We present results of nonlinear numerical simulations of gravity wave driven shear flow oscillations in the equatorial plane of the solar radiative interior. These results show that many of the assumptions of quasi-linear theory are not valid. When only two waves are forced (prograde and retrograde) oscillatory mean flow is maintained; but critical layers often form and are dynamically important. When a spectrum of waves is forced, the non-linear wave-wave interactions are dynamically important, often acting to decrease the maintenance of a mean flow. The (in)coherence of such wave-wave interactions must be taken into account when describing wave driven mean flows.
Quantitative data on the solar wind, solar magnetic fields, solar eruptions, solar neutrinos, and on the planetary material orbiting the Sun all indicate the presence of an iron-rich solar interior and a neutron star at the core of the Sun. Solar magnetic fields are deep-seated remnants from the core and/or Bose-Einstein condensation of Fe-rich material into a rotating superconductor. Neutron emission from the core triggers a series of reactions that produce solar luminosity, the H carrier gas that maintains mass separation in the Sun, and an outpouring of 3 E43 H+ ions per year in the solar w…
The rotation rate of the solar radiative zone is an important diagnostic for angular-momentum transport in the tachocline and below. In this paper we study the contribution of viscous and magnetic stresses to the global angular-momentum balance. By considering a simple linearized toy model, we discuss the effects of field geometry and applied boundary conditions on the predicted rotation profile and rotation rate of the radiative interior. We compare these analytical predictions with fully nonlinear simulations of the dynamics of the radiative interior, as well as with observations. We discuss…
Measurements are reviewed showing that the interior of the Sun, the inner planets, and ordinary meteorites consist mostly of the same elements: Iron, oxygen, nickel, silicon, magnesium, sulfur and calcium. These results do not support the standard solar model.
Solar oscillations consist of a rich spectrum of internal acoustic waves and surface gravity waves, stochastically excited by turbulent convection. They have been monitored almost continuously over the last ten years with high-precision Doppler images of the solar surface. The purpose of helioseismology is to retrieve information about the structure and the dynamics of the solar interior from the frequencies, phases, and amplitudes of solar waves. Methods of analysis are being developed to make three-dimensional images of subsurface motions and temperature inhomogeneities in order to study con…
It is shown that the metal abundance in the solar interior is constrained from the current solar neutrino experiment, even if one allows neutrino conversion in the sun due to neutrino oscillation. The result shows that the metal abundance in the interior should be within the range 0.4 - 1.4 times that in the surface, supporting the idea that the sun formed by a contraction of a gas cloud with an almost homogeneous composition.
Recent seismic observations coming from acoustic and gravity modes clearly show that the solar standard model has reached its limits and can no longer be used to interpret satisfactorily seismic observations. In this paper, we present a review of the non-standard processes that may be added to the solar models in order to improve our understanding of the helioseismic data. We also present some results obtained when applying ``non-standard'' stellar evolution to the modelling of the Sun.
Some basic properties of the solar convection zone are considered and the use of helioseismology as an observational tool to determine its depth and internal angular velocity is discussed. Aspects of solar magnetism are described and explained in the framework of dynamo theory. The main focus is on mean field theories for the Sun's magnetic field and its differential rotation.
The temporal variations of the rotation rate in the solar interior are studied using frequency splittings from Global Oscillations Network Group (GONG) data obtained during the period 1995-99. We find alternating latitudinal bands of faster and slower rotation which appear to move towards the equator with time - similar to the torsional oscillations seen at the solar surface. This flow pattern appears to persist to a depth of about 0.1R_sun and in this region its magnitude is well correlated with solar activity indices. We do not find any periodic or systematic changes in the rotation rate nea…
Helioseismology has allowed us to infer the rotation in the greater part of the solar interior with high precision and resolution. The results show interesting conflicts with earlier theoretical expectations, indicating that the the Sun is host to complex dynamical phenomena, so far hardly understood. This has important consequences for our ideas about the evolution of stellar rotation, as well as for models for the generation of the solar magnetic field. Here we provide an overview of our current knowledge about solar rotation, much of it obtained from observations from the SOHO spacecraft, a…
We calculate the excitation of low frequency gravity waves by turbulent convection in the sun and the effect of the angular momentum carried by these waves on the rotation profile of the sun's radiative interior. We find that the gravity waves generated by convection in the sun provide a very efficient means of coupling the rotation in the radiative interior to that of the convection zone. In a differentially rotating star, waves of different azimuthal number have their frequencies in the local rest frame of the star Doppler shifted by different amounts. This leads to a difference in their loc…
We relate the MSW effect to the efective absorption of the electronic collective motion energy by retaining the imaginary part of the index of refraction associated with the charged-current scattering and show that the small angle MSW solution to the solar neutrino anomaly can be used as a probe of the physical conditions of the solar interior if it is correct. We find that the constraint on the absorption imposed by the small angle MSW solution and the theoretical estimate of the absorption by the Boltzmann kinetic theory are consistent, which shows that a consistent theoretical picture can b…
The richness and very high accuracy of the observed frequencies of solar oscillations provide tight constraints on the structure of the solar interior and hence on the assumptions underlying the calculation of solar models. This permits the use of the Sun as a laboratory for investigating the physics of stellar interiors. Important examples are the study of the equation of state in the convection zone, and the strong evidence for the importance of gravitational settling in the solar interior. On the other hand, the importance of studies of other stars is emphasized: for example, convective cor…
Observed solar neutrino fluxes are employed to constrain the interior composition of the Sun. Including the effects of neutrino flavor mixing, the results from Homestake, Sudbury, and Gallium experiments constrain the Mg, Si, and Fe abundances in the solar interior to be within a factor 0.89 to 1.34 of the surface values with 68% confidence. If the O and/or Ne abundances are increased in the interior to resolve helioseismic discrepancies with recent standard solar models, then the nominal interior Mg, Si, and Fe abundances are constrained to a range of 0.83 to 1.24 relative to the surface. Add…
Despite recent major advances, the opacity remains a source of substantial uncertainty in the calculation of solar models, and hence of solar oscillation frequencies. Hence it is of substantial interest to investigate the sensitivity of solar structure to changes in the opacity. Furthermore, we may hope from the precise helioseismic inferences of solar structure to obtain information about possible corrections to the opacities used in the model calculation. Here we carry out detailed calculations of the influence on solar models of changes in the opacity, including also evolutionary effects. W…
Efforts to understand unusual weather or abrupt changes in climate have been plagued by deficiencies of the standard solar model (SSM). While it assumes that our primary source of energy began as a homogeneous ball of hydrogen (H) with a steady, well-behaved H-fusion reactor at its core, observations instead reveal a very heterogeneous, dynamic Sun. As examples, the upward acceleration and departure of H+ ions from the surface of the quiet Sun and abrupt climatic changes, including geomagnetic reversals and periodic magnetic storms that eject material from the solar surface are not explained b…
We argue that a variety of solar data suggest that the activity-cycle timescale variability of the total irradiance, is produced by structural adjustments of the solar interior. Assuming these adjustments are induced by variations of internal magnetic fields, we use measurements of the total irradiance and effective temperature over the period from 1978 to 1992, to infer the magnitude and location of the magnetic field. Using an updated stellar evolution model, which includes magnetic fields, we find that the observations can be explained by fields whose peak values range from 120k to 2.3k gau…
Ring diagram analysis can be used to study large scale velocity fields in the outer part of the solar convection zone. All previous works assume that the peak profiles in the solar oscillation power spectrum are symmetric. However, it has now been demonstrated that the peaks are not symmetric. In this work we study how the explicit use of asymmetric peak profiles in ring-diagram analysis influences the estimated velocity fields. We find that the use of asymmetric profiles leads to significant improvement in the fits, but the estimated velocity fields are not substantially different from those …
We present self-consistent numerical simulations of the sun's convection zone and radiative interior using a two-dimensional model of its equatorial plane. The background reference state is a one-dimensional solar structure model. Turbulent convection in the outer convection zone continually excites gravity waves which propagate throughout the stable radiative interior and deposit their angular momentum. We find that angular velocity variations in the tachocline are driven by angular momentum transported by overshooting convective plumes rather than the nonlinear interaction of waves. The mean…
The latest solar atmosphere models include non-LTE corrections and 3D hydrodynamic convection simulations. These models predict a significant reduction in the solar metal abundance, which leads to a serious conflict between helioseismic data and the predictions of solar interiors models. We demonstrate that the helioseismic constraints on the surface convection zone depth and helium abundance combined with stellar interiors models can be used to define the goodness of fit for a given chemical composition. After a detailed examination of the errors in the theoretical models we conclude that mod…
We consider radiative electromagnetic corrections, at order α, to the process $e^+ e^- \to ν\barν$ at finite density and temperature. This process represents one of the main contributions to the cooling of stellar environments in the late stages of star evolution. We find that these corrections affect the energy loss rate by a factor $(-4 ÷1) %$ with respect to the tree level estimate, in the temperature and density ranges where the neutrino pair production via e^+ e^- annihilation is the most efficient cooling mechanism.
With the recent results of helioseismology aboard SOHO, solar models are more and more constrained (Brun, Turck-Chieze and Morel 1998 (astro-ph/9806272)). New physical processes, mainly connected to macroscopic motions, must be introduced to understand these new observations. In this poster, we present solar models including a turbulent pressure in the outer layers and mixing due to the tachocline (Spiegel and Zahn 1992). Our results lead us to conclude that: - Turbulent pressure improves the absolute value of the acoustic mode frequencies (~ 10 microHz at 4mHz), - Mixing in a tachocline thick…
We present results from an investigation of the dynamical behavior of buoyant magnetic flux rings in the radiative interior of a uniformly rotating early-type star. Our physical model describes a thin, axisymmetric, toroidal flux tube that is released from the outer boundary of the convective core, and is acted upon by buoyant, centrifugal, Coriolis, magnetic tension, and aerodynamic drag forces. We find that rings emitted in the equatorial plane can attain a stationary equilibrium state that is stable with respect to small displacements in radius, but is unstable when perturbed in the meridio…
We have analyzed changes in the acoustic oscillation eigenfrequencies measured over the past 7 years by the GONG, MDI and LOWL instruments. The observations span the period from 1994 to 2001 that corresponds to half a solar cycle, from minimum to maximum solar activity. These data were inverted to look for a signature of the activity cycle on the solar stratification. A one-dimensional structure inversion was carried out to map the temporal variation of the radial distribution of the sound speed at the boundary between the radiative and convective zones. Such variation could indicate the prese…
Gravity modes are the best probes to infer the properties of the solar radiative zone that represents 98% of the Sun's total mass. It is usually assumed that high-frequency g modes give information about the structure of the solar interior whereas low-frequency g modes are more sensitive to the solar dynamics (the internal rotation). In this work, we develop a new methodology, based on the analysis of the almost constant separation of the dipole gravity modes, to introduce new constraints on the solar models. To validate this analysis procedure, several solar models -- including different phys…
We present preliminary results of 2D radiative modelling of He I lines in solar prominences, using a new numerical code developed by us (Leger, Chevallier and Paletou 2007). It treats self-consistently the radiation transfer and the non-LTE statistical equilibrium of H and, in a second stage, the one of He using a detailed atomic model. Preliminary comparisons with new visible plus near-infrared observations made at high spectral resolution with THeMIS are very satisfactory.
Element settling inside the Sun now becomes detectable from the comparison of the observed oscillation modes with the results of the theoretical models. This settling is due, not only to gravitation, but also to thermal diffusion and radiative acceleration (although this last effect is small compared to the two others). It leads to abundance variations of helium and heavy elements of $\cong 10%$ below the convective zone. Although not observable from spectroscopy, such variations lead to non-negligible modifications of the solar internal structure and evolution. Helioseismology is a powerful t…
The effects of radiative energy exchange on the convective instability of a weak field magnetic structure, which lead to a prediction and a physical explanation of the magnetic flux dependent field strength, are examined in detail using a real model stratification for the photospheric and convection zone structure of the Sun. Adopting the generalised Eddington approximation for the radiative transfer, which is valid both in the optically thick and the thin limits, we model the lateral radiative energy exchange by the tube with the external medium with a self-consistent inclusion of vertical ra…
We suggest that the observed long-period Alfv{é}n waves in the solar wind may be generated in the solar interior due to the pulsation of the Sun in the fundamental radial mode. The period of this pulsation is about 1 hour. The pulsation causes a periodical variation of density and large-scale magnetic field, this affecting the Alfv{é}n speed in the solar interior. Consequently the Alfv{é}n waves with the half frequency of pulsation (i.e. with the double period) can be parametrically amplified in the interior below the convection zone due to the recently suggested swing wave-wave interaction. T…
The difference in the adiabatic gradient gamma_1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft d…
This is the first paper in a series that deals with solar-physics applications of the equation-of-state formalism based on the formulation of the so-called "Feynman-Kac (FK) representation". Here, the FK equation of state is presented and adapted for solar applications. Its domain of validity is assessed. The practical application to the Sun will be dealt with in Paper II. Paper III will extend the current FK formalism to a higher order. Use of the FK equation of state is limited to physical conditions for which more than 90% of helium is ionized. This incudes the inner region of the Sun out t…
The internal gravity waves of low frequency which are emitted at the base of the solar convection zone are able to extract angular momentum from the radiative interior. We evaluate this transport with some simplifying assumptions: we ignore the Coriolis force, approximate the spectrum of turbulent convection by the Kolmogorov law, and couple this turbulence to the internal waves through their pressure fluctuations, following Press (1981) and Garcia Lopez & Spruit (1991). The local frequency of an internal wave varies with depth in a differentially rotating star, and it can vanish at some locat…
The primary inversion of the accurately measured frequencies of solar oscillations determines the mechanical properties of the Sun, i.e., the sound speed and density as a function of solar radius. In order to infer the temperature and hydrogen abundance profiles inside the Sun, it becomes necessary to use, in addition, the equations of thermal equilibrium along with the input physics, such as opacities, equation of state and nuclear reaction rates. It then becomes possible to estimate the effects of uncertainties in opacity and nuclear reaction rates on the inferred thermal and composition pro…
The solar interior has been scrutinized by two different and independent probes during the last twenty years with important revisions of the solar model, including a recent heavy element abundance revision. Today, we get a quantitatively coherent picture (even incomplete) of the solar (stellar) radiative zones. In this review, we recall the clues for solar gravitational settling definitively established by the seismic determination of the photospheric helium content. We comment also on the need for mixing in the transition region between radiation and convection in the case of the Sun and of p…
We re-examine the sensitivity of solar neutrino oscillations to noise in the solar interior using the best current estimates of neutrino properties. Our results show that the measurement of neutrino properties at KamLAND provides new information about fluctuations in the solar environment on scales to which standard helioseismic constraints are largely insensitive. We also show how the determination of neutrino oscillation parameters from a combined fit of KamLAND and solar data depends strongly on the magnitude of solar density fluctuations. We argue that a resonance between helioseismic and …
The role of carbon monoxide as a cooling agent for the thermal structure of the mid-photospheric to low-chromospheric layers of the solar atmosphere in internetwork regions is investigated. The treatment of radiative cooling via spectral lines of carbon monoxide (CO) has been added to the radiation chemo-hydrodynamics code CO5BOLD. [...] The CO opacity indeed causes additional cooling at the fronts of propagating shock waves in the chromosphere. There, the time-dependent approach results in a higher CO number density compared to the equilibrium case and hence in a larger net radiative cooling …
The solar magnetism is no more considered as a purely superficial phenomenon. The SoHO community has shown that the length of the solar cycle depends on the transition region between radiation and convection. Nevertheless, the internal solar (stellar) magnetism stays poorly known. Starting in 2008, the American instrument HMI/SDO and the European microsatellite PICARD will enrich our view of the Sun-Earth relationship. Thus obtaining a complete MHD solar picture is a clear objective for the next decades and it requires complementary observations of the dynamics of the radiative zone. For that …
The diagnosis of new high-resolution spectropolarimetric observations of solar prominences made in the visible and near-infrared mainly, requires a radiative modelling taking into account for both multi-dimensional geometry and complex atomic models. Hereafter we contribute to the improvement of the diagnosis based on the observation of He I multiplets, by considering 2D non-LTE unpolarized radiation transfer, and taking also into account the atomic fine structure of helium. It is an improvement and a direct application of the multi-grid Gauss-Seidel/SOR iterative scheme in 2D cartesian geomet…
The GOLFNG (Global Oscillations at Low Frequency New Generation) instrument is devoted to the search for solar gravity and acoustic modes, and also chromospheric modes from space. This instrument which is a successor to GOLF/SOHO will contribute to improve our knowledge of the dynamics of the solar radiative zone. It is a 15 points resonant scattering spectrometer, working on the D1 sodium line. A ground-based prototype is under construction to validate the difficult issues. It will be installed at the Teide Observatory, on Tenerife in 2006 to analyse the separation of the effects of the magne…
Meridional flows with velocities of a few meters per second are observed in the uppermost regions of the solar convection zone. The amplitude and pattern of the flows deeper in the solar interior, in particular near the top of the radiative region, are of crucial importance to a wide range of solar magnetohydrodynamical processes. In this paper, we provide a systematic study of the penetration of large-scale meridional flows from the convection zone into the radiative zone. In particular, we study the effects of the assumed boundary conditions applied at the convective-radiative interface on t…
Although 98% of the solar material consists of hydrogen and helium, the remaining chemical elements contribute in a discernible way to the thermodynamic quantities. The contribution of various heavy elements in a set of thermodynamic quantities has been examined. It has emerged that prominent signatures of individual elements exist, and that these effects are greatest in the ionization zones, typically located near the bottom of the convection zone. The main result is that part of the features found here depend strongly both on the given species (atom or ion) and its detailed internal partitio…
We derive expectations for signatures in the measured travel times of waves that interact with thermal anomalies and jets. A series of numerical experiments that involve the dynamic linear evolution of an acoustic wave field in a solar-like stratified spherical shell in the presence of fully 3D time-stationary perturbations are performed. The imprints of these interactions are observed as shifts in wave travel times, which are extracted from these data through methods of time-distance helioseismology \citep{duvall}. In situations where at least one of the spatial dimensions of the scatterer wa…
Mass-fractionation enriches light elements and the lighter isotopes of each element at the solar surface, making a photosphere that is 91 percent H and 9 percent He. The solar interior consists mostly of elements that comprise 99 percent of ordinary meteorites (Fe, O, Ni, Si, S, Mg and Ca) elements made in the deep interior of a supernova. Solar energy arises from a series of nuclear reactions triggered by neutron-emission from the collapsed supernova core on which the Sun formed. Solar mass-fractionation, solar neutrinos, and the annual solar-wind outpouring of 3 E43 H atoms from the solar su…
Modeling the variability of the solar spectral irradiance is a key factor for understanding the solar influence on the climate of the Earth. As a first step to calculating the solar spectral irradiance variations we reproduce the solar spectrum for the quiet Sun over a broad wavelength range with an emphasis on the UV. We introduce the radiative transfer code COSI which calculates solar synthetic spectra under conditions of non-local thermodynamic equilibrium (NLTE). A self-consistent simultaneous solution of the radiative transfer and the statistical equation for the level populations guarant…
We present results from numerical modeling of emerging flux regions on the solar surface. The modeling was carried out by means of 3D radiative MHD simulations of the rise of buoyant magnetic flux tubes through the convection zone and into the photosphere. Due to the strong stratification of the convection zone, the rise results in a lateral expansion of the tube into a magnetic sheet, which acts as a reservoir for small-scale flux emergence events at the scale of granulation. The interaction of the convective downflows and the rising magnetic flux undulates it to form serpentine field lines e…
We evaluate the logarithmic derivative of the depth of the solar convective zone with respect to the logarithm of the radiative opacity. We use this expression to show that the radiative opacity near the base of the solar convective zone (CZ) must be known to an accuracy of +- 1% in order to calculate the CZ depth to the accuracy of the helioseismological measurement, R(CZ) = (0.713 +- 0.001)R(Sun). The radiative opacity near the base of the CZ that is obtained from OPAL tables must be increased by about 21% in the Bahcall-Pinsonneault (2004) solar model if one wants to invoke opacity errors i…
Helioseismology has provided very detailed inferences about rotation of the solar interior. Within the convection zone the rotation rate roughly shares the latitudinal variation seen in the surface differential rotation. The transition to the nearly uniformly rotating radiative interior takes place in a narrow tachocline, which is likely important to the operation of the solar magnetic cycle.The convection-zone rotation displays zonal flows, regions of slightly more rapid and slow rotation, extending over much of the depth of the convection zone and converging towards the equator as the solar …
We update the best constraints on fluctuations in the solar medium deep within the solar Radiative Zone to include the new SNO-salt solar neutrino measurements. We find that these new measurements are now sufficiently precise that neutrino oscillation parameters can be inferred independently of any assumptions about fluctuation properties. Constraints on fluctuations are also improved, with amplitudes of 5% now excluded at the 99% confidence level for correlation lengths in the range of several hundred km. Because they are sensitive to correlation lengths which are so short, these solar neutri…
The nuclear reaction e + He3 + He4 ---> e + Be7 is considered at thermonuclear energies. The motion of the electron is treated within the adiabatic approximation and the He3-He4 scattering state is calculated using an effective He3-He4 potential constructed via the Marchenko inverse scattering method. The reaction rate thus obtained for solar interior conditions is approximately 10^{-4} of the corresponding rate for the radiative capture He3 + He4 ----> Be7 + gamma. However, at the conditions corresponding to the early stages of the primordial nucleosynthesis, the non-radiative fusion is five …
It is shown that in the presence of a background magnetic field within solar interior a cavity for low frequency MHD eigen modes (with periods 1-10 days) near equatorial plane can arise. The lower boundary of the cavity coincides with the centre of the Sun while the upper one corresponds to the Alfven resonant layer where high accumulation of wave energy takes place. The localization and the width of the Alfven resonance layer are determined by: (i) the node number of eigen modes n = 1, 2,..., (ii) by the angle of oblique propagation of waves with respect to the magnetic field, and (iii) by a …
We derive a self similar solution for the propagation of an extreme relativistic (or Newtonian) radiative spherical blast wave into a surrounding cold medium. The solution is obtained under the assumption that the radiation process is fast, it takes place only in the vicinity of the shock and that it radiates away a fixed fraction of the energy generated by the shock. In the Newtonian regime these solutions generalize the Sedov-Taylor adiabatic solution and the pressure-driven fully radiative solution. In the extreme relativistic case these solutions generalize the Blandford-McKee adiabatic so…
Precise numerical standard solar models (SSMs) now agree with one another and with helioseismological observations in the convective and outer radiative zones. Nevertheless these models obscure how luminosity, neutrino production and g-mode core helioseismology depend on such inputs as opacity and nuclear cross sections. Although the Sun is not homologous, its inner core by itself is chemically evolved and almost homologous, because of its compactness, radiative energy transport, and ppI-dominated luminosity production. We apply luminosity-fixed homology transformations to the core to estimate…
We consider a generalized model of seismic-wave propagation that takes into account the effect of a central magnetic field in the Sun. We determine the g-mode spectrum in the perturbative magnetic field limit using a one-dimensional Magneto-Hydrodynamics (MHD) picture. We show that central magnetic fields of about 600-800 kG can displace the pure g-mode frequencies by about 1%, as hinted by the helioseismic interpretation of GOLF observations.
We reexamine the transition magnetic moment solution to the solar neutrino problem. We argue that the absence of large time variations in the Super-Kamiokande rate provides strong evidence against spin-flavor flip in the solar convective zone. Spin-flavor flip could, however, occur in the primordial magnetic field in the radiative zone. We compute the longest lived toroidal mode for this field and show that spin-flavor flip in the radiative zone can account for all available solar data.
We show that in weakly non-ideal plasmas, like the solar interior, both non-extensivity and quantum uncertainty (a' la Galitskii and Yakimets) should be taken into account to derive equilibrium ion distribution functions and to estimate nuclear reaction rates and solar neutrino fluxes.
