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We have used solar oscillation frequencies and frequency splittings obtained over solar cycles 23 and 24 to investigate whether the base of the solar convection zone shows any departure from spherical symmetry. We used the even-order splitting coefficients, a 2– a 8, and estimated the contributions from each one separately. The average asphericity over the two solar cycles was determined using frequencies and splittings obtained with a 9216-day time series. We find that evidence of asphericity is, at best, marginal: the a 2 component is consistent with no asphericity, the a 4 and a 6 components yield results at a level a little greater than 1 σ, while the a 8 component shows a signature below 1 σ. The combined results indicate that the time average of the departure from the spherically symmetric position of the base of the convection zone is ≲0.0001 R ⊙. We have also used helioseismic data obtained from time series of lengths of 360, 576, 1152, and 2304 days in order to examine the consistency of the results and evaluate whether there is any time variation. We find that the evidence for time variation is statistically marginal in all cases, except for the a 6 component, for which tests consistently yield p -values of less than 0.05. [ABSTRACT FROM AUTHOR]

We present an analytical model that unifies many of the inertial waves that have been recently observed on the surface of the Sun, as well as many other modes that have been theoretically predicted—but have yet to be observed—into a single family of mixed inertial modes . By mixed, we mean that the prograde- and retrograde-propagating members of this family have different restoring forces and hence different behavior. Thermal Rossby waves exist as prograde-propagating waves, while the high-frequency retrograde (HFR) wave is one example of a member of the retrograde branch. This family of mixed modes has fully 3D motions that satisfy the anelastic form of the continuity condition. As such, the horizontal velocity is both vortical and divergent with the later flow component associated with a dynamically important radial velocity. The modes are differentiated by the number of nodes in latitude, with the lowest latitudinal order corresponding to the traditional thermal Rossby wave of Busse, the first latitudinal overtone to the mixed mode of Bekki et al., and the second overtone to the HFR wave discovered by Hanson et al. There also exist infinitely more modes of higher latitudinal order whose frequencies increase as the order increases. These higher overtones may correspond to many of the inertial modes that have been recently identified by numerical eigenmode solvers.

We have carried out inversions of travel times as measured by Gizon et al. to infer the internal profile of the solar meridional circulation (MC). A linear inverse problem has been solved by the regularized least-squares method with a constraint that the angular momentum (AM) transport by MC should be equatorward (HK21-type constraint). Our motivation for using this constraint is based on the result by Hotta & Kusano (hereafter HK21), where the solar equator-fast rotation was reproduced successfully without any manipulation. The inversion result indicates that the MC profile is a double-cell structure if the so-called HK21 regime, in which AM transported by MC sustains the equator-fast rotation, correctly describes the physics inside the solar convective zone. The sum of the squared residuals computed with the inferred double-cell MC profile is comparable to that computed with the single-cell MC profile obtained when we exclude the HK21-type constraint, showing that both profiles can explain the data more or less at the same level. However, we also find that adding the HK21-type constraint degrades the resolution of the averaging kernels. Although it is difficult for us to determine the large-scale morphology of the solar MC at the moment, our attempt highlights the relevance of investigating the solar MC profile from both theoretical and observational perspectives.

Recently discovered inertial waves, observed on the solar surface, likely extend to the deeper layers of the Sun. Utilizing helioseismic techniques, we explore these motions, allowing us to discern inertial mode eigenfunctions in both radial and latitudinal orientations. We analyze 8 yr of space-based observations (2010–2017) taken by the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory using normal mode coupling. Couplings between the same and different-degree acoustic modes and different frequency bins are measured in order to capture the various length scales of the inertial modes. We detect inertial modes at high latitude with azimuthal order t = 1 and frequency ∼ −80 nHz, measured in a corotating frame with a rotation frequency of 453.1 nHz. This mode is present in the entire convection zone. The presence of Rossby modes may be seen down to a depth of ∼0.83 R _⊙ , and the Rossby signal is indistinguishable from noise below that depth for high azimuthal order. We find that the amplitudes of these modes increase with depth down to around 0.92 R _⊙ and decrease below that depth. We find that the latitudinal eigenfunctions of Rossby modes deviate from sectoral spherical harmonics if we use a similar approach as adopted in earlier studies. We find that spatial leakage and even pure noise in the measurements of nonsectoral components can also explain the abovementioned characteristics of the latitudinal eigenfunctions. This realization underscores the necessity for careful interpretation when considering the latitudinal eigenfunctions of Rossby modes. Exploring the depth-dependent characteristics of these modes will enable us to capture interior dynamics distinctly, separate from p-mode seismology.

Magnetic flux emergence from the convection zone into the photosphere and beyond is a critical component of the behavior of large-scale solar magnetism. Flux rarely emerges amid field-free areas at the surface, but when it does, the interaction between the magnetism and plasma flows can be reliably explored. Prior ensemble studies have identified weak flows forming near emergence locations, but the low signal-to-noise ratio (S/N) required averaging over the entire data set, erasing information about variation across the sample. Here, we apply deep learning to achieve an improved S/N, enabling a case-by-case study. We find that these associated flows are dissimilar across instances of emergence and also occur frequently in the quiet convective background. Our analysis suggests the diminished influence of supergranular-scale convective flows and magnetic buoyancy on flux rise. Consistent with numerical evidence, we speculate that small-scale surface turbulence and/or deep convective processes play an outsized role in driving flux emergence.

We have used solar oscillation frequencies and frequency splittings obtained over solar cycles 23 and 24 to investigate whether the base of the solar convection zone shows any departure from spherical symmetry. We used the even-order splitting coefficients, a _2 – a _8 , and estimated the contributions from each one separately. The average asphericity over the two solar cycles was determined using frequencies and splittings obtained with a 9216-day time series. We find that evidence of asphericity is, at best , marginal: the a _2 component is consistent with no asphericity, the a _4 and a _6 components yield results at a level a little greater than 1 σ , while the a _8 component shows a signature below 1 σ . The combined results indicate that the time average of the departure from the spherically symmetric position of the base of the convection zone is ≲0.0001 R _⊙ . We have also used helioseismic data obtained from time series of lengths of 360, 576, 1152, and 2304 days in order to examine the consistency of the results and evaluate whether there is any time variation. We find that the evidence for time variation is statistically marginal in all cases, except for the a _6 component, for which tests consistently yield p -values of less than 0.05.

We recently presented the first 3D numerical simulation of the solar interior for which tachocline confinement was achieved by a dynamo-generated magnetic field. In this follow-up study, we analyze the degree of confinement as the magnetic field strength changes (controlled by varying the magnetic Prandtl number) in a coupled radiative zone (RZ) and convection zone (CZ) system. We broadly find three solution regimes, corresponding to weak, medium, and strong dynamo magnetic field strengths. In the weak-field regime, the large-scale magnetic field is mostly axisymmetric with regular, periodic polarity reversals (reminiscent of the observed solar cycle) but fails to create a confined tachocline. In the strong-field regime, the large-scale field is mostly nonaxisymmetric with irregular, quasi-periodic polarity reversals and creates a confined tachocline. In the medium-field regime, the large-scale field resembles a strong-field dynamo for extended intervals but intermittently weakens to allow temporary epochs of strong differential rotation. In all regimes, the amplitude of poloidal field strength in the RZ is very well explained by skin-depth arguments, wherein the oscillating field that gives rise to the skin depth (in the medium- and strong-field cases) is a nonaxisymmetric field structure at the base of the CZ that rotates with respect to the RZ. These simulations suggest a new picture of solar tachocline confinement by the dynamo, in which nonaxisymmetric, very long-lived (effectively permanent) field structures rotating with respect to the RZ play the primary role, instead of the regularly reversing axisymmetric field associated with the 22 yr cycle.

The physical connection between thermal convection in the solar interior and the solar wind remains unclear due to their significant scale separation. Using an extended version of the three-dimensional radiative magnetohydrodynamic code RAMENS, we perform the first comprehensive simulation of the solar wind formation, starting from the wave excitation and the small-scale dynamo below the photosphere. The simulation satisfies various observational constraints as a slow solar wind emanating from the coronal hole boundary. The magnetic energy is persistently released in the simulated corona, showing a hot upward flow at the interface between open and closed fields. To evaluate the energetic contributions from Alfvén wave and interchange reconnection, we develop a new method to quantify the cross-field energy transport in the simulated atmosphere. The measured energy transport from closed coronal loops to open field accounts for approximately half of the total. These findings suggest a significant role of the supergranular-scale interchange reconnection in solar wind formation.

We present evidence of hitherto undiscovered global-scale oscillations in the near-surface shear layer of the Sun. These oscillations are seen as large-scale variations of radial shear in both the zonal and meridional flows relative to their mean values. The variations cover all or most of a visible hemisphere, and reverse with a timescale on the order of a solar rotation. A large annual variation in the meridional shear anomaly is understandable in terms of the tilt of the rotation axis, but the rapid oscillations of the shear anomalies in both zonal and the meridional directions appear to be modulated in a more complex, not-quite-annual way, although the latter are also strongly modulated by the projected rotational axis angle. Small-scale anomalies in the neighborhood of active regions lend support to their solar origin and physical interpretation. These results were obtained by analyzing ring-diagram fits of low-order modes in high-resolution Doppler data from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory.

One key aspect of understanding the solar dynamo mechanism and the evolution of solar magnetism is to properly describe the emergence of solar active regions. In this Letter, we describe the Lagrangian photospheric flows dynamics during a simulated flux emergence that produces an active region formed by pores. We analyze the lower photospheric flow organization prior, during and following the rise of an active region, uncovering the repelling and attracting photospheric structures that act as sources and sinks for magnetic element transport. Our results show that around 10 hr before the simulated emergence, considerable global changes are taking place on mesogranular scales indicated by an increase of the number of regions acting as a source to the multiple and scattered emergences of small-scale magnetic flux. At the location of active region’s appearance, the converging flows become weaker and there is an arising of a diverging region 8 hr before the emergence time. Our study also indicates that the strong concentration of magnetic field affects the flow dynamics beyond the area of the actual simulated pores, leading to complex and strongly diverging flows in the neighboring regions. Our findings suggest that the Lagrangian analysis is a powerful tool to describe the changes in the photospheric flows due to magnetic flux emergence.

Using an analytic model, we derive the eigenfrequencies for thermal Rossby waves that are trapped radially and latitudinally in an isentropically stratified atmosphere. We ignore the star’s curvature and work in an equatorial f-plane geometry. The propagation of inertial waves is found to be sensitive to the relative direction of the wavevector to the zonal direction. Prograde propagating thermal Rossby waves are naturally trapped in the radial direction for frequencies above a critical threshold, which depends on the angle of propagation. Below the threshold frequency, there exists a continuous spectrum of prograde and retrograde inertial waves that are untrapped in an isentropic atmosphere but can be trapped by gradients in the specific entropy density. Finally, we discuss the implications of these waves on recent observations of inertial oscillations in the Sun, as well as in numerical simulations.

Starting from the fully compressible fluid equations in a plane-parallel atmosphere, we demonstrate that linear internal gravity waves are naturally pseudo-incompressible in the limit that the wave frequency ω is much less than that of surface gravity waves, i.e., $\omega \ll \sqrt{{{gk}}_{h}}$ , where g is the gravitational acceleration and k _h is the horizontal wavenumber. We accomplish this by performing a formal expansion of the wave functions and the local dispersion relation in terms of a dimensionless frequency $\varepsilon =\omega /\sqrt{{{gk}}_{h}}$ . Further, we show that, in this same low-frequency limit, several forms of the anelastic approximation, including the Lantz–Braginsky–Roberts formulation, poorly reproduce the correct behavior of internal gravity waves. The pseudo-incompressible approximation is achieved by assuming that Eulerian fluctuations of the pressure are small in the continuity equation—whereas, in the anelastic approximation, Eulerian density fluctuations are ignored. In an adiabatic stratification, such as occurs in a convection zone, the two approximations become identical. However, in a stable stratification, the differences between the two approximations are stark and only the pseudo-incompressible approximation remains valid.

Within the convection zone of a rotating star, the presence of the Coriolis force stabilizes long-wavelength convective modes. These modes, which would have been unstable if the star lacked rotation, are called overstable convective modes or thermal Rossby waves. We demonstrate that the Sun’s rotation rate is sufficiently rapid that the lower half of its convection zone could possess overstable modes. Further, we present an analytic solution for atmospheric waves that reside within a polytropic stratification. We explore in detail the properties of the overstable and unstable wave modes that exist when the polytrope is weakly unstable to convective overturning. Finally, we discuss how the thermal Rossby waves that reside within the convection zone of a star might couple with the prograde branch of the g modes that are trapped within the star’s radiative zone. We suggest that such coupling might enhance the photospheric visibility of a subset of the Sun’s g modes.

The stability of a thin magnetic tube located at different depths of the convective zone has been studied numerically and analytically. Three spectral regions are shown to be responsible for different processes related to solar activity. Numerical simulation shows that Parker instability in the high frequency domain (wave number m > 20) may accelerate magnetic fibrils to emerge into the solar atmosphere at supersonic speed. Such a physical process may be responsible for impulsive CME generation. [ABSTRACT FROM AUTHOR]