Solar Interior Research Articles

Constraints on the properties of macroscopic transport in the Sun from combined lithium and beryllium depletion

The Sun is a privileged laboratory of stellar evolution, thanks to the quality and complementary nature of available constraints. Using these observations, we are able to draw a detailed picture of its internal structure and dynamics, which forms the basis of the successes of solar modelling. Amongst such observations, constraints on the depletion of lithium and beryllium are key tracers of the required efficiency and extent of macroscopic mixing just below the solar convective envelope. Thanks to revised determinations of these abundances, we may use them in conjunction with other existing spectroscopic and helioseismic constraints to study in detail the properties of macroscopic transport. We aim to constrain the efficiency of macroscopic transport at the base of the solar convective zone (BCZ) and determining the compatibility of the observations with a suggested candidate linked with the transport of angular momentum in the solar radiative interior. We use recent spectroscopic observations of lithium and beryllium abundance and include them in solar evolutionary model calibrations. We test the agreement of such models in terms of position of the convective envelope, helium mass fraction in the convective zone, sound speed profile inversions, and neutrino fluxes. We constrain the required efficiency and extent of the macroscopic mixing at the base of the BCZ, finding that a power-law density with an index, n, between 3 and 6 would reproduce the data, with efficiencies at the BCZ of about $6000; cm^ /s $, depending on the value of n. We also confirm that macroscopic mixing worsens the agreement with neutrino fluxes and that the current implementations of the magnetic Tayler instability are unable to explain the observations.

Investigating numerical stability by scaling heat conduction in a 1D hydrodynamic model of the solar atmosphere

Numerical models of the solar atmosphere are widely used in solar research and provide insights into unsolved problems such as the heating of coronal loops. A prerequisite for such simulations is an initial condition for the plasma temperature and density. Many explicit numerical schemes employ high-order derivatives that require some diffusion, for example isotropic diffusion, for each independent variable to maintain numerical stability. Otherwise, significant numerical inaccuracies and subsequent wiggles will occur and grow at steep temperature gradients in the solar transition region. We tested how to adapt the isotropic heat conduction to the grid resolution so that the model is capable of resolving varying temperature gradients. Our ultimate goal is to construct an atmospheric stratification that can serve as an initial condition for multi-dimensional models. Our temperature stratification spans from the solar interior to the outer corona. From that, we computed the hydrostatic density stratification. Since numerical and analytical derivatives are not identical, the model needs to settle to a numerical equilibrium to fit all model parameters, such as mass diffusion and radiative losses. To compensate for energy losses in the corona, we implemented an artificial heating function that mimics the expected heat input from the 3D field-line braiding mechanism. Our heating function maintains and stabilises the obtained coronal temperature stratification. However, the diffusivity parameters need to be adapted to the grid spacing. Unexpectedly, we find that higher grid resolutions may need larger diffusivities --- contrary to the common understanding that high-resolution models are automatically more realistic and would need less diffusivity. Smaller grid spacing causes larger temperature gradients in the solar transition region and hence a greater potential for numerical problems. We conclude that isotropic heat conduction is an efficient remedy when using explicit schemes with high-order numerical derivatives.

New Upper Limit on the Axion-Photon Coupling with an Extended CAST Run with a Xe-Based Micromegas Detector.

Hypothetical axions provide a compelling explanation for dark matter and could be emitted from the hot solar interior. The CERN Axion Solar Telescope has been searching for solar axions via their back conversion to x-ray photons in a 9-T 10-m long magnet directed toward the Sun. We report on an extended run with the International Axion Observatory pathfinder detector, doubling the previous exposure time. The detector was operated with a xenon-based gas mixture for part of the new run, providing technical insights for future configurations. No counts were detected in the 95% signal-encircling region during the new run, while 0.75 were expected. The new data improve the axion-photon coupling limit to 5.8×10^{-11} GeV^{-1} at 95% CL (for m_{a}≲0.02 eV), the most restrictive experimental limit to date.

Convective Magnetic Flux Emergence Simulations from the Deep Solar Interior to the Photosphere: Comprehensive Study of Flux Tube Twist

The emergence of magnetic flux from the deep convection zone plays an important role in solar magnetism, such as the generation of active regions and triggering of various eruptive phenomena, including jets, flares, and coronal mass ejections. To investigate the effects of magnetic twist on flux emergence, we performed numerical simulations of flux tube emergence using the radiative magnetohydrodynamic code R2D2 and conducted a systematic survey on the initial twist. Specifically, we varied the twist of the initial tube both positively and negatively from zero to twice the critical value for kink instability. As a result, regardless of the initial twist, the flux tube was lifted by the convective upflow and reached the photosphere to create sunspots. However, when the twist was too weak, the photospheric flux was quickly diffused and not retained long as coherent sunspots. The degree of magnetic twist measured in the photosphere conserved the original twist relatively well and was comparable to actual solar observations. Even in the untwisted case, a finite amount of magnetic helicity was injected into the upper atmosphere because the background turbulence added helicity. However, when the initial twist exceeded the critical value for kink instability, the magnetic helicity normalized by the total magnetic flux was found to be unreasonably larger than the observations, indicating that the kink instability of the emerging flux tube may not be a likely scenario for the formation of flare-productive active regions.

Exploring the Dynamic Rotational Profile of the Hotter Solar Atmosphere: A Multiwavelength Approach Using SDO/AIA Data

Understanding the global rotational profile of the solar atmosphere and its variation is fundamental to uncovering a comprehensive understanding of the dynamics of the solar magnetic field and the extent of coupling between different layers of the Sun. In this study, we employ the method of image correlation to analyze the extensive data set provided by the Atmospheric Imaging Assembly of the Solar Dynamic Observatory in different wavelength channels. We find a significant increase in the equatorial rotational rate (A) and a decrease in absolute latitudinal gradient (∣B∣) at all temperatures representative of the solar atmosphere, implying an equatorial rotation up to 4.18% and 1.92% faster and less differential when compared to the rotation rates for the underlying photosphere derived from Doppler measurement and sunspots respectively. In addition, we also find a significant increase in equatorial rotation rate (A) and a decrease in differential nature (∣B∣ decreases) at different layers of the solar atmosphere. We also explore a possible connection from the solar interior to the atmosphere and interestingly found that A at r = 0.94 R ⊙ and 0.965 R ⊙ show an excellent match with 171 Å, 304 Å, and 1600 Å, respectively. Furthermore, we observe a positive correlation between the rotational parameters measured from 1600 Å, 131 Å, 193 Å, and 211 Å with the yearly averaged sunspot number, suggesting a potential dependence of the solar rotation on the appearance of magnetic structures related to the solar cycle or the presence of cycle dependence of solar rotation in the solar atmosphere.

Detection of solar internal flows with numerical simulation and machine learning

Abstract The solar interior is filled with turbulent thermal convection, which plays a key role in energy and momentum transport and generation of the magnetic field. Turbulent flows in the solar interior cannot be optically detected due to its significant optical depth. Currently, helioseismology is the only way to detect the internal dynamics of the Sun. However, long-duration data with a high cadence is required and only a temporal average can be inferred. To address these issues effectively, in this study, we develop a novel method to infer solar internal flows using a combination of radiation magnetohydrodynamic numerical simulations and machine/deep learning. With the application of our new method, we can evaluate the large-scale flow at 10 Mm depth from the solar surface with three snapshots separated by an hour. We also apply the method to observational data. Our method is highly consistent with the helioseismology, although the amount of input data is significantly reduced.

Dense plasma opacity from excited states method.

The self-consistent inclusion of plasma effects in opacity calculations is a significant modeling challenge. As density increases, such effects can no longer be treated perturbatively. Building on a a recently published model that addresses this challenge, we calculate opacities of oxygen at solar interior conditions. The new model includes the effects of treating the free electrons consistently with the bound electrons, and the influence of free electron energy and entropy variations are explored. It is found that, relative to a state-of-the-art-model that does not include these effects, the bound free opacity of the oxygen plasmas considered can increase by 10%.

Applications of atomic data to studies of the Sun

The Sun is a standard reference object for astrophysics and also a fascinating subject of study in its own right. X-ray and extreme ultraviolet movies of the Sun’s atmosphere show an extraordinary diversity of plasma phenomena, from barely visible bursts and jets to coronal mass ejections that impact a large portion of the solar surface. The processes that produce these phenomena, heat the corona and power the solar wind remain actively studied and accurate atomic data are essential for interpreting observations and making model predictions. For the Sun’s interior intense effort is focused on resolving the “solar problem,” (a discrepancy between solar interior models and helioseismology measurements) and atomic data are central to both element abundance measurements and interior physics such as opacity and nuclear reaction rates. In this article, topics within solar interior and solar atmosphere physics are discussed and the role of atomic data described. Areas of active research are highlighted and specific atomic data needs are identified.Graphical abstractAn image of a solar active region obtained with the 193 A channel of SDO/AIA, showing plasma at around 1.5 million degrees.

Effect of Thermal Environment on Heat Transfer Mechanism of Solar-Powered Balloon

Solar energy units, as an ideal alternative, can be supplied to the balloons by mounting them over the envelope of the balloon. To avoid superheating and superpressure, the solar-powered balloon’s thermal efficiency should be controlled. In the current research, the thermal model of a solar-powered zero-pressure balloon has been built up and simulated in FORTRAN via iterative techniques and validated with published experimental data. The simulation of stratospheric solar-powered balloon flight has been carried out in real seasonal atmospheric conditions. The temperature variation of solar panels, interior helium, and balloon envelope material has been observed and compared with the unpowered balloon in winter and summer atmospheric conditions. The output power performance of the photovoltaic panel placed over the balloon with and without thermal effect has been reported. Furthermore, the characteristic length, angle, and area of the solar panel effects on photovoltaic panel temperature and output power are discussed in detail. The maximum temperature of the helium and envelope of the solar-powered balloon is obtained as 350.03 K and 351.19 K, respectively, and is notable in the summer solstice compared with the unpowered balloon. This research would help design the energy unit of the stratospheric balloon for long endurance.

Testing the volume integrals of travel-time sensitivity kernels for flows

Context. Helioseismic inversions largely rely on sensitivity kernels, in which 3D spatial functions describe how the changes in the solar interior translate into the change in helioseismic observables. These sensitivity kernels in most cases come from the forward modelling that is used in the most advanced solar models. Aims. We aim to test the sensitivity kernels by comparing their volume integrals with measured values from helioseismic travel times. Methods. By manipulating the tracking rate, we mimicked the additional zonal velocity in the Dopplergram datacubes. These datacubes were then processed by a standard travel-time measurements pipeline. We investigated the dependence of the east-west travel time averaged over a box around the disc centre on the implanted tracking velocity. The slope of this dependence is directly proportional to the total volume integral of the sensitivity kernel that corresponds to the travel-time geometry that is used. Results. The agreement between measurements and models for travel times that are computed with a ridge filtering is very good to acceptable. The dependence we sought to determine indeed resembles a linear function, and its slope agrees with the expected volume integral from the forward-modelled sensitivity kernel. The agreement is poorer for the phase-speed filtered datacubes. The disagreement is particularly strong for the slowest phase speeds (filters td1–td4). For the higher phase speeds, our result indicates that the measured kernel integrals are systematically larger than expected from the forward modelling. We admit our testing procedure may not be appropriate for high phase speeds and higher radial modes.

Effects of negative ions on equilibrium solar plasmas in the fabric of gravito-electrostatic sheath model

The gravito-electrostatic sheath (GES) model, exploring the solar wind plasma (SWP) origin from the solar interior plasma (SIP) via the solar surface boundary (SSB), is revaluated by including realistic negative ionic species. A constructive numerical analysis of the structuring equations shows that the SIP volume shrinks with an increase in the negative ion concentration. This shrinking nature is independent of ion mass and plasma temperature. The electric potential is insensitive to the negative ion concentration, mass, and plasma temperature. The solar plasma flow dynamics is studied with the Mach number and current density profiles. The sonic transition of the SWP depends on the Ti/Te-ratio. The current density responds to the negative ion density and Ti/Te−ratio in both the SIP and SWP. A deviation from the local quasi-neutrality state is observed in the SIP. The GES model equations result in a modified GES-Bohm sheath criterion in a well justifiable and validated form. The obtained results are then compared with the various observed outcomes and previous GES-based predictions. The relevance of this multi-parametric solar plasma analysis is lastly emphasized on the basis of the current solar research progressions.

A Linear Model for Inertial Modes in a Differentially Rotating Sun

Inertial wave modes in the Sun are of interest owing to their potential to reveal new insight into the solar interior. These predominantly retrograde-propagating modes in the solar subsurface appear to deviate from the thin-shell Rossby–Haurwitz model at high azimuthal orders. We present new measurements of sectoral inertial modes at m > 15 where the modes appear to become progressively less retrograde compared to the canonical Rossby–Haurwitz dispersion relation in a corotating frame. We use a spectral eigenvalue solver to compute the spectrum of solar inertial modes in the presence of differential rotation. Focussing specifically on equatorial Rossby modes, we find that the numerically obtained mode frequencies lie along distinct ridges, one of which lies strikingly close to the observed mode frequencies in the Sun. We also find that the n = 0 ridge is deflected strongly in the retrograde direction. This suggests that the solar measurements may not correspond to the fundamental n = 0 Rossby–Haurwitz solutions as was initially suspected, but to those for a higher n. The numerically obtained eigenfunctions also appear to sit deep within the convection zone—unlike those for the n = 0 modes—which differs substantially from solar measurements and complicates inference.

Study of solar brightness profiles in the 18–26 GHz frequency range with INAF radio telescopes

Context. The Sun is an extraordinary workbench, on which several fundamental astronomical parameters can be measured with high precision. Among these parameters, the solar radius R⊙ plays an important role in several aspects, for instance, in evolutionary models. Moreover, it conveys information about the structure of the different layers that compose the solar interior and its atmosphere. Despite the efforts to obtain accurate measurements of R⊙, the subject is still debated, and measurements are puzzling and/or lacking in many frequency ranges. Aims. We determine the mean, equatorial, and polar radii of the Sun (Rc, Req, and Rpol) in the frequency range 18.1 − 26.1 GHz. We employed single-dish observations from the newly appointed Medicina Gavril Grueff Radio Telescope and the Sardinia Radio Telescope (SRT) in five years, from 2018 to mid-2023, in the framework of the SunDish project for solar monitoring. Methods. Two methods for calculating the radius at radio frequencies were employed and compared: the half-power, and the inflection point. To assess the quality of our radius determinations, we also analysed the possible degrading effects of the antenna beam pattern on our solar maps using two 2D models (ECB and 2GECB). We carried out a correlation analysis with the evolution of the solar cycle by calculating Pearson’s correlation coefficient ρ in the 13-month running means. Results. We obtained several values for the solar radius, ranging between 959 and 994 arcsec, and ρ, with typical errors of a few arcseconds. These values constrain the correlation between the solar radius and solar activity, and they allow us to estimate the level of solar prolatness in the centimeter frequency range. Conclusions. Our R⊙ measurements are consistent with the values reported in the literature, and they provide refined estimates in the centimeter range. The results suggest a weak prolateness of the solar limb (Req > Rpol), although Req and Rpol are statistically compatible within 3σ errors. The correlation analysis using the solar images from the Grueff Radio Telescope shows (1) a positive correlation between solar activity and the temporal variation in Rc (and Req) at all observing frequencies, and (2) a weak anti-correlation between the temporal variation of Rpol and solar activity at 25.8 GHz.

On the Penetration of Large-scale Flows into Stellar Radiative Zones

The propagation of meridional circulation below the base of the convection zone (CZ) of low-mass stars may play a crucial role in the transport of angular momentum and also significantly contribute to the transport of chemical species and magnetic fields within their stable radiative zone (RZ). We systematically study these large-scale mean flows by performing three-dimensional global numerical simulations in a spherical shell that consists of a convective region overlying a stably stratified region. We find that the meridional flows can penetrate distances as large as ∼0.21r o (where r o is the outer radius) below the base of the CZ, provided that the Eddington–Sweet timescale t ES is much shorter than the viscous timescale t ν , as measured by the parameter σ=(tES/tν)1/2 . In the solar-like regime, where σ ≲ 1 in the upper RZ, we find that the angular momentum transport in the deep RZ is determined primarily by the action of the Coriolis force on meridional flows. In contrast, in models run in the σ > 1 regime, the meridional flows become weaker and the viscous effects dominate. We find that the penetration lengthscale δ MC of these mean flows when σ ≲ 1 is proportional to σ −0.22. Our findings may provide a better understanding of the role of the meridional flows in the dynamics of the solar interior and inform future numerical studies that are focused on capturing solar-like dynamics self-consistently.

Quantitative passive imaging by iterative holography: the example of helioseismic holography

In passive imaging, one attempts to reconstruct some coefficients in a wave equation from correlations of observed randomly excited solutions to this wave equation. Many methods proposed for this class of inverse problem so far are only qualitative, e.g. trying to identify the support of a perturbation. Major challenges are the increase in dimensionality when computing correlations from primary data in a preprocessing step, and often very poor pointwise signal-to-noise ratios. In this paper, we propose an approach that addresses both of these challenges: it works only on the primary data while implicitly using the full information contained in the correlation data, and it provides quantitative estimates and convergence by iteration. Our work is motivated by helioseismic holography, a well-established imaging method to map heterogenities and flows in the solar interior. We show that the back-propagation used in classical helioseismic holography can be interpreted as the adjoint of the Fréchet derivative of the operator which maps the properties of the solar interior to the correlation data on the solar surface. The theoretical and numerical framework for passive imaging problems developed in this paper extends helioseismic holography to nonlinear problems and allows for quantitative reconstructions. We present a proof of concept in uniform media.

Two-sided Loop Solar Jet Driven by the Eruption of a Small Filament in a Big Filament Channel

Similar to the cases of anemone jets, two-sided loop solar jets can also be produced by either flux emergence from the solar interior or small-scale filament eruptions. Using high-quality data from the Solar Dynamics Observatory, we have analyzed a two-sided loop solar jet triggered by the eruption of a small filament. The jet occurred in a pre-existing big filament channel. The detailed processes involved in the eruption of the small filament, the interaction between the erupted filament and the big filament channel, and the launch of the two-sided loop jet are presented. The observations further revealed notable asymmetry between the two branches of the jet spire: the northeastern branch is narrow and short, while the southern branch is wide and long and accompanied by discernible untwisting motions. We explored the unique appearance of the jet by employing the method of local potential field extrapolation to calculate the coronal magnetic field configuration around the jet. The photospheric magnetic flux below the small filament underwent cancellation for approximately 7 hr before the filament eruption, and the negative flux near the southern footpoint of the filament decreased by about 56% during this interval. Therefore, we propose that the primary photospheric driver of the filament eruption and the associated two-sided loop jet in this event is flux cancellation rather than flux emergence.

The study of angular distance distribution to the solar flares during different solar cycles

The angular distance of the solar flares to the projective point of the center of the solar disk on the solar spherical surface has been studied by the heliographical or helioprojective coordinates, during the periods 1975–2021 for GOES events and 2002–2021 for RHESSI events, hereafter “distance.” It gives a specific distribution curvature. It has also been noted that when using the number of solar flare events in each satellite, GOES or RHESSI, or even using the sum of the flux (class) or importance parameter, it obtains the same result, which is that the shape of the distribution curve remains in its shape without any significant change. In addition, it has been shown that the distribution curve contains a specific number of peaks. These peaks have a specific distance from the center of the solar disk that is very similar to the projection of the solar interior layers on the solar disk. For this reason, the names of these four main peaks have been given as follows: (1) the core circle (0–15°): it is a projection of the solar core onto the solar disk, (2) radiative ring (15–45°), and (3) the convection ring (45–55°). The limb ring is 80–90°. This result makes us wonder why the number of events in the middle of the solar disk is few, and also small at the solar limb, while many in the other parts in the solar disk. This suggests that we need to understand the sun better than before, and it also suggests that solar flares are connected to each other through the solar interior layers, the extent of which may reach the convection zone or perhaps beyond that, or the opacity of the convection zone may be less than the currently estimated value.

Connection between Subsurface Layers and Surface Magnetic Activity over Multiple Solar Cycles Using GONG Observations

We investigate the spatiotemporal evolution of high-degree acoustic-mode frequencies of the Sun and surface magnetic activity over the course of multiple solar cycles, to improve our understanding of the connection between the solar interior and atmosphere. We focus on high-degree p-modes due to their ability to characterize conditions in the shear layer just below the solar surface, and analyze 22 yr of oscillation frequencies obtained from the Global Oscillation Network Group. Considering 10.7 cm radio flux measurements, the sunspot number, and the local magnetic activity index as solar-activity proxies, we find strong correlation between the mode frequencies and each activity index. We further investigate the hemispheric asymmetry associated with oscillation frequencies and magnetic activity proxies, and find that both were dominant in the southern hemisphere during the descending phase of cycle 23, while in cycle 24 these quantities fluctuated between northern and southern hemispheres. Analyzing the frequencies at different latitudes with the progression of solar cycles, we observe that the variations at midlatitudes were dominant in the southern hemisphere during the maximum-activity period of cycle 24, but the values overlap as the cycle advances toward the minimum phase. The mode frequencies at the beginning of cycle 25 are found to be dominant in the southern hemisphere following the pattern of magnetic activity. The analysis provides added evidence that the variability in oscillation frequencies is caused by both strong and weak magnetic fields.

Solar Tachocline Confinement by the Nonaxisymmetric Modes of a Dynamo Magnetic Field

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.

Heliophysics Great Observatories and international cooperation in Heliophysics: An orchestrated framework for scientific advancement and discovery

We suggest that the next era of Heliophysics should focus on the Sun–Heliosphere and Geospace as each a system-of-systems, and recommend a coordinated, deliberate, worldwide scientific effort to answer long-standing questions that will remain unanswered without a unified program. Many of the biggest unanswered science questions that remain across Heliophysics center around the interconnectivity of the different physical systems and the role of mesoscale dynamics in modulating, regulating, and controlling that interconnected behavior. Heliophysics has made key progress understanding both the large-scale dynamics and the microphysical processes that occur in these dynamic systems. Such understanding grew out of a systematic approach to study both limits of the system, from global, with the coordinated missions of the International Solar Terrestrial Physics (ISTP) program, to micro, with largely uncoordinated (albeit coincident) missions such as Cluster, Time History of Events and Macroscale Interactions during Substorms (THEMIS), Van Allen Probes, Magnetospheric Multiscale (MMS), Parker Solar Probe, and Solar Orbiter. We suggest that the international Heliophysics community should embark on a grand program to study these system-of-systems holistically, with coordinated, multipoint measurements. We particularly recommend an emphasis on resolving the mesoscale dynamics that links micro to global, and a whole-of-science approach that includes ground-based measurements and advanced numerical modeling. In effect, we propose a mesoscale ISTP type program that would consist of a system of Great Observatories capable of revealing the connections among systems from the solar interior to the top of Earth’s atmosphere. The paradigm and specific approaches outlined in this paper could serve as a strategic imperative and overarching theme that binds our Solar and Space Physics communities together under a common scientific objective. By its very nature, the type of program we argue for would be large, with several coordinated elements, and international in scope. It would include space-borne missions and coordinated ground-based observatories, artificial intelligence/machine learning (AI/ML) methods of analyzing large and complex datasets, and next-generation numerical modeling. The need to coordinate and integrate these different elements is independent of any specific mission implementation. Hence, we suggest the Heliophysics community organize around an ISTP-type program, ISTPNext, with associated Heliophysics “Great Observatories”.