity of simplifying assumptions in the equation of continuity, which have often been used in the linear models of solar inertial modes. We compute the linear eigenmodes of the Sun's convection zone in the inertial frequency range using the Dedalus code. This single framework enables us to compare the sensitivity of the modes to different model setups, such as the compressible setup and the Boussinesq and anelastic approximations. We consider both the cases of uniform rotation and solar differential rotation (as given by helioseismology). We find that the compressible and anelastic models have almost identical eigenmodes under uniform rotation and solar differential rotation. On the other hand, the absence of density stratification in the Boussinesq model results in significantly different eigenmodes under these setups. The differences are most prominent for the non-toroidal modes with significant radial motions mainly due to the absence of the compressional $\beta$ effect. The anelastic approximation simplifies the calculations and reduces the numerical cost without affecting the solar inertial modes. The Boussinesq or incompressible approximations cannot be used to model the solar inertial modes accurately. Given the strong influence of differential rotation on the eigenmodes, an acceptable setup is to use the anelastic approximation together with the solar differential rotation.

astro-ph.SR↗

arXiv2024

Solar Inertial Modes

The Sun's global inertial modes are very sensitive to the solar differential rotation and to properties of the deep solar convection zone which are currently poorly constrained. These properties include the superadiabatic temperature gradient, the latitudinal entropy gradient, and the turbulent viscosity. The inertial modes also play a key role in controlling the Sun's large-scale structure and dynamics, in particular the solar differential rotation. This paper summarizes recent observations and advances in the (linear and nonlinear) modeling of the solar inertial modes.

astro-ph.SR↗

arXiv2024

The Sun's differential rotation is controlled by high-latitude baroclinically unstable inertial modes

Rapidly rotating fluids have a rotation profile which depends only on the distance from the rotation axis, in accordance with the Taylor-Proudman theorem. Although the Sun was expected to be such a body, helioseismology showed that the rotation rate in the convection zone is closer to constant on radii. It has been postulated that this deviation is due to the poles being warmer than the equator by a few degrees. Using numerical simulations, we show that the pole-to-equator temperature difference cannot exceed 7 Kelvin as a result of the back-reaction of the high-latitude baroclinically unstable inertial modes. The observed amplitudes of the modes further indicate that this maximum temperature difference is reached in the Sun. We conclude that the Sun's latitudinal differential rotation reaches its maximum allowed value.

astro-ph.SR↗

arXiv2023

Numerical study of non-toroidal inertial modes with l=m+1 radial vorticity in the Sun's convection zone

Various types of inertial modes have been observed and identified on the Sun, including the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. Recent observations further report a detection of equatorially-antisymmetric radial vorticity modes which propagate in a retrograde direction about three times faster than those of the equatorial Rossby modes when seen in the corotating frame with the Sun. Here, we study the properties of these equatorially-antisymmetric vorticity modes using a realistic linear model of the Sun's convection zone. We find that they are essentially non-toroidal, involving a substantial radial flow at the equator. Thus, the background density stratification plays a critical role in determining their dispersion relation. The solar differential rotation is also found to have a significant impact by introducing the viscous critical layers and confining the modes near the base of the convection zone. Furthermore, we find that their propagation frequencies are strikingly sensitive to the background superadiabaticity $δ$ because the buoyancy force acts as an additional restoring force for these non-toroidal modes. The observed frequencies are compatible with the linear model only when the bulk of the convection zone is weakly subadiabatic ($-5\times 10^{-7} \lesssim δ\lesssim -2.5\times 10^{-7}$). Our result is consistent with but tighter than the constraint independently derived in a previous study ($δ<2 \times 10^{-7}$) employing the high-latitude inertial mode. It is implied that, below the strongly superadiabatic near-surface layer, the bulk of the Sun's convection zone might be much closer to adiabatic than typically assumed and may even be weakly subadiabatic.

astro-ph.SR↗

arXiv2023

Dynamics of solar large-scale flows

The Sun's axisymmetric large-scale flows, differential rotation and meridional circulation, are thought to be maintained by the influence of rotation on the thermal-convective motions in the solar convection zone. These large-scale flows are crucial for maintaining the Sun's global magnetic field. Over the last several decades, our understanding of large-scale motions in the Sun has significantly improved, both through observational and theoretical efforts. Helioseismology has constrained the flow topology in the solar interior, and the growth of supercomputers has enabled simulations that can self-consistently generate large scale flows in rotating spherical convective shells. In this chapter, we review our current understanding of solar convection and the large-scale flows present in the Sun, including those associated with the recently discovered inertial modes of oscillation. We discuss some issues still outstanding, and provide an outline of future efforts needed to address these.

astro-ph.SR↗

arXiv2022

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

The Babcock-Leighton (BL) flux-transport model is a widely-accepted dynamo model of the Sun. This dynamo model has been extensively studied in a two-dimensional (2D) mean-field framework in both kinematic and non-kinematic regimes. Recent three-dimensional (3D) models have been restricted to the kinematic regime. In these models, the surface poloidal flux is produced by the emergence of bipolar magnetic regions (BMRs) that are tilted according to Joy's law. We investigate the prescription for emergence of a BMR in 3D non-kinematic simulations. We also report initial results of cyclic BL dynamo simulation. We extend a conventional 2D mean-field model of the BL flux-transport dynamo into 3D non-kinematic regime. The large-scale mean flows are driven by the parameterized $Λ$-effect in this model. For the induction equation, we use a BL source term by which the surface BMRs are produced in response to the dynamo-generated toroidal field inside the convection zone. We find that, in the 3D non-kinematic regime, the tilt angle of a newly-emerged BMR is very sensitive to the prescription for the subsurface structure of the BMR. Anti-Joy tilt angles are found unless the BMR is deeply embedded in the convection zone. We also find that the leading spot tends to become stronger than the following spot. The anti-Joy's law trend and the morphological asymmetry of the BMRs can be explained by the Coriolis force acting on the Lorentz-force-driven flows. Furthermore, we demonstrate that the solar-like magnetic cycles can be successfully obtained if the Joy's law is explicitly given in the BL $α$-effect. In these cyclic dynamo simulation, a strong Lorentz force feedback leads to cycle modulations in the differential rotation and meridional circulation. The non-axisymmetric components of the flows are found to exist as inertial modes such as the equatorial Rossby modes.

astro-ph.SR↗

arXiv2022

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

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. 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. 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 0.96R. The simulations cover a duration of about 15 solar years. Various large-scale modes at low frequencies are extracted from the simulation. Their characteristics are compared to those from the linear model and to the observations. Among other modes, both the equatorial Rossby modes and the columnar convective modes are seen in the simulation. The columnar convective modes contain most of the large-scale velocity power outside the tangential cylinder and substantially contribute to the heat and angular momentum transport. 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 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 modes between the equatorial Rossby modes and the columnar convective modes 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.

astro-ph.SR↗

arXiv2022

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

On the one hand, several types of global-scale inertial modes of oscillation have been observed on the Sun. They include the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. On the other hand, the columnar convective modes (predicted by simulations; also known as banana cells or thermal Rossby waves) remain elusive. We aim to investigate the influence of turbulent diffusivities, non-adiabatic stratification, differential rotation, and a latitudinal entropy gradient on the linear global modes of the rotating solar convection zone. We solve numerically for the eigenmodes of a rotating compressible fluid inside a spherical shell. We identify modes in the inertial frequency range including the columnar convective modes, as well as modes of mixed character. The corresponding mode dispersion relations and eigenfunctions are computed for azimuthal orders $m \leq 16$. The three main results are as follows. Firstly, we find that, for $m \gtrsim 5$, the radial dependence of the equatorial Rossby modes with no radial node ($n=0$) is radically changed from the traditional expectation ($r^m$) for turbulent diffusivities $\gtrsim 10^{12}$ cm$^2$ s$^{-1}$. Secondly, we find mixed modes, i.e. modes that share properties of the equatorial Rossby modes with one radial node ($n=1$) and the columnar convective modes. Thirdly, we show that the $m=1$ high-latitude mode in the model is consistent with the solar observations when the latitudinal entropy gradient corresponding to a thermal wind balance is included (baroclinally unstable mode). To our knowledge, this work is the first realistic eigenvalue calculation of the global modes of the rotating solar convection zone. This calculation reveals a rich spectrum of modes in the inertial frequency range, which can be directly compared to the observations. In turn, the observed modes can inform us about the solar convection zone.

astro-ph.SR↗

arXiv2021

Solar inertial modes: Observations, identification, and diagnostic promise

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.

astro-ph.SR↗

arXiv2018

Consequences of high effective Prandtl number on solar differential rotation and convective velocity

Observations suggest that the large-scale convective velocities obtained by solar convection simulations might be over-estimated (convective conundrum). One plausible solution to this could be the small-scale dynamo which cannot be fully resolved by global simulations. The small-scale Lorentz force suppresses the convective motions and also the turbulent mixing of entropy between upflows and downflows, leading to a large effective Prandtl number ($\Pr$). We explore this idea in three-dimensional global rotating convection simulations at different thermal conductivity ($κ$), i.e., at different $\Pr$. In agreement with previous non-rotating simulations, the convective velocity is reduced with the increase of $\Pr$ as long as the thermal conductive flux is negligible. A subadiabatic layer is formed near the base of the convection zone due to continuous deposition of low entropy plumes in low-$κ$ simulations. The most interesting result of our low-$κ$ simulations is that the convective motions are accompanied by a change in the convection structure that is increasingly influenced by small-scale plumes. These plumes tend to transport angular momentum radially inward and thus establish an anti-solar differential rotation, in striking contrast to the solar rotation profile. If such low diffusive plumes, driven by the radiative-surface cooling, are present in the Sun, then our results cast doubt on the idea that a high effective $\Pr$ may be a viable solution to the solar convective conundrum. Our study also emphasizes that any resolution of the conundrum that relies on the downward plumes must take into account angular momentum transport as well as heat transport.

astro-ph.SR↗

arXiv2016

Double-Cell Type Solar Meridional Circulation Based on Mean-Field Hydrodynamic Model

The main object of the paper is to present the condition of the non-diffusive part of the Reynolds stress for driving the double-cell structure of the solar meridional circulation, which has been revealed by recent helioseismic observations. By conducting a set of mean-field hydrodynamic simulations, we confirm for the first time that the double-cell meridional circulation can be achieved along with the solar-like differential rotation when the Reynolds stress transports the angular momentum upward in the lower part and downward in the upper part of the convection zone. It is concluded that, in a stationary state, the accumulated angular momentum via the Reynolds stress in the middle layer is advected to both the upper and lower parts of the convection zone by each of the two meridional circulation cells, respectively.

astro-ph.SR↗