Solar Cycle Variations of Rotation and Asphericity in the Near-Surface Shear Layer

The precise shape of the Sun is sensitive to the influence of gravity, differential rotation, local turbulence and magnetic fields. It has been previously shown that the solar shape exhibits asphericity that evolves with the 11-year cycle. Thanks to the capability of the SoHO/MDI and SDO/HMI instruments to observe with an unprecedented accuracy the surface gravity oscillation (f) modes, it is possible to extract information concerning the coefficients of rotational frequency splitting, a1, a3 and a5, that measure the differential rotation, together with the a2, a4 and a6 asphericity coefficients. Analysis of these helioseismology data for almost two solar cycles, from 1996 to 2017, reveals a close correlation of the a1 and a5 coefficients with the solar activity, whilst a3 exhibits a long-term trend and a weak correlation in the current cycle indicating a substantial change of the global rotation, potentially associated with a long-term evolution of the solar cycles. Looking in more details, the asphericity coefficients, a2, a4 and a6 are more strongly associated with the solar cycle when applying a time lag of respectively 0.1, 1.6 and -1.6 years. The magnitude of a6-coefficient varies in phase with the sunspot number (SN), but its amplitude is ahead of the SN variation. The last measurements made in mid 2017 indicate that the magnitude of a6-coefficient has probably reached its minimum; therefore, the next solar minimum can be expected by the end of 2018 or in the beginning of 2019. The so-called seismic radius in the range of f-mode angular degree: l=137-299 exhibits a temporal variability in anti-phase with the solar activity; its relative value decreased by 2.3E-05 in Solar Cycle 23 and 1.7E-05 in Cycle 24. Such results will be useful for better understanding the physical mechanisms which act inside the Sun, and so, better constrain dynamo models for forecasting the solar cycles.Comment: 13 pages, 3 figures, to appear in Journal of Atmospheric and Solar-Terrestrial Physics (JASTP

The Sun Asphericities: Astrophysical Relevance

Of all the fundamental parameters of the Sun (diameter, mass, temperature...), the gravitational multipole moments (of degree l and order m) that determine the solar moments of inertia, are still poorly known. However, at the first order (l=2), the quadrupole moment is relevant to many astrophysical applications. It indeed contributes to the relativistic perihelion advance of planets, together with the post-Newtonian (PN) parameters; or to the precession of the orbital plane about the Sun polar axis, the latter being unaffected by the purely relativistic PN contribution. Hence, a precise knowledge of the quadrupole moment is necessary for accurate orbit determination, and alternatively, to obtain constraints on the PN parameters. Moreover, the successive gravitational multipole moments have a physical meaning: they describe deviations from a purely spherical mass distribution. Thus, their precise determination gives indications on the solar internal structure. Here, we explain why it is difficult to compute these parameters, how to derive the best values, and how they will be determined in a near future by means of space experiments.Comment: 14 pages, 9 figures (see published version for a better resolution), submited to Proceedings of the Royal Society: Mathematical, Physical and Engineering Science

Solar latitudinal distortions : from observations to theory

Astronomy and Astrophysics, v. 419, p. 1133-1140, 2004. http://dx.doi.org/10.1051/0004-6361:20041093International audienceSolar diameters have been measured from different ground-based instruments on different sites all around the world. There are values dating back to three centuries ago, but the revival of interest began in the 1970s when it was claimed that a temporal periodic modulation had been found. The interest of such measurements, pinpointed from only two decades, may not lie in these temporal variations, but in the fact that a latitudinal heliographic dependence may exist. Such a solar shape distortion has been deduced from the analysis of solar astrolabe data sorted by heliographic latitudes, but observational evidence has also been obtained by means of a scanning heliometer (Pic du Midi Observatory). Latitudinal dependence implies sub-surfacic physical mechanisms and can be explained theoretically. Thus, in spite of the fact that ground-based observations are altered by seeing effects that may amplify or superimpose noise, it can be advanced that the solar shape is not a pure spheroid. We present here a new theory based upon the thermal-wind equation, which explains the observed distorted solar shape. Using the W parameter (called here asphericity-luminosity parameter), we show that large negative values (W ranging from around −0.075 up to −0.6) leading to a prolate Sun, are unlikely. The best range of W lies between around −0.075 and +0.6. Concerning observations, only space missions (or balloon flights) will be able to reach a clear conclusion. A space mission called PICARD is scheduled to be launched by 2008: one of its major aims is to measure these asphericities with astrometric precision

Active Latitude Oscillations Observed on the Sun

We investigate periodicities in mean heliographic latitudes of sunspot groups, called active latitudes, for the last six complete solar cycles (1945-2008). For this purpose, the Multi Taper Method and Morlet Wavelet analysis methods were used. We found the following: 1) Solar rotation periodicities (26-38 days) are present in active latitudes of both hemispheres for all the investigated cycles (18 to 23). 2) Both in the northern and southern hemispheres, active latitudes drifted towards the equator starting from the beginning to the end of each cycle by following an oscillating path. These motions are well described by a second order polynomial. 3) There are no meaningful periods between 55 and about 300 days in either hemisphere for all cycles. 4) A 300 to 370 day periodicity appears in both hemispheres for Cycle 23, in the northern hemisphere for Cycle 20, and in the southern hemisphere for Cycle 18.Comment: Accepted for publication by Solar Physic

Solar gravitational energy and luminosity variations

Due to non-homogeneous mass distribution and non-uniform velocity rate inside the Sun, the solar outer shape is distorted in latitude. In this paper, we analyze the consequences of a temporal change in this figure on the luminosity. To do so, we use the Total Solar Irradiance (TSI) as an indicator of luminosity. Considering that most of the authors have explained the largest part of the TSI modulation with magnetic network (spots and faculae) but not the whole, we could set constraints on radius and effective temperature variations (dR, dT). However computations show that the amplitude of solar irradiance modulation is very sensitive to photospheric temperature variations. In order to understand discrepancies between our best fit and recent observations of Livingston et al. (2005), showing no effective surface temperature variation during the solar cycle, we investigated small effective temperature variation in irradiance modeling. We emphasized a phase-shift (correlated or anticorrelated radius and irradiance variations) in the (dR, dT)-parameter plane. We further obtained an upper limit on the amplitude of cyclic solar radius variations, deduced from the gravitational energy variations. Our estimate is consistent with both observations of the helioseismic radius through the analysis of f-mode frequencies and observations of the basal photospheric temperature at Kitt Peak. Finally, we suggest a mechanism to explain faint changes in the solar shape due to variation of magnetic pressure which modifies the granules size. This mechanism is supported by our estimate of the asphericity-luminosity parameter, which implies an effectiveness of convective heat transfer only in very outer layers of the Sun.Comment: 17 pages, 2 figure, 1 table, published in New Astronom

Are non-magnetic mechanisms such as temporal solar diameter variations conceivable for an irradiance variability?

Irradiance variability has been monitored from space for more than two decades. Even if data are coming from different sources, it is well established that a temporal variability exists which can be set to as approximately 0.1%, in phase with the solar cycle. Today, one of the best explanation for such an irradiance variability is provided by the evolution of the solar surface magnetic fields. But if some 90 to 95% can be reproduced, what would be the origin of the 10 to 5% left? Non magnetic effects are conceivable. In this paper we will consider temporal variations of the diameter of the Sun as a possible contributor for the remaining part. Such an approach imposes strong constraints on the solar radius variability. We will show that over a solar cycle, variations of no more than 20 mas of amplitude can be considered. Such a variability (far from what is reported by observers conducting measurements by means of ground-based solar astrolabes) may explain a little part of the irradiance changes not explained by magnetic features. Further requirements are needed that may help to reach a conclusion. Dedicated space missions are necessary (for example PICARD, GOLF-NG or SDO, scheduled for a launch around 2008); it is also proposed to reactivate SDS flights for such a purpose.Comment: 8 pages, 2 eps figures, published in Solar Physic