Solar Convection Zone Research Articles

Properties of Solar Rossby Waves from Normal Mode Coupling and Characterizing Its Systematics

Abstract Rossby waves play an important role in mediating the angular momentum of rotating spherical fluids, creating weather on Earth and tuning exoplanet orbits in distant stellar systems. Their recent discovery in the solar convection zone provides an exciting opportunity to appreciate the detailed astrophysics of Rossby waves. Large-scale Rossby waves create subtle drifts in acoustic oscillations in the convection zone, which we measure using helioseismology to image properties of Rossby waves in the interior. We analyze 20 yr of space-based observations, from 1999 to 2018, to measure Rossby-mode frequencies, line widths, and amplitudes. Spatial leakage affects the measurements of normal-mode eigenfunction coupling (which we refer to as “normal-mode coupling” in this paper) and complicates the analysis of separating out specific harmonic degree and azimuthal number of features on the Sun. Here we demonstrate a novel approach to overcome this difficulty and test it by performing synthetic tests. We find that the rms velocity of the modes is of the order of 0.5 m s−1 at the surface.

Generation of the Sun’s Radial Magnetic Field by Global Hydrodynamic Flows

A theory on the emergence of global hydrodynamic flows of matter and the generation of global magnetic fields in the solar convective zone is proposed. The unstable profile of differential rotation plays a crucial role in it: all hydrodynamic flows on the Sun (poloidal circulation, torsion oscillations, and spatiotemporal variations of the poloidal flow) are generated due to the loss of stability of differential rotation. None of the models known to us, wherein torsion oscillations and variations of the meridional circulation are typically calculated separately and are thus considered to be independent flows, reproduce this result. The calculations within our model suggest, on the contrary, that the indicated flows are actually toroidal and poloidal components of a single, 3-dimensional global flow. The decisive role of torsion oscillations in the generation of the radial alternating magnetic field is highlighted in the present study. It is demonstrated by numerical simulation that the time-varying radial magnetic field on the surface of the Sun reaches its maximum at the poles, where it changes polarity with a period of ~22 years. This process may be identified with the observed effect of polarity reversal of the polar field within the Hale magnetic cycle. It is demonstrated that the lines of zero values (polarity reversal) of the surface radial magnetic field pass through the maxima of the velocity modulus of zonal flows (torsion oscillations). In addition, the lines of magnetic polarity reversal of the radial field and the maximum velocities of surface zonal flows drift from the poles to the equator. It is noted that the obtained results on the latitudinal evolution of surface zonal flows correlate with the behavior of deep zonal flows determined by processing helioseismological data.

Space Weather Challenge and Forecasting Implications of Rossby Waves

AbstractRossby waves arise in thin layers within fluid regions of stars and planets. These global wave‐like patterns occur due to the variation in Coriolis forces with latitude. In the past several years observational evidence has indicated that there are also Rossby waves in the Sun. Although Rossby waves have been detected in the Sun's photosphere and corona, they most likely originate in the solar tachocline, the sharp shear layer at the base of the solar convection zone, where the differential rotation driven by convection transitions to the solidly rotating radiative interior. These waves differ from their Earth's counterparts by being strongly modified by toroidal magnetic fields in the solar tachocline. Recent simulations of magnetohydrodynamics of tachocline Rossby waves and magnetic fields are demonstrated to produce strong “tachocline nonlinear oscillations,” which have periods similar to those observed in the solar atmosphere—enhanced periods of solar activity, or “seasons”—occurring at intervals between six months and two years. These seasonal/subseasonal bursts produce the strongest eruptive space weather events. Thus, a key to forecasting the timing, amplitude, and location of future activity bursts, and hence space weather events, could lie in our ability to forecast the phase and amplitude of Rossby waves and associated tachocline nonlinear oscillations. Accurately forecasting the properties of solar Rossby waves and their impact on space weather will require linking surface activity observations to the magnetohydrodynamics of tachocline Rossby waves, using modern data assimilation techniques. Both short‐term (hours to days) and long‐term (decadal to millennial) forecasts of space weather and climate are now being made. We highlight in this article the potential of solar Rossby waves for forecasting space weather on intermediate time scales, of several weeks to months up to a few years ahead.

Exploring the latitude and depth dependence of solar Rossby waves using ring-diagram analysis

Context. Global-scale equatorial Rossby waves have recently been unambiguously identified on the Sun. Like solar acoustic modes, Rossby waves are probes of the solar interior. Aims. We study the latitude and depth dependence of the Rossby wave eigenfunctions. Methods. By applying helioseismic ring-diagram analysis and granulation tracking to observations by HMI aboard SDO, we computed maps of the radial vorticity of flows in the upper solar convection zone (down to depths of more than 16 Mm). The horizontal sampling of the ring-diagram maps is approximately 90 Mm (∼7.5°) and the temporal sampling is roughly 27 hr. We used a Fourier transform in longitude to separate the different azimuthal orders m in the range 3 ≤ m ≤ 15. At each m we obtained the phase and amplitude of the Rossby waves as functions of depth using the helioseismic data. At each m we also measured the latitude dependence of the eigenfunctions by calculating the covariance between the equator and other latitudes. Results. We conducted a study of the horizontal and radial dependences of the radial vorticity eigenfunctions. The horizontal eigenfunctions are complex. As observed previously, the real part peaks at the equator and switches sign near ±30°, thus the eigenfunctions show significant non-sectoral contributions. The imaginary part is smaller than the real part. The phase of the radial eigenfunctions varies by only ±5° over the top 15 Mm. The amplitude of the radial eigenfunctions decreases by about 10% from the surface down to 8 Mm (the region in which ring-diagram analysis is most reliable, as seen by comparing with the rotation rate measured by global-mode seismology). Conclusions. The radial dependence of the radial vorticity eigenfunctions deduced from ring-diagram analysis is consistent with a power law down to 8 Mm and is unreliable at larger depths. However, the observations provide only weak constraints on the power-law exponents. For the real part, the latitude dependence of the eigenfunctions is consistent with previous work (using granulation tracking). The imaginary part is smaller than the real part but significantly nonzero.

ПРО "КОРОЛІВСЬКУ ЗОНУ" СОНЯЧНИХ ПЛЯМ І ПОДВІЙНИЙ МАКСИМУМ СОНЯЧНОГО ЦИКЛУ

Cyclic regeneration of the large-scale magnetic field of the Sun underlies all the phenomena known collectively as “solar activity”. The sunspot cycle is arguably the best known manifestation of the solar magnetic cycle. We outlined here the scenario of reconstructing of toroidal magnetic field in the solar convection zone (SCZ), which, on our opinion, may help to understand why magnetic fields rise to the solar surface only in the sunspot “royal zone” and what is reason of the phenomenon of double maximum of sunspots cycle. The effect of magnetic pumping (advection) caused by radial inhomogeneity of matter with taking into account Sun’s rotation, in conjunction with deep meridional circulation, play a key role in proposed scenario. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the SCZ. Therefore, we examined two “antibuoyancy” effects: macroscopic turbulent diamagnetism and magnetic advection caused by radial inhomogeneity of fluid density in the SCZ, which we call as the ∇ρ effect. The Sun’s rotation substantially modifies the ∇ρ effect. The reconstructing of the toroidal field was examined assuming the balance between mean-field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. We found that the reconstructing of large-scale magnetism develops differently in the near-polar and equatorial domains of the SCZ. In the near-polar domain, two downward pumping effects (macroscopic diamagnetism and rotational pumping) act against magnetic buoyancy and, as a result, they neutralize magnetic buoyancy and block the toroidal field (which is generated by the Ω effect) near the tachocline. Therefore, these two antibuoyancy effects might be the reason why sunspots at the near-polar zones are never observed. In other words, strong deep-seated fields at high latitudes may well be there, but they not produce sunspots. At the same time, in the deep layers of the equatorial domain, the rotational turbulent pumping due to the latitudinal convection anisotropy changes its direction to the opposite one (from downward to upward), thereby facilitating the migration of the field to the surface. We call this transport as first (upward) magnetic advection surge. The fragments of this floating up field can be observed after a while as sunspots at latitudes of the “royal zone”. Meanwhile, a deep equator-ward meridional flow ensures transporting of deep-seated toroidal field, which is blocked near pole in tachocline, from high latitudes to low ones where are favourable conditions for the floating up of the strong field. Here this belated strong field is transported upward to solar surface (the second upward magnetic advection surge). Ultimately, two time-delayed upward magnetic surges may cause on the surface in the “royal zone” the first and second maxima of sunspots cycle.

Entropy Rain: Dilution and Compression of Thermals in Stratified Domains

Abstract Large-scale convective flows called giant cells were once thought to transport the Sun’s luminosity in the solar convection zone, but recent observations have called their existence into question. In place of large-scale flows, some authors have suggested the solar luminosity may instead be transported by small droplets of rapidly falling, low-entropy fluid. This “entropy rain” could propagate as dense vortex rings, analogous to rising buoyant thermals in the Earth’s atmosphere. In this work, we develop an analytical theory describing the evolution of dense, negatively buoyant thermals. We verify the theory with 2D cylindrical and 3D Cartesian simulations of laminar, axisymmetric thermals in highly stratified atmospheres. Our results show that dense thermals fall in two categories: a stalling regime in which the droplets slow down and expand, and a falling regime in which the droplets accelerate and shrink as they propagate downwards. We estimate that solar downflows are in the falling regime and maintain their entropy perturbation against diffusion until they reach the base of the convection zone. This suggests that entropy rain may be an effective nonlocal mechanism for transporting the solar luminosity.

Comparison of time–distance inversion methods applied to SDO/HMI Dopplergrams

Context. The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) satellite has been observing the Sun since 2010. The uninterrupted series of Dopplergrams are ideal for studying the dynamics of the upper solar convection zone. Within the Joint Science Operations Center (JSOC) the time–distance inversions for flows and sound-speed perturbations were introduced. The automatic pipeline has produced flow and sound-speed maps every 8 h. We verify the results of JSOC inversions by comparing the data products to equivalent results from inverse modelling obtained by an independent inversion pipeline. Aims. We compared the results from the JSOC pipeline for horizontal flow components and the perturbations of the speed of sound at set of depths with equivalent results from an independently implemented pipeline using a different time–distance inversion scheme. Our inversion pipeline allows inversion for all quantities at once while allowing minimisation of the crosstalk between them. This gives us an opportunity to discuss the possible biases present in the JSOC data products. Methods. For the tests we used the subtractive optimally localised averaging (SOLA) method with a minimisation of the cross-talk. We compared three test inversions for each quantity at each target depth. At first, we used the JSOC setup to reproduce the JSOC results. Subsequently, we used the extended pipeline to improve these results by incorporating more independent travel-time measurements but keeping the JSOC-indicated localisation in the Sun. Finally, we inverted for flow components and sound-speed perturbations using a localisation kernel with properties advertised in the JSOC metadata. Results. We successfully reproduced the horizontal flow components. The sound-speed perturbations are strongly affected by the high level of the cross-talk in JSOC products. This leads to larger amplitudes in the inversions for the sound-speed perturbations. Different results were obtained when a target function localised around the target depth was used. This is a consequence of non-localised JSOC averaging kernels. We add that our methodology also allows inversion for the vertical flow.

A proposal to measure iron opacity at conditions close to the solar convective zone-radiative zone boundary

A major problem in stellar modelling is the discrepancy between solar models and helioseismology data in the position of the convective zone-radiative zone boundary in the sun. This could be explained by a large uncertainty in the calculated opacity data and recent experimental data on iron using the Sandia National Laboratory Z facility have shown large differences, up to a factor of 4, between measurement and prediction at plasma conditions close to the convective zone-radiative zone boundary. This paper describes a proposal for a radiative burn-through experiment to be fielded on NIF to observe if a radiation wave transit through a Fe2O3 sample is consistent with the factor of 2–4 change in the iron opacity seen in the Z experiments. A target design and the diagnostic method are described. A detailed radiation-hydrodynamic model has been used to generate synthetic results and explore the sensitivities and experimental accuracy needed for the proposed measurement.

Semiconservative reduced speed of sound technique for low Mach number flows with large density variations

Context. The reduced speed of sound technique (RSST) has been used for efficient simulation of low Mach number flows in solar and stellar convection zones. The basic RSST equations are hyperbolic and are suitable for parallel computation by domain decomposition. The application of RSST is limited to cases in which density perturbations are much smaller than the background density. In addition, nonconservative variables are required to be evolved using this method, which is not suitable in cases where discontinuities such as shock waves coexist in a single numerical domain. Aims. In this study, we suggest a new semiconservative formulation of the RSST that can be applied to low Mach number flows with large density variations. Methods. We derive the wave speed of the original and newly suggested methods to clarify that these methods can reduce the speed of sound without affecting the entropy wave. The equations are implemented using the finite volume method. Several numerical tests are carried out to verify the suggested methods. Results. The analysis and numerical results show that the original RSST is not applicable when mass density variations are large. In contrast, the newly suggested methods are found to be efficient in such cases. We also suggest variants of the RSST that conserve momentum in the machine precision. The newly suggested variants are formulated as semiconservative equations, which reduce to the conservative form of the Euler equations when the speed of sound is not reduced. This property is advantageous when both high and low Mach number regions are included in the numerical domain. Conclusions. The newly suggested forms of RSST can be applied to a wider range of low Mach number flows.

Detection of Rossby Waves in the Sun using Normal-mode Coupling

Abstract Rossby waves play a fundamental role in angular momentum processes in rotating fluids. In addition to the potential to shed light on physical mechanisms operating in the solar convection zone, the recent detection of Rossby waves in the Sun also serves as a means of comparison between different helioseismic methods. Time–distance helioseismology, ring-diagram analysis, and other techniques have all proven successful in recovering the Rossby-wave dispersion relation from analyses of Helioseismic and Magnetic Imager data (HMI). In this article, we demonstrate that analyses of two years of HMI global-mode-oscillation data using the technique of normal-mode coupling also show signatures of Rossby waves. In addition to providing an independent means of inferring Rossby waves, this detection lends credence to the methodology of mode coupling and encourages a more complete exploration of its possibilities.

Weak influence of near-surface layer on solar deep convection zone revealed by comprehensive simulation from base to surface.

The solar convection zone is filled with turbulent convection in highly stratified plasma. Several theoretical and observational studies suggest that the numerical calculations overestimate the convection velocity. Since all deep convection zone calculations exclude the solar surface due to substantial temporal and spatial scale separations, the solar surface, which drives the thermal convection with efficient radiative cooling, has been thought to be the key to solve this discrepancy. Thanks to the recent development in massive supercomputers, we are successful in performing the comprehensive calculation covering the whole solar convection zone. We compare the results with and without the solar surface in the local domain and without the surface in the full sphere. The calculations do not include the rotation and the magnetic field. The surface region has an unexpectedly weak influence on the deep convection zone. We find that just including the solar surface cannot solve the problem.

Some travels in the land of nonlinear convection and magnetism

Rotating stars with convection zones are the great builders of magnetism in our universe. Seeking to understand how turbulent convection actually operates, and so too the dynamo action that it can achieve, has advanced through distinctive stages in which Jean-Paul Zahn was often a central player, or joined by his former students. Some of the opening steps in dealing with the basic nonlinearity in such dynamics involved modal equations (with specified horizontal structure) to study convective amplitudes and heat transports achieved as solutions equilibrated by feeding back on the mean stratification. These dealt in turn with laboratory convection, with penetrative convection in Boussinesq settings, then with compressible penetration via anelastic equations in simple geometries, and finally with stellar penetrative convection in A-type stars that coupled two convection zones. Advances in computation power allowed 2-D fully compressible simulations, and then 3-D modeling including rotation, to revisit some of these convection and penetration settings within planar layers. With externally imposed magnetic fields threading the 2-D layers, magnetoconvection could then be studied to see how the flows concentrated the fields into complex sheets, or how new classes of traveling waves could result. The era of considering turbulent convection in rotating spherical shells had also arrived, using 3-D MHD codes such as ASH to evaluate how the solar differential rotation is achieved and maintained. Similarly the manner in which global magnetic fields could be built by dynamo action within the solar convection zone took center stage, finding that coherent wreaths of strong magnetism could be built, and also cycling solutions with field reversals. The coupling of convection and magnetism continues as a vibrant research subject. It is also clear that stars like the Sun do not give up their dynamical mysteries readily when highly turbulent systems are at play.

ДОСЛІДЖЕННЯ ЦИКЛІЧНОСТІ МАГНЕТИЗМУ СОНЦЯ В МЕЖАХ ТЕОРІЇ МАКРОСКОПІЧНОЇ МАГНІТОГІДРОДИНАМІКИ

Since the mid-70s of the last century, a new direction in theoretical studies of the evolution of the global magnetism of the Sun in the framework of macroscopic MHD has been launched at the Astronomical Observatory of the Taras Shevchenko National University of Kyiv. The paper presents the results of a study of the processes of generation and restructuring of a large-scale (global) magnetic field based on the αΩ-dynamo model, taking into account new turbulent effects discovered in the theory of macroscopic MHD and data of helioseismological experiments on the internal rotation of the Sun. It was established that a sharp radial gradient of turbulent velocity in the lower half of the solar convective zone (SCZ) leads to a change in the sign of the azimuthal component of the helicity parameter α, resulting in the formation of a relatively thin layer of negative α-effect near the bottom of the SCZ. It was found that the layer of negative α-effect, together with the sign of the radial gradient of the angular velocity, detected in helioseismological experiments, makes it possible to explain the direction of migration of dynamo-waves on the solar surface. The magnetic saturation of the α-effect (alpha-quenching) in the deep layers of the SCZ was calculated. An explanation of the protracted duration of the 23rd solar cycle of about 13 years is proposed. For this, we used the observed data on a significant increase of the annual module of the magnetic fields of sunspots in the 23rd cycle. The calculated north-south asymmetry of the structure of the global magnetic field provides an opportunity to explain the phenomenon of the seeming magnetic “monopole”, which is observed during reversal of polar magnetism. It was found that the values of turbulent electrical conductivity and turbulent magnetic permeability of the solar plasma are significantly less than the corresponding gas-kinetic parameters. Therefore, the turbulent dissipation of solar magnetic fields is enhanced by 4–9 orders of magnitude compared with classical ohmic dissipation. Macroscopic turbulent diamagnetism of solar plasma was investigated. It has been found that in the lower part of the SCZ, turbulent diamagnetism acts against magnetic buoyancy, thus fulfilling the role of “negative magnetic buoyancy”. As a result of the balance of the effects of magnetic buoyancy and turbulent diamagnetism, a layer of blocked magnetic field of magnitude ≈ 3000 G is formed in the depths of the SCZ. The turbulent advection of a magnetic field in an inhomogeneous plasma density of the SCZ was studied. It was found that in the lower half of the SCZ of the equatorial domain, turbulent advection is directed upwards. As a result of the combined action of magnetic buoyancy and turbulent advection, deep strong toroidal fields are carried to the surface of the Sun in the latitudinal “royal zone” of sunspots. The role of horizontal turbulent diamagnetism in ensuring the long-term stability of sunspots was noted. To explain the observed phenomenon of double maxima of the solar spot cycle, a scenario was developed containing the generation of a magnetic field in the tachocline at the bottom of the SCZ and subsequent removal of this magnetic field from the depth layers to the surface in the latitudinal “royal zone”. The role of the radial omega-effect in the radiant zone in explaining the observed asymmetry in the amplitude of two neighbouring 11-years sunspot cycles was noted.

Large-Scale Magnetic Field Fragmentation in Flux-Tubes Near the Base of the Solar Convection Zone

Magnetic quenching of turbulent thermal diffusivity leads to instability of the large-scale field with the production of spatially isolated regions of enhanced field. This conclusion follows from a linear stability analysis in the framework of mean-field magnetohydrodynamics that allows for thermal diffusivity dependence on the magnetic field. The characteristic growth time of the instability is short compared to the 11-year period of solar activity. The characteristic scale of the increased field regions measures in tens of mega-meters. The instability can produce magnetic inhomogeneities whose buoyant rise to the solar surface forms the solar active regions. The magnetic energy of the field concentrations coincides in order of magnitude with the energy of the active regions.

Long Term Evolution of Solar Meridional Circulation and Phase Synchronization Viewed Through a Symmetrical Kuramoto Model

The solar-cycle oscillations of the toroidal and poloidal components of the solar magnetic field in the northern solar hemisphere have a persistent phase difference of about $\pi $ . We propose a symmetrical Kuramoto model with three coupled oscillators as a simple way to understand this anti-synchronization. We solve an inverse problem and reconstruct natural frequencies of the top and bottom oscillators under the conditions of a constant coupling strength and a non-delayed coupling. These natural frequencies are associated with angular velocities of the meridional flow circulation near the solar surface and in the deep layer of the solar convection zone. A relationship between our reconstructions of the shallow and the deep meridional flow speed during recent Solar Cycles 21 – 23 is in agreement with estimates obtained in helioseismology and flux-transport dynamo modeling. The reconstructed top oscillator speed presents significant solar-cycle like variations that agree with recent helioseismical reconstructions. The evolution of reconstructed natural frequencies strongly depends on the coupling strength. We find two stable regimes in the case of strong coupling with a change of regime during anomalous solar cycles. We see the onset of a new transition in Solar Cycle 24. We estimate the admitted range of coupling values and find evidence of cross-equatorial coupling between solar hemispheres not accounted for by the model.

A study of the emergence of flux rope from the solar convection zone into the atmosphere by using a novel numerical method

In this paper, we successfully use our newly developed numerical method to study the process of the emergence of magnetic flux rope from the solar convection zone into the atmosphere with a stratified hydro-static equilibrium as the initial ambient state. Our simulation has obtained some key characteristics revealed by observation or other researchers' simulations. To achieve the process from emergence until eruption requires a numerical scheme with low numerical diffusion. Otherwise, the emergence process will be suppressed by diffusion of magnetic flux during the long emergence period caused by the great gradient for density and pressure in the ambient state. The results demonstrate that our code can simulate the emergence process very well, which allows us to explore flux emergence mechanisms.

Cycle-dependent and cycle-independent surface tracers of solar magnetic activity

AbstractWe consider several tracers of magnetic activity that separate cycle-dependent contributions to the background solar magnetic field from those that are independent of the cycle. The main message is that background fields include two relative separate populations. The background fields with a strength up to 100 Mx cm−2 are very poorly correlated with the sunspot numbers and vary little with the phase of the cycle. In contrast, stronger magnetic fields demonstrate pronounced cyclic behaviour. Small-scale solar magnetic fields demonstrate features of fractal intermittent behaviour, which requires quantification. We investigate how the observational estimate of the solar magnetic flux density B depends on resolution D in order to obtain the scaling In BD = −k In D + a in a reasonably wide range. The quantity k demonstrates cyclic variations typical of a solar activity cycle. k depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity a demonstrates some cyclic variation, but it is much weaker than in the case of k. The scaling is typical of fractal structures. The results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection. Here we discuss the message for solar dynamo studies hidden in the above results.

Nonkinematic solar dynamo models with double-cell meridional circulation

Employing the standard solar interior model as input we construct a dynamically-consistent nonlinear dynamo model that takes into account the detailed description of the Λ- effect, turbulent pumping, magnetic helicity balance, and magnetic feedback on the differential rotation and meridional circulation. The background mean-field hydrodynamic model of the solar convection zone accounts the solar-like angular velocity profile and the double-cell meridional circulation. We investigate an impact of the nonlinear magnetic field generation effects on the long-term variability and properties of the magnetic cycle. The nonlinear dynamo solutions are studied in the wide interval of the α effect parameter from a slightly subcritical to supercritical values. It is found that the magnetic cycle period decreases with the increasing cycle's magnitude. The periodic long-term variations of the magnetic cycle are excited in case of the overcritical α effect. These variations result from the hemispheric magnetic helicity exchange. It depends on the magnetic diffusivity parameter and the magnetic helicity production rate. The large-scale magnetic activity modifies the distribution of the differential rotation and meridional circulation inside convection zone. It is found that the magnetic feedback on the global flow affects the properties of the long-term magnetic cycles. We confront our findings with solar and stellar magnetic activity observations.

Towards a novel stellar opacity measurement scheme using stability properties of double ablation front structures

A novel method for bringing sample elements to hydrodynamic conditions relevant to the base of the solar convection zone is investigated. The method is designed in the framework of opacity measurements and exploits the temporal and spatial stability of hydrodynamic parameters in counter-propagating Double Ablation Front (DAF) structures. The physics of symmetric DAF structures is first studied in 1D geometries to assess the influence of tracer layers in the target. These results are used to propose an experimental design compatible with the OMEGA [Boehly et al., Opt. Commun. 133(1-6), 495–506 (1997)] laser. Radiative-hydrodynamic simulations conducted using the Chic code [Breil et al., Comput. Fluids 46, 161–167 (2011).] in 2D-axisymmetric geometries suggest that a Fe sample can be brought to an electron temperature of ∼160 eV and electron number density of ∼1.35 × 1023 cm−3. These parameters are reached during a 500 ps window with temporal variations of the order of 10 eV and 1022 cm−3, respectively. This allows for potential time-integrated spectral measurements. During that time, the sample is almost at local thermal equilibrium and 2D spatial gradients in the sample are less than 5% in a 360 μm diameter cylindrical volume, including the potential effects of Hot Electrons (HE) and typical uncertainties related to target fabrication and laser performances. The effects of HEs are assessed using an inline model in Chic. The HEs are found to deposit most of their energy in the cold and dense ablator between the two fronts, leading to a small efficiency loss on the DAF parameters. The calculations also suggest that negligible amounts of unabsorbed HEs are present in the probed volume, thus not affecting the atomic properties of the sample. Potential extensions of the current design to higher sample temperatures within the OMEGA capabilities are briefly discussed.

Solar-cycle Variations of Meridional Flows in the Solar Convection Zone Using Helioseismic Methods

Abstract The solar meridional flow is an axisymmetric flow in solar meridional planes, extending through the convection zone. Here we study its solar-cycle variations in the convection zone using SOHO/MDI helioseismic data from 1996 to 2010, including two solar minima and one maximum. The travel-time difference between northward and southward acoustic waves is related to the meridional flow along the wave path. Applying the ray approximation and the SOLA inversion method to the travel-time difference measured in a previous study, we obtain the meridional flow distributions in 0.67 ≤ r ≤ 0.96R ⊙ at the minimum and maximum. At the minimum, the flow has a three-layer structure: poleward in the upper convection zone, equatorward in the middle convection zone, and poleward again in the lower convection zone. The flow speed is close to zero within the error bar near the base of the convection zone. The flow distribution changes significantly from the minimum to the maximum. The change above 0.9R ⊙ shows two phenomena: first, the poleward flow speed is reduced at the maximum; second, an additional convergent flow centered at the active latitudes is generated at the maximum. These two phenomena are consistent with the surface meridional flow reported in previous studies. The change in flow extends all the way down to the base of the convection zone, and the pattern of the change below 0.9R ⊙ is more complicated. However, it is clear that the active latitudes play a role in the flow change: the changes in flow speed below and above the active latitudes have opposite signs. This suggests that magnetic fields could be responsible for the flow change.