Context. Over the past 40 years, helioseismology has been enormously successful in the study of the solar interior. A shortcoming has been the lack of a convincing detection of the solar g modes, ...which are oscillations driven by gravity and are hidden in the deepest part of the solar body – its hydrogen-burning core. The detection of g modes is expected to dramatically improve our ability to model this core, the rotational characteristics of which have, until now, remained unknown. Aims. We present the identification of very low frequency g modes in the asymptotic regime and two important parameters that have long been waited for: the core rotation rate, and the asymptotic equidistant period spacing of these g modes. Methods. The GOLF instrument on board the SOHO space observatory has provided two decades of full-disk helioseismic data. The search for g modes in GOLF measurements has been extremely difficult because of solar and instrumental noise. In the present study, the p modes of the GOLF signal are analyzed differently: we search for possible collective frequency modulations that are produced by periodic changes in the deep solar structure. Such modulations provide access to only very low frequency g modes, thus allowing statistical methods to take advantage of their asymptotic properties. Results. For oscillatory periods in the range between 9 and nearly 48 h, almost 100 g modes of spherical harmonic degree 1 and more than 100 g modes of degree 2 are predicted. They are not observed individually, but when combined, they unambiguously provide their asymptotic period equidistance and rotational splittings, in excellent agreement with the requirements of the asymptotic approximations. When the period equidistance has been measured, all of the individual frequencies of each mode can be determined. Previously, p-mode helioseismology allowed the g-mode period equidistance parameter P0 to be bracketed inside a narrow range, between approximately 34 and 35 min. Here, P0 is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non-synodic reference with very high accuracy, and they imply a mean weighted rotation of 1277 ± 10 nHz (9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 ± 23 nHz (period of one week) of the solar core itself, which is a factor 3.8 ± 0.1 faster than the rotation of the radiative envelope. Conclusions. The g modes are known to be the keys to a better understanding of the structure and dynamics of the solar core. Their detection with these precise parameters will certainly stimulate a new era of research in this field.
Solar activity has significantly changed over the last two Schwabe cycles. After a long and deep minimum at the end of Cycle 23, the weaker activity of Cycle 24 contrasts with the previous cycles. In ...this work, the response of the solar acoustic oscillations to solar activity is used in order to provide insights into the structural and magnetic changes in the sub-surface layers of the Sun during this on-going unusual period of low activity. We analyze 18 yr of continuous observations of the solar acoustic oscillations collected by the Sun-as-a-star GOLF instrument on board the SoHO spacecraft. From the fitted mode frequencies, the temporal variability of the frequency shifts of the radial, dipolar, and quadrupolar modes are studied for different frequency ranges that are sensitive to different layers in the solar sub-surface interior. The low-frequency modes show nearly unchanged frequency shifts between Cycles 23 and 24, with a time evolving signature of the quasi-biennial oscillation, which is particularly visible for the quadrupole component revealing the presence of a complex magnetic structure. The modes at higher frequencies show frequency shifts that are 30% smaller during Cycle 24, which is in agreement with the decrease observed in the surface activity between Cycles 23 and 24. The analysis of 18 yr of GOLF oscillations indicates that the structural and magnetic changes responsible for the frequency shifts remained comparable between Cycle 23 and Cycle 24 in the deeper sub-surface layers below 1400 km as revealed by the low-frequency modes. The frequency shifts of the higher-frequency modes, sensitive to shallower regions, show that Cycle 24 is magnetically weaker in the upper layers of Sun.
We study the impact of a fossil magnetic field on the physical quantities which describe the structure of a young Sun of 500 Myr. We consider for the first time a non-force-free field composed of a ...mixture of poloidal and toroidal magnetic fields and propose a specific configuration to illustrate our purpose. In this paper, we estimate the relative role of the different terms which appear in the modified stellar structure equations. We note that the Lorentz tension plays a non-negligible role in addition to the magnetic pressure. This is interesting because most of the previous stellar evolution codes ignored that term and the geometry of the field. The solar structure perturbations are, as already known, small and consequently we have been able to estimate each term semi-analytically. We develop a general treatment to calculate the global modification of the structure and of the energetic balance. We also estimate the gravitational multipolar moments associated with the presence of a fossil large-scale magnetic field in radiative zone. The values given for the young Sun help the future implementation in stellar evolution codes. This work can be repeated for any other field configuration and prepares the achievement of a solar magnetohydrodynamic model where we will follow the transport of such field on secular time-scales and the associated transport of momentum and chemicals. The described method will be applied at the present Sun and the results will be compared with the coming balloon or space measurements.
Context. Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on ...rotation profiles. Aims. Our aim is to obtain seismic constraints on the internal transport and surface loss of the angular momentum of oscillating solar-like stars. To this end, we study the evolution of rotational splittings from the pre-main sequence to the red-giant branch for stochastically excited oscillation modes. Methods. We modified the evolutionary code CESAM2K to take rotationally induced transport in radiative zones into account. Linear rotational splittings were computed for a sequence of 1.3 M sub(middot in circle) models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. Results. We find that transport by meridional circulation and shear turbulence yields far too high a core rotation rate for red-giant models compared with recent seismic observations. We discuss several uncertainties in the physical description of stars that could have an impact on the rotation profiles. For instance, we find that the Goldreich-Schubert-Fricke instability does not extract enough angular momentum from the core to account for the discrepancy. In contrast, an increase of the horizontal turbulent viscosity by 2 orders of magnitude is able to significantly decrease the central rotation rate on the red-giant branch. Conclusions. Our results indicate that it is possible that the prescription for the horizontal turbulent viscosity largely underestimates its actual value or else a mechanism not included in current stellar models of low mass stars is needed to slow down the rotation in the radiative core of red-giant stars.
The Standard Solar Model (SSM) is an important reference in Astrophysics as the Sun stays today the most observed star. This model is used to predict the internal observables like neutrino fluxes and ...oscillation frequencies and consequently to validate its assumptions for its generalization to other stars. The model outputs result from the resolution of the classical stellar equations and the knowledge of fundamental physics like nuclear reaction rates, screening, photon interaction, plasma physics. The plasma conditions remained unmeasurable in laboratory for long due to the high temperature and high density conditions of the solar interior. Today, neutrino detections and helioseismology aboard SoHO have largely revealed the solar interior, in particular the nuclear solar core so one can estimate the reliability of SSM and also its coherence with the different indicators and between them. This has been possible thanks to a Seismic Solar Model (SeSM) which takes into account in addition the observed sound speed profile. Seismology quantifies also some internal dynamical processes that need to be properly introduced in the description of stars. This review describes the different steps of building of the SSM, its predictions and the comparisons with observations. It discusses the accuracy of such model compared to the accuracy of the SeSM. The noticed differences and observational constraints put some limits on other possible processes like dark matter, magnetic field or waves and determine the directions of progress for the near future that will come from precise emitted neutrino fluxes. High density laser facilities promise also unprecedented checks of energy transfer by photons and nuclear reaction rates.
ABSTRACT Seismic observations have led to doubts or ambiguities concerning the opacity calculations used in stellar physics. Here, we concentrate on the iron-group opacity peak, due to iron, nickel, ...and chromium, located around T = 200,000 K for densities from , which creates some convective layers in stellar radiative envelopes for masses between 3 and 18 . These conditions were extensively studied in the 1980s. More recently, inconsistencies between OP and OPAL opacity calculations have complicated the interpretation of seismic observations as the iron-group opacity peak excites acoustic and gravity modes in SPB, β Cephei, and sdB stars. We investigate the reliability of the theoretical opacity calculations using the modern opacity codes ATOMIC and SCO-RCG. We show their temperature and density dependence for conditions that are achievable in the laboratory and equivalent to astrophysical conditions. We also compare new theoretical opacity spectra with OP spectra and quantify how different approximations impact the Rosseland mean calculations.This detailed study estimates new ATOMIC and SCO-RCG Rosseland mean values for astrophysical conditions which we compare to OP values. Some puzzling questions are still under investigation for iron, but we find a strong increase in the Rosseland mean nickel opacity of a factor between 2 and 6 compared to OP. This appears to be due to the use of extrapolated atomic data for the Ni opacity within the OP calculations. A study on chromium is also shown.
We study the effects of different descriptions of the solar surface convection on the eigenfrequencies of p modes. 1D evolution calculations of the whole Sun and 3D hydrodynamic and ...magnetohydrodynamic simulations of the current surface are performed. These calculations rely on realistic physics. Averaged stratifications of the 3D simulations are introduced in the 1D solar evolution or in the structure models. The eigenfrequencies obtained are compared to those of 1D models relying on the usual phenomenologies of convection and to observations of the Michelson Doppler Imager instrument aboard the Solar Heliospheric Observatory (SoHO). We also investigate how the magnetic activity could change the eigenfrequencies and the solar radius, assuming that, 3 Mm below the surface, the upgoing plasma advects a 1.2 kG horizontal field. All models and observed eigenfrequencies are fairly close below 3 mHz. Above 3 mHz the eigenfrequencies of the phenomenological convection models are above the observed eigenfrequencies. The frequencies of the models based on the 3D simulations are slightly below the observed frequencies. Their maximum deviation is 3 μHz at 3 mHz but drops below 1 μHz at 4 mHz. Replacing the hydrodynamic by the magnetohydrodynamic simulation increases the eigenfrequencies. The shift is negligible below 2.2 mHz and then increases linearly with frequency to reach 1.7 μHz at 4 mHz. The impact of the simulated activity is a 14 mas shrinking of the solar layers near the optical depth unity.
The equator-to-pole radius difference (Δ
r
=
R
eq
−
R
pol
) is a fundamental property of our star, and understanding it will enrich future solar and stellar dynamical models. The solar oblateness (Δ
...⊙
) corresponds to the excess ratio of the equatorial solar radius (
R
eq
) to the polar radius (
R
pol
), which is of great interest for those working in relativity and different areas of solar physics. Δ
r
is known to be a rather small quantity, where a positive value of about 8 milli-arcseconds (mas) is suggested by previous measurements and predictions. The
Picard
space mission aimed to measure Δ
r
with a precision better than 0.5 mas. The
Solar Diameter Imager and Surface Mapper
(SODISM) onboard
Picard
was a Ritchey–Chrétien telescope that took images of the Sun at several wavelengths. The SODISM measurements of the solar shape were obtained during special roll maneuvers of the spacecraft by 30° steps. They have produced precise determinations of the solar oblateness at 782.2 nm. After correcting measurements for optical distortion and for instrument temperature trend, we found a solar equator-to-pole radius difference at 782.2 nm of 7.9±0.3 mas (5.7±0.2 km) at one
σ
. This measurement has been repeated several times during the first year of the space-borne observations, and we have not observed any correlation between oblateness and total solar irradiance variations.
The
Solar Diameter Imager and Surface Mapper
(SODISM) onboard the
Picard
space mission provides wide-field images of the photosphere and chromosphere of the Sun in five narrow bandpasses centered at ...215.0, 393.37, 535.7, 607.1, and 782.2 nm. The
Picard
spacecraft was successfully launched on 15 June 2010 into a Sun-synchronous dawn–dusk orbit. The
Picard
space mission represents a European asset in collecting solar observations useful to improve Earth climatic models. The scientific payload consists of the SODISM imager and of two radiometers,
SOlar VAriability Picard
(SOVAP) and
PREcision MOnitor Sensor
(PREMOS), which measure the Total Solar Irradiance (TSI) and part of the Solar Spectral Irradiance (SSI).
The SODISM telescope continuously monitors solar activity from the middle ultraviolet to the near infrared spectral ranges and produces solar images that feed SSI reconstruction models. Further, SODISM probes the solar interior
via
a helioseismic analysis of the solar disc and limb images at 535.7 nm, and
via
astrometric investigations at the limb. The latter allows us to deduce the spectral dependence of the solar limb profile, and the asphericity of the Sun. Furthermore, SODISM data taken during the transit of Venus allow a determination of the absolute value of the solar diameter. This paper provides a detailed description of the SODISM instrument, including thermo-optical analysis, its different modes of observation, and its first performance in space.
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