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The operation of the solar dynamo, with all of its remarkable spatio-temporal ordering, remains an outstanding problem of modern solar physics. A number of mechanisms that might plausibly contribute to its operation have been proposed, but the relative role played by each remains unclear. This uncertainty stems from continuing questions concerning the speed and structure of deep-seated convective flows. Those flows are in-turn thought to sustain both the Sun's turbulent EMF and the large-scale flows of differential rotation and meridional circulation suspected of influencing the dynamo's organization and timing. Continued progress in this area is complicated by (i) inconsistencies between helioseismic measurements of convective and meridional flow made with different techniques and instruments, and (ii) a lack of high-latitude data for convection, differential rotation, and meridional flow. We suggest that the path forward to resolving these difficulties is twofold. First, the acquisition of long-term helioseismic and emissivity measurements obtained from a polar vantage point is vital to complete our picture of the Sun's outer convection zone. Second, sustained and expanded investment in theory-oriented and combined theory/observational research initiatives will be crucial to fully exploit these new observations and to resolve inconsistencies between existing measurements., Comment: White paper submitted to the Decadal Survey for Solar and Space Physics 2024-2033. 7 pages; 4 figures

Simulating deep solar convection and its coupled mean-field motions is a formidable challenge where few observational results constrain models that suffer from the non-physical influence of the grid resolution. We present hydrodynamic global Implicit Large-Eddy simulations (ILES) of deep solar convection performed with the EULAG-MHD code, and explore the effects of grid resolution on the properties of rotating and non-rotating convection. The results, based on low-order moments and turbulent spectra reveal that convergence could be achieved in non-rotating simulations provided sufficient resolution in the radial direction. The flow is highly anisotropic, with the energy contained in horizontal divergent motions exceeding by more than three orders of magnitude their radial counterpart. By contrast, in rotating simulations the largest energy is in the toroidal part of the horizontal motions. As the grid resolution increases, the turbulent correlations change in such a way that a solar-like differential rotation, obtained in the simulation with the coarser grid, transitions to the anti-solar differential rotation. The reason for this change is the contribution of the effective viscosity to the balance of the forces driving large-scale flows. As the effective viscosity decreases, the angular momentum balance improves, yet the force balance in the meridional direction lessens, favoring a strong meridional flow that advects angular momentum towards the poles. The results suggest that obtaining the correct distribution of angular momentum may not be a mere issue of numerical resolution. Accounting for additional physics, such as magnetism or the near-surface shear layer, may be necessary in simulating the solar interior., Comment: 23 pages, 16 figures, submitted to ApJ

Global hydrodynamic simulations of internal solar dynamics have focused on replicating the conditions for solar-like differential rotation and meridional circulation using the results of helioseismic inversions as a constraint. Inferences of meridional circulation, however, have provided controversial results showing the possibility of one, two, or multiple cells along the radius. To resolve this controversy and develop a more robust understanding of global flow regimes in the solar interior, we apply a "forward-modeling" approach to the analysis of helioseismic signatures of meridional circulation profiles obtained from numerical simulations. We employ the global acoustic modeling code GALE to simulate the propagation of acoustic waves through regimes of mean mass flows generated by global hydrodynamic and magnetohydrodynamic models: EULAG, the Pencil Code, and the Rayleigh code. These models are used to create synthetic dopplergram data products, used as inputs for local time-distance helioseismology techniques. Helioseismic travel-time signals from solutions obtained through global numerical simulations are compared directly with inferences from solar observations, in order to set additional constraints on global model parameters in a direct way. We show that even though these models are able to replicate solar-like differential rotation, the resulting rotationally-constrained convection develops a multi-cell global meridional circulation profile that is measurably inconsistent with local time-distance inferences of solar observations. However, we find that the development of rotationally-unconstrained convection close to the model surface is able to maintain solar-like differential rotation, while having a significant impact on the helioseismic travel-time signal, replicating solar observations within one standard deviation of the error due to noise., Comment: 13 pages, 7 figures

Computational heliophysics has shed light on the fundamental physical processes inside the Sun, such as the differential rotation, meridional circulation, and dynamo-generation of magnetic fields. However, despite the substantial advances, the current results of 3D MHD simulations are still far from reproducing helioseismic inferences and surface observations. The reason is the multi-scale nature of the solar dynamics, covering a vast range of scales, which cannot be solved with the current computational resources. In such a situation, significant progress has been achieved by the mean-field approach, based on the separation of small-scale turbulence and large-scale dynamics. The mean-field simulations can reproduce solar observations, qualitatively and quantitatively, and uncover new phenomena. However, they do not reveal the complex physics of large-scale convection, solar magnetic cycles, and the magnetic self-organization that causes sunspots and solar eruptions. Thus, developing a synergy of these approaches seems to be a necessary but very challenging task., Comment: 20 pages, 11 figures, submitted for publication in Proceedings of IAU Symposium 362 "Predictive Power of Computational Astrophysics as a Discovery Tool"

Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as double-cell meridional circulation with strong and weak reversals. The velocities are generated using a mean-field hydrodynamic and dynamo model -- moving through the regimes with minimal parameter changes; counter-rotation near the base of the tachocline is induced by sign inversion of the non-diffusive action of turbulent Reynolds stresses ($\Lambda$-effect) due to the radial inhomogeneity of the Coriolis number. By mimicking the stochastic excitation of resonant modes in the convective interior, we simulate realization noise present in solar observations. Using deep-focusing to analyze differences in travel-time signatures between the four regimes, as well as comparing to solar observations, we show that current helioseismology techniques may offer important insights about the location and strength of the return flow, however, that it may not currently be possible to definitively distinguish between profiles of single-cell or double-cell meridional circulation.

A time-distance helioseismic technique, similar to the one used by Ilonidis et al (2011), is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager (MDI) and the Helioseismic Magnetic Imager (HMI). In the context of similar measurements of quiet sun regions, three of the five studied active regions show strong phase travel time shifts several hours prior to emergence. These results form the basis of a discussion of noise in the derived phase travel time maps and possible criteria to distinguish between true and false positive detection of emerging flux.

We present a 3-dimensional (3D) numerical solver of the linearized compressible Euler equations (GALE -- Global Acoustic Linearized Euler), used to model acoustic oscillations throughout the solar interior. The governing equations are solved in conservation form on a fully global spherical mesh ($0 \le \phi \le 2\pi$, $0 \le \theta \le \pi$, $0 \le r \le R_{\odot}$) over a background state generated by the standard Solar Model S. We implement an efficient pseudo-spectral computational method to calculate the contribution of the compressible material derivative dyad to internal velocity perturbations, computing oscillations over arbitrary 3D background velocity fields. This model offers a foundation for a "forward-modeling" approach, using helioseismology techniques to explore various regimes of internal mass flows. We demonstrate the efficacy of the numerical method presented in this paper by reproducing observed solar power spectra, showing rotational splitting due to differential rotation, and applying local helioseismology techniques to measure travel times created by a simple model of single-cell meridional circulation.

Various models of solar subsurface stratification are tested in the global EULAG-MHD solver to simulate diverse regimes of near-surface convective transport. Sub- and superadiabacity are altered at the surface of the model ($ r > 0.95~R_{\odot}$) to either suppress or enhance convective flow speeds in an effort to investigate the impact of the near-surface layer on global dynamics. A major consequence of increasing surface convection rates appears to be a significant alteration of the distribution of angular momentum, especially below the tachocline where the rotational frequency predominantly increases at higher latitudes. These hydrodynamic changes correspond to large shifts in the development of the current helicity in this stable layer ($r<0.72R_{\odot}$), significantly altering its impact on the generation of poloidal and toroidal fields at the tachocline and below, acting as a major contributor towards transitions in the dynamo cycle. The enhanced near-surface flow speed manifests in a global shift of the toroidal field ($B_{\phi}$) in the butterfly diagram - from a North-South symmetric pattern to a staggered anti-symmetric emergence.

Various models of solar sub-surface stratification are tested in the global EULAG-MHD solver to simulate diverse regimes of near-surface convective transport. Sub- and superadiabacity are altered at the surface of the model ($ r > 0.95~R_{\odot}$) to either suppress or enhance convective flow speeds in an effort to investigate the impact of the near-surface layer on global dynamics. A major consequence of increasing surface convection rates appears to be a significant alteration of the distribution of angular momentum, especially below the tachocline where the rotational frequency predominantly increases at higher latitudes. These hydrodynamic changes correspond to large shifts in the development of the current helicity in this stable layer ($r<0.72R_{\odot}$), significantly altering its impact on the generation of poloidal and toroidal fields at the tachocline and below, acting as a major contributor towards transitions in the dynamo cycle. The enhanced near-surface flow speed manifests in a global shift of the toroidal field ($B_{\phi}$) in the butterfly diagram -- from a North-South symmetric pattern to a staggered anti-symmetric emergence., Comment: The wrong article was accidentally submitted, it will be resubmitted in its full form along with a link to the published article in ApJ, so that it can be more easily linked to NASA ADS