Turbulence in the Sun is suppressed on large scales and confined to equatorial regions.

Convection in the Sun's outer envelope generates turbulence and drives differential rotation, meridional circulation, and the global magnetic cycle. We develop a greater understanding of these processes by contrasting observations with simulations of global convection. These comparisons also enhance our comprehension of the physics of distant Sun-like stars. Here, we infer toroidal flow power as a function of wave number, frequency, and depth in the solar interior through helioseismic analyses of space-based observations. The inferred flows grow with spatial wave number and temporal frequency and are confined to low latitudes, supporting the argument that rotation induces systematic differences between the poles and equator. In contrast, the simulations used here show the opposite trends-power diminishing with increasing wave number and frequency while flow amplitudes become weakest at low latitudes. These differences highlight gaps in our understanding of solar convection and point to challenges ahead.

Machine learning reveals systematic accumulation of electric current in lead-up to solar flares.

Solar flares-bursts of high-energy radiation responsible for severe space weather effects-are a consequence of the occasional destabilization of magnetic fields rooted in active regions (ARs). The complexity of AR evolution is a barrier to a comprehensive understanding of flaring processes and accurate prediction. Although machine learning (ML) has been used to improve flare predictions, the potential for revealing precursors and associated physics has been underexploited. Here, we train ML algorithms to classify between vector-magnetic-field observations from flaring ARs, producing at least one M-/X-class flare, and nonflaring ARs. Analysis of magnetic-field observations accurately classified by the machine presents statistical evidence for (i) ARs persisting in flare-productive states-characterized by AR area-for days, before and after M- and X-class flare events; (ii) systematic preflare buildup of free energy in the form of electric currents, suggesting that the associated subsurface magnetic field is twisted; and (iii) intensification of Maxwell stresses in the corona above newly emerging ARs, days before first flares. These results provide insights into flare physics and improving flare forecasting.

Numerical analysis of the lattice Boltzmann method for simulation of linear acoustic waves.

We analyze a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook as well as the general multirelaxation-time collision operators. By calculating the dispersion relation for various 2D lattices, we show that the D2Q5 lattice is the most suitable model for the linear acoustic problem. We also implement a grid-refinement algorithm for the LB scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts. Our results show that the LB scheme performance is comparable to the classical second-order finite-difference schemes. Given its efficiency for parallel computation, the LB method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media.

Sensitivity of helioseismic measurements of normal-mode coupling to flows and sound-speed perturbations.

In this article, we derive and compute the sensitivity of measurements of coupling between normal modes of oscillation in the Sun to underlying flows. The theory is based on first-born perturbation theory, and the analysis is carried out using the formalism described by Lavely & Ritzwoller (1992). Albeit tedious, we detail the derivation and compute the sensitivity of specific pairs of coupled normal modes to anomalies in the interior. Indeed, these kernels are critical for the accurate inference of convective flow amplitudes and large-scale circulations in the solar interior. We resolve some inconsistencies in the derivation of Lavely & Ritzwoller (1992) and reformulate the fluid-continuity condition. We also derive and compute sound-speed kernels, paving the way for inverting for thermal anomalies alongside flows.

Anomalously weak solar convection.

Convection in the solar interior is thought to comprise structures on a spectrum of scales. This conclusion emerges from phenomenological studies and numerical simulations, though neither covers the proper range of dynamical parameters of solar convection. Here, we analyze observations of the wavefield in the solar photosphere using techniques of time-distance helioseismology to image flows in the solar interior. We downsample and synthesize 900 billion wavefield observations to produce 3 billion cross-correlations, which we average and fit, measuring 5 million wave travel times. Using these travel times, we deduce the underlying flow systems and study their statistics to bound convective velocity magnitudes in the solar interior, as a function of depth and spherical-harmonic degree ℓ. Within the wavenumber band ℓ < 60, convective velocities are 20-100 times weaker than current theoretical estimates. This constraint suggests the prevalence of a different paradigm of turbulence from that predicted by existing models, prompting the question: what mechanism transports the heat flux of a solar luminosity outwards? Advection is dominated by Coriolis forces for wavenumbers ℓ < 60, with Rossby numbers smaller than approximately 10(-2) at r/R([symbol: see text]) = 0.96, suggesting that the Sun may be a much faster rotator than previously thought, and that large-scale convection may be quasi-geostrophic. The fact that isorotation contours in the Sun are not coaligned with the axis of rotation suggests the presence of a latitudinal entropy gradient.