Radiative Zone Research Articles

The 2D dynamics of radiative zones of low-mass stars

Context. Helioseismology and asteroseismology allow us to probe the differential rotation deep within low-mass stars. In the solar convective envelope, the rotation varies with latitude with an equator rotating faster than the pole, which results in a shear applied on the radiative zone below. However, a polar acceleration of the convective envelope can be obtained through 3D numerical simulations in other low-mass stars and the dynamical interaction of the surface convective envelope with the radiative core needs to be investigated in the general case. Aim. In the context of secular evolution, we aim to describe the dynamics of the radiative core of low-mass stars to get a deeper understanding of the internal transport of angular momentum in such stars, which results in a solid rotation in the Sun from 0.7R⊙ to 0.2R⊙ and a weak radial core-envelope differential rotation in solar-type stars. This study requires at least a 2D description to capture the latitudinal variations of the differential rotation. Methods. We build 2D numerical models of a radiative core on the top of which we impose a latitudinal shear so as to reproduce a conical or cylindrical differential rotation in a convective envelope. We perform a systematic study over the Rossby number Ro = ΔΩ/2Ω0 measuring the latitudinal differential rotation at the radiative–;convective interface. We provide a 2D description of the differential rotation and the associated meridional circulation in the incompressible and stably stratified cases using the Boussinesq approximation. Results. The imposed shear generates a geostrophic flow implying a cylindrical differential rotation in the case of an isotropic viscosity. When compared to the baroclinic flow that arises from the stable stratification, we find that the geostrophic flow is dominant when the Rossby number is high enough (Ro ≥ 1) with a cylindrical rotation profile. For low Rossby numbers (Ro < 1), the baroclinic solution dominates with a quasi-shellular rotation profile. Using scaling laws from 3D simulations, we show that slow rotators (Ω0 < 30Ω⊙) are expected to have a cylindrical rotation profile. Fast rotators (Ω0 > 30Ω⊙) may have a shellular profile at the beginning of the main sequence in stellar radiative zones. Conclusions. This study enables us to predict different types of differential rotation and emphasizes the need for a new generation of 2D rotating stellar models developed in synergy with 3D numerical simulations. The shear induced by a surface convective zone has a strong impact on the dynamics of the underlying radiative zone in low-mass stars. However, it cannot produce a flat internal rotation profile in a solar configuration calling for additional processes for the transport of angular momentum in both radial and latitudinal directions.

An automated design process for short pulse laser driven opacity experiments

Stellar-relevant conditions can be reached by heating a buried layer target with a short pulse laser. Previous design studies of iron buried layer targets found that plasma conditions are dominantly controlled by the laser energy while the accuracy of the inferred opacity is limited by tamper emission and optical depth effects. We developed a process to simultaneously optimize laser and target parameters to meet a variety of design goals. We explored two sets of design cases: a set focused on conditions relevant to the upper radiative zone of the sun (electron temperatures of 200 to 400 eV and densities greater than 1/10 of solid density) and a set focused on reaching temperatures consistent with deep within the radiative zone of the sun (500 to 1000 eV) at a fixed density. We found optimized designs for iron targets and determined that the appropriate dopant, for inferring plasma conditions, depends on the goal temperature: magnesium for up to 300 eV, aluminum for 300 to 500 eV, and sulfur for 500 to 1000 eV. The optimal laser energy and buried layer thickness increase with goal temperature. The accuracy of the inferred opacity is limited to between 11% and 31%, depending on the design. Overall, short pulse laser heated iron experiments reaching stellar-relevant conditions have been designed with consideration of minimizing tamper emission and optical depth effects while meeting plasma condition and x-ray emission goals.

The Formation of Super-Earths by Tidally Forced Turbulence

Abstract The Kepler observations indicate that many exoplanets are super-Earths, which brings about a puzzle for the core-accretion scenario. Since observed super-Earths are in the range of critical mass, they accrete gas efficiently and become gas giants. Theoretically, super-Earths are predicted to be rare in the core-accretion framework. To resolve this contradiction, we propose that the tidally forced turbulent diffusion may affect the heat transport inside the planet. Thermal feedback induced by turbulent diffusion is investigated. We find that the tidally forced turbulence generates pseudo-adiabatic regions within radiative zones, which pushes the radiative-convective boundaries inward. This decreases the cooling luminosity and enhances the Kelvin–Helmholtz (KH) timescale. For a given lifetime of protoplanetary disks (PPDs), there exists a critical threshold for the turbulent diffusivity, ν critical. If ν turb > ν critical, the KH timescale is longer than the disk lifetime and the planet becomes a super-Earth, rather than a gas giant. We find that even a small value of turbulent diffusion has influential effects on the evolution of super-Earths. The ν critical increases with the core mass. We further ascertain that, within the minimum-mass extrasolar nebula, ν critical increases with the semimajor axis. This may explain the feature that super-Earths are common in inner PPD regions, while gas giants are common in outer PPD regions. The predicted envelope mass fraction is not fully consistent with observations. We discuss physical processes, such as late core assembly and mass-loss mechanisms, that may be operating during super-Earth formation.

Helioseismic models of the sun with a low heavy element abundance

Helioseismology and neutrino experiments probing the internal structure of the Sun have yieldedmuch information, such as the adiabatic elasticity index, density, and sound speed in the convective and radiative zones, the depth of the convective zone, and the flux of neutrinos from the core. The standard model of the Sun does not adequately reproduce these characteristics, with models with low heavy element contents (mass fraction of metals Z = 0.013 in the convective zone) deviating from the helioseismic data appreciably more strongly than models with high heavy element contents (Z = 0.018). However, a spectroscopic low Z value is supported by studies reconstructing the Γ 1 profile in the adiabatic part of the convective zone based on the oscillation frequencies. Models of the convective zone show a good agreement precisely for low Z values. This study attempts to construct a model for the Sun with low Z that satisfies the helioseismic constraints. This model requires changes in the p + p reaction cross section and the opacities in the radiative zone. In our view, the helioseismic result for the mass concentrated in the convective zone testifies that the p + p reaction cross section or the electron-screening coefficient in the solar core must be increased by several percent over the current values. This requires a comparatively small correction to the opacities (by less than 5%), in order to obtain a solar model with low Z that is in agreement with the results of helioseismology and the observed solar neutrino fluxes.

Can plume-induced internal gravity waves regulate the core rotation of subgiant stars?

Context.The seismic data provided by the space-borne missions CoRoT andKeplerenabled us to probe the internal rotation of thousands of evolved low-mass stars. Subsequently, several studies showed that current stellar evolution codes are unable to reproduce the low core rotation rates observed in these stars. These results indicate that an additional angular momentum transport process is necessary to counteract the spin up due to the core contraction during the post-main sequence evolution. For several candidates, the transport induced by internal gravity waves (IGW) could play a non-negligible role.Aims.We aim to investigate the effect of IGW generated by penetrative convection on the internal rotation of low-mass stars from the subgiant branch to the beginning of the red giant branch.Methods.A semi-analytical excitation model was used to estimate the angular momentum wave flux. The characteristic timescale associated with the angular momentum transport by IGW was computed and compared to the contraction timescale throughout the radiative region of stellar models at different evolutionary stages.Results.We show that IGW can efficiently counteract the contraction-driven spin up of the core of subgiant stars if the amplitude of the radial-differential rotation (between the center of the star and the top of the radiative zone) is higher than a threshold value. This threshold depends on the evolutionary stage and is comparable to the differential rotation rates inferred for a sample of subgiant stars observed by the satelliteKepler. Such an agreement can therefore be interpreted as the consequence of a regulation mechanism driven by IGW. This result is obtained under the assumption of a smooth rotation profile in the radiative region and holds true even if a wide range of values is considered for the parameters of the generation model. In contrast, on the red giant branch, we find that IGW remain insufficient, on their own, to explain the observations because of an excessive radiative damping.Conclusions.IGW generated by penetrative convection are able to efficiently extract angular momentum from the core of stars on the subgiant branch and accordingly have to be taken into account. Moreover, agreements with the observations reinforce the idea that their effect is essential to regulate the amplitude of the radial-differential rotation in subgiant stars. On the red giant branch, another transport mechanism must likely be invoked.

Origin and Evolution of Magnetic Field in PMS Stars: Influence of Rotation and Structural Changes

Abstract During stellar evolution, especially in the pre-main-sequence phase, stellar structure and rotation evolve significantly, causing major changes in the dynamics and global flows of the star. We wish to assess the consequences of these changes on stellar dynamo, internal magnetic field topology, and activity level. To do so, we have performed a series of 3D HD and MHD simulations with the ASH code. We choose five different models characterized by the radius of their radiative zone following an evolutionary track computed by a 1D stellar evolution code. These models characterized stellar evolution from 1 to 50 Myr. By introducing a seed magnetic field in the fully convective model and spreading its evolved state through all four remaining cases, we observe systematic variations in the dynamical properties and magnetic field amplitude and topology of the models. The five MHD simulations develop a strong dynamo field that can reach an equipartition state between the kinetic and magnetic energies and even superequipartition levels in the faster-rotating cases. We find that the magnetic field amplitude increases as it evolves toward the zero-age main sequence. Moreover, the magnetic field topology becomes more complex, with a decreasing axisymmetric component and a nonaxisymmetric one becoming predominant. The dipolar components decrease as the rotation rate and the size of the radiative core increase. The magnetic fields possess a mixed poloidal-toroidal topology with no obvious dominant component. Moreover, the relaxation of the vestige dynamo magnetic field within the radiative core is found to satisfy MHD stability criteria. Hence, it does not experience a global reconfiguration but slowly relaxes by retaining its mixed stable poloidal-toroidal topology.

Baroclinically-driven flows and dynamo action in rotating spherical fluid shells

The dynamics of stably stratified stellar radiative zones is of considerable interest due to the availability of increasingly detailed observations of Solar and stellar interiors. This article reports the first non-axisymmetric and time-dependent simulations of flows of anelastic fluids driven by baroclinic torques in stably stratified rotating spherical shells – a system serving as an elemental model of a stellar radiative zone. With increasing baroclinicity a sequence of bifurcations from simpler to more complex flows is found in which some of the available symmetries of the problem are broken subsequently. The poloidal component of the flow grows relative to the dominant toroidal component with increasing baroclinicity. The possibility of magnetic field generation thus arises and this paper proceeds to provide some indications for self-sustained dynamo action in baroclinically-driven flows. We speculate that magnetic fields in stably stratified stellar interiors are thus not necessarily of fossil origin as it is often assumed.

Extreme value statistics for two-dimensional convective penetration in a pre-main sequence star

We examine a penetration layer formed between a central radiative zone and a large convection zone in the deep interior of a young low-mass star. Using the Multidimensional Stellar Implicit Code (MUSIC) to simulate two-dimensional compressible stellar convection in a spherical geometry over long times, we produce statistics that characterize the extent and impact of convective penetration in this layer. We apply extreme value theory to the maximal extent of convective penetration at any time. We compare statistical results from simulations which treat non-local convection, throughout a large portion of the stellar radius, with simulations designed to treat local convection in a small region surrounding the penetration layer. For each of these situations, we compare simulations of different resolution, which have different velocity magnitudes. We also compare statistical results between simulations that radiate energy at a constant rate to those that allow energy to radiate from the stellar surface according to the local surface temperature. Based on the frequency and depth of penetrating convective structures, we observe two distinct layers that form between the convection zone and the stable radiative zone. We show that the probability density function of the maximal depth of convective penetration at any time corresponds closely in space with the radial position where internal waves are excited. We find that the maximal penetration depth can be modeled by a Weibull distribution with a small shape parameter. Using these results, and building on established scalings for diffusion enhanced by large-scale convective motions, we propose a new form for the diffusion coefficient that may be used for one-dimensional stellar evolution calculations in the large P\'eclet number regime. These results should contribute to the 321D link.

The Sun’s Fast Dynamo Action

We provide a synthesis model demonstrating the fast dynamo action of the Sun. The latter is essentially accomplished via two toroidal structures presumably formed in the tachocline and placed symmetrically with respect to the equatorial plane. The two tori are characterized by several prominent key-properties as follows: First, in each a surplus charge is entrapped for the time period of an 11-year sunspot cycle; for the next cycle the charge changes sign. Second, the net charge of Torus, moving with the solar rotational speed (U), generates a huge toroidal current which, in turn, builds up an intense poloidal magnetic field. Third, each Torus is placed at a specific distance from the Radiative Zone, so that the U of an entrapped charge carrier equals the local propagation velocity for an electromagnetic disturbance (v). Thus, two Torus electrons satisfy the condition that the repulsive electrostatic force equals the attractive magnetic force caused from the two elementary currents. Fourth, the surplus charge steadily increases; electrons are systematically attracted inwards or repealed outwards via the poloidal field. The charges remain without any Debye shielding action in the Torus-core region, while they demonstrate a Debye anti-shielding effect closer to the Radiative Zone. Thus, the Torus charge moves with zero resistivity and rotational speed U; the Torus core region behaves like a gigantic superconductor at the extremely high temperatures of tachocline. Fifth, the tori move equatorward drifting on a surface being an ellipsoid by revolution on which the condition U=v is satisfied. Moreover, we present a preliminary 3D solar circuit with the ability to reverse the magnetic field in each 22-year cycle. Finally, we discuss many longstanding unresolved questions in the context of the proposed model.

Confinement of the solar tachocline by a cyclic dynamo magnetic field

The surprising thinness of the solar tachocline is still not understood with certainty today. Among the numerous possible scenarios suggested to explain its radial confinement, one hypothesis is based on Maxwell stresses that are exerted by the cyclic dynamo magnetic field of the Sun penetrating over a skin depth below the turbulent convection zone. Our goal is to assess under which conditions (turbulence level in the tachocline, strength of the dynamo-generated field, spreading mechanism) this scenario can be realized in the solar tachocline. We develop a simplified 1D model of the upper tachocline under the influence of an oscillating magnetic field imposed from above. The turbulent transport is parametrized with enhanced turbulent diffusion (or anti-diffusion) coefficients. Two main processes that thicken the tachocline are considered; either turbulent viscous spreading or radiative spreading. An extensive parameter study is carried out to establish the physical parameter regimes under which magnetic confinement of the tachocline that is due to a surface dynamo field can be realized. We have explored a large range of magnetic field amplitudes, viscosities, ohmic diffusivities and thermal diffusivities. We find that, for large but still realistic magnetic field strengths, the differential rotation can be suppressed in the upper radiative zone (and hence the tachocline confined) if weak turbulence is present (with an enhanced ohmic diffusivity of $\eta > 10^{7-8} \, cm^2/s$), even in the presence of radiative spreading. Our results show that a dynamo magnetic field can, in the presence of weak turbulence, prevent the inward burrowing of a tachocline subject to viscous diffusion or radiative spreading.

Tidal heating and stellar irradiation of hot Jupiters

We study the interaction between stellar irradiation and tidal heating in gaseous planets with short orbital periods. The intentionally simplified atmospheric model we employ makes the problem analytically tractable and permits the derivation of useful scaling relations. We show that many tidal models provide thermal feedback, producing interior radiative zones and leading to enhanced g-mode dissipation with a wide spectrum of resonances. These resonances are dynamically tuned by the thermal feedback, and so represent a novel form of thermomechanical feedback, coupling vibrational modes to the very slow thermal evolution of the planet. We then show that stellar irradiation allows the heat produced by these modes to be trapped at depth with high efficiency, leading to entropy increase in the central convective region, as well as expansion of the planet's radius sufficient to match observed swelling. We find that thermally driven winds play an essential role in this process by making the thermal structure of the atmosphere spherically symmetric within a few scale heights of the photosphere. We characterize the relationship between the swelling factor, the orbital period and the host star and determine the time-scale for swelling. We show that these g modes suffice to produce bloating on the order of the radius of the planet over Gyr time-scales when combined with significant insolation and we provide analytic relations for the relative magnitudes of tidal heating and insolation.

Effects of Preionization in Radiative Shocks. II. Application to the Herbig–Haro Objects

Abstract In an earlier paper we treated the preionization problem in shocks over the velocity range 20 km s−1 km s−1 in a fully self-consistent manner. Here we investigate in detail the effect of the upstream UV photon field generated in the radiative zone of shocks in the range in which hydrogen is only partly ionized 20 km s−1 ( km s−1). We show that, as a result of superheating in the nonequilibrium preshock plasma, both the magnetic parameter and the Mach number of the shock are strongly affected by the preionization state of the gas, which controls to a large extent the radiative spectrum of the shock. We use these models to provide specific line diagnostics for Herbig–Haro objects, which allow us to solve for both the preshock density and shock velocity, and we present detailed models of the HH 34 jet, which allows us to derive the shock conditions, mass-loss rate, momentum flux, and chemical abundances in the jet. We show that the refractory elements Mg, Ca, Fe, and Ni are enhanced by 0.22 dex over the solar values, which provides interesting clues about the jet-launching mechanism in pre-main-sequence evolution.

What Happens to Am Stars After They Leave the Main Sequence?

The Am, or “Metallic-line,” stars have too strong line strengths of the iron peak elements for their temperatures and too weak He, Ca, etc. Michaud showed that the A4-F2 V stars, which occur in the same area of the main sequence as the Am stars, have radiative zones below their photospheres where diffusion acts to push metals upward into the photospheres by radiation pressure and lets Ca, etc. sink downward, but only if the stars are slow rotators. Slow rotation can be caused by the formation of disks or by tidal interactions in binaries. The Am stars are rich in binaries with P < 100 days; the rapidly rotation A4-F2 V stars have no such binaries. The special peculiarities do not occur in stars above the luminosity class V stars, except among the ρ Puppis stars, so the radiative zones must disappear and the atmospheres become well mixed with the interiors. The suggestion that the ρ Puppis stars are the descendents of the Am stars fails because there are too few ρ Puppis stars by a factor of about 100. Then by searching for binaries among evolved stars I conclude that the Am stars plus A4-F2 V normal stars evolve into A7-F9 IV stars and then into F2-F9 (or later) III stars with normal abundances.

On Differential Rotation and Overshooting in Solar-like Stars

Abstract We seek to characterize how the change of global rotation rate influences the overall dynamics and large-scale flows arising in the convective envelopes of stars covering stellar spectral types from early G to late K. We do so through numerical simulations with the ASH code, where we consider stellar convective envelopes coupled to a radiative interior with various global properties. As solar-like stars spin down over the course of their main sequence evolution, such a change must have a direct impact on their dynamics and rotation state. We indeed find that three main states of rotation may exist for a given star: anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow poles), or a cylindrical rotation profile. Under increasingly strict rotational constraints, the last profile can further evolve into a Jupiter-like profile, with alternating prograde and retrograde zonal jets. We have further assessed how far the convection and meridional flows overshoot into the radiative zone and investigated the morphology of the established tachocline. Using simple mixing length arguments, we are able to construct a scaling of the fluid Rossby number , which we calibrate based on our 3D ASH simulations. We can use this scaling to map the behavior of differential rotation versus the global parameters of stellar mass and rotation rate. Finally, we isolate a region on this map (R of ≳ 1.5–2) where we posit that stars with an anti-solar differential rotation may exist in order to encourage observers to hunt for such targets.

Magnetic fields in non-convective regions of stars.

We review the current state of knowledge of magnetic fields inside stars, concentrating on recent developments concerning magnetic fields in stably stratified (zones of) stars, leaving out convective dynamo theories and observations of convective envelopes. We include the observational properties of A, B and O-type main-sequence stars, which have radiative envelopes, and the fossil field model which is normally invoked to explain the strong fields sometimes seen in these stars. Observations seem to show that Ap-type stable fields are excluded in stars with convective envelopes. Most stars contain both radiative and convective zones, and there are potentially important effects arising from the interaction of magnetic fields at the boundaries between them; the solar cycle being one of the better known examples. Related to this, we discuss whether the Sun could harbour a magnetic field in its core. Recent developments regarding the various convective and radiative layers near the surfaces of early-type stars and their observational effects are examined. We look at possible dynamo mechanisms that run on differential rotation rather than convection. Finally, we turn to neutron stars with a discussion of the possible origins for their magnetic fields.

Computational design of short pulse laser driven iron opacity experiments

The resolution of current disagreements between solar parameters calculated from models and observations would benefit from the experimental validation of theoretical opacity models. Iron's complex ionic structure and large contribution to the opacity in the radiative zone of the sun make iron a good candidate for validation. Short pulse lasers can be used to heat buried layer targets to plasma conditions comparable to the radiative zone of the sun, and the frequency dependent opacity can be inferred from the target's measured x-ray emission. Target and laser parameters must be optimized to reach specific plasma conditions and meet x-ray emission requirements. The HYDRA radiation hydrodynamics code is used to investigate the effects of modifying laser irradiance and target dimensions on the plasma conditions, x-ray emission, and inferred opacity of iron and iron-magnesium buried layer targets. It was determined that plasma conditions are dominantly controlled by the laser energy and the tamper thickness. The accuracy of the inferred opacity is sensitive to tamper emission and optical depth effects. Experiments at conditions relevant to the radiative zone of the sun would investigate the validity of opacity theories important to resolving disagreements between solar parameters calculated from models and observations.

THE EVOLUTION OF GAS GIANT ENTROPY DURING FORMATION BY RUNAWAY ACCRETION

ABSTRACT We calculate the evolution of gas giant planets during the runaway gas accretion phase of formation, to understand how the luminosity of young giant planets depends on the accretion conditions. We construct steady-state envelope models, and run time-dependent simulations of accreting planets with the code Modules for Experiments in Stellar Astrophysics. We show that the evolution of the internal entropy depends on the contrast between the internal adiabat and the entropy of the accreted material, parametrized by the shock temperature T 0 and pressure P 0. At low temperatures ( – , depending on model parameters), the accreted material has a lower entropy than the interior. The convection zone extends to the surface and can drive a high luminosity, leading to rapid cooling and cold starts. For higher temperatures, the accreted material has a higher entropy than the interior, giving a radiative zone that stalls cooling. For , the surface–interior entropy contrast cannot be accommodated by the radiative envelope, and the accreted matter accumulates with high entropy, forming a hot start. The final state of the planet depends on the shock temperature, accretion rate, and starting entropy at the onset of runaway accretion. Cold starts with require low accretion rates and starting entropy, and the temperature of the accreting material needs to be maintained close to the nebula temperature. If instead the temperature is near the value required to radiate the accretion luminosity, , as suggested by previous work on radiative shocks in the context of star formation, gas giant planets form in a hot start with .

Implications of the generation of internal gravity waves by penetrative convection for the internal rotation evolution of low-mass stars

Due to the space-borne missions CoRoT and Kepler , noteworthy breakthroughs have been made in our understanding of stellar evolution, and in particular about the angular momentum redistribution in stellar interiors. Indeed, the high-precision seismic data provide with the measurement of the mean core rotation rate for thousands of low-mass stars from the subgiant branch to the red giant branch. All these observations exhibit much lower core rotation rates than expected by current stellar evolution codes and they emphasize the need for an additional transport process. In this framework, internal gravity waves (herefater, IGW) could play a signifivative role since they are known to be able to transport angular momentum. In this work, we estimate the effciency of the transport by the IGW that are generated by penetrative convection at the interface between the convective and the radiative regions. As a first step, this study is based on the comparison between the timescale for the waves to modify a given rotation profile and the contraction/expansion timescale throughout the radiative zone of 1.3M⊙ stellar models. We show that IGW, on their own, are ineffcient to slow down the core rotation of stars on the red giant branch, where the radiative damping becomes strong enough and prevent the IGW from reaching the innermost layers. However, we find that IGW generated by penetrative convection could effciently modify the core rotation of subgiant stars as soon as the amplitude of the radial differential rotation between the core and the base of the convective zone is high enough, with typical values close to the observed rotation rates in these stars. This result argues for the necessity to account for IGW generated by penetrative convection in stellar modeling and in the angular momentum redistribution issue.

Comparative Analyses of Brookhaven National Laboratory Nuclear Decay Measurements and Super-Kamiokande Solar Neutrino Measurements: Neutrinos and Neutrino-Induced Beta-Decays as Probes of the Deep Solar Interior

An experiment carried out at the Brookhaven National Laboratory over a period of almost 8 years acquired 364 measurements of the beta-decay rates of a sample of ${}^{32}\mbox{Si}$ and, for comparison, of a sample of ${}^{36}\mbox{Cl}$ . The experimenters reported finding “small periodic annual deviations of the data points from an exponential decay … of uncertain origin”. We find that power-spectrum and spectrogram analyses of these datasets show evidence not only of the annual oscillations, but also of transient oscillations with frequencies near 11 year−1 and 12.5 year−1. Similar analyses of 358 measurements of the solar neutrino flux acquired by the Super-Kamiokande neutrino observatory over a period of about 5 years yield evidence of an oscillation near 12.5 year−1 and another near 9.5 year−1. An oscillation near 12.5 year−1 is compatible with the influence of rotation of the radiative zone. We suggest that an oscillation near 9.5 year−1 may be indicative of rotation of the solar core, and that an oscillation near 11 year−1 may have its origin in a tachocline between the core and the radiative zone. Modulation of the solar neutrino flux may be attributed to an influence of the Sun’s internal magnetic field by the Resonant Spin Flavor Precession (RSFP) mechanism, suggesting that neutrinos and neutrino-induced beta decays can provide information about the deep solar interior.

The Sun–Earth connect 2: Modelling patterns of a fractal Sun in time and space using the fine structure constant

Abstract Self-similar matrices of the fine structure constant of solar electromagnetic force and its inverse, multiplied by the Carrington synodic rotation, have been previously shown to account for at least 98% of the top one hundred significant frequencies and periodicities observed in the ACRIM composite irradiance satellite measurement and the terrestrial 10.7cm Penticton Adjusted Daily Flux data sets. This self-similarity allows for the development of a time–space differential equation (DE) where the solutions define a solar model for transmissions through the core, radiative, tachocline, convective and coronal zones with some encouraging empirical and theoretical results. The DE assumes a fundamental complex oscillation in the solar core and that time at the tachocline is smeared with real and imaginary constructs. The resulting solutions simulate for tachocline transmission, the solar cycle where time-line trajectories either ‘loop’ as Hermite polynomials for an active Sun or ‘tail’ as complementary error functions for a passive Sun. Further, a mechanism that allows for the stable energy transmission through the tachocline is explored and the model predicts the initial exponential coronal heating from nanoflare supercharging. The twisting of the field at the tachocline is then described as a quaternion within which neutrinos can oscillate. The resulting fractal bubbles are simulated as a Julia Set which can then aggregate from nanoflares into solar flares and prominences. Empirical examples demonstrate that time and space fractals are important constructs in understanding the behaviour of the Sun, from the impact on climate and biological histories on Earth, to the fractal influence on the spatial distributions of the solar system. The research suggests that there is a fractal clock underpinning solar frequencies in packages defined by the fine structure constant, where magnetic flipping and irradiance fluctuations at phase changes, have periodically impacted on the Earth and the rest of the solar system since time immemorial.