Evaluation of a Selected Case of the Minimum Dissipative Rate Method for Non-Force-Free Solar Magnetic Field Extrapolations

The minimum dissipative rate (MDR) method for deriving a coronal non-force-free magnetic field solution is partially evaluated. These magnetic field solutions employ a combination of three linear (constant-α) force-free-field solutions with one being a potential field (i.e., α=0). The particular case of the solutions where the other two α’s are of equal magnitude but of opposite sign is examined. This is motivated by studying the SOLIS (Synoptic Optical Long-term Investigation of the Sun (SOLIS), a National Solar Observatory facility) vector magnetograms of AR 10987, which show a global α value consistent with an α=0 value as evaluated by (∇×B) _z /B _z over the region. Typical of the current state of the observing technology, there is no definitive twist for input into the general MDR method. This suggests that the special α case, of two α’s with equal magnitudes and opposite signs, is appropriate given the data. Only for an extensively twisted active region does a dominant, nonzero α normally emerge from a distribution of local values. For a special set of conditions, is it found that (i) the resulting magnetic field is a vertically inflated magnetic field resulting from the electric currents being parallel to the photosphere, similar to the results of Gary and Alexander (Solar Phys. 186:123, 1999), and (ii) for α≈(α _max/2), the Lorentz force per unit volume normalized by the square of the magnetic field is on the order of 1.4×10⁻¹⁰ cm⁻¹. The Lorentz force (F _L) is a factor of ten higher than that of the magnetic force d(B ²/8π)/dz, a component of F _L. The calculated photospheric electric current densities are an order of magnitude smaller than the maximum observed in all active regions. Hence both the Lorentz force density and the generated electric current density seem to be physically consistent with possible solar dynamics. The results imply that the field could be inflated with an overpressure along the neutral line. However, the implementation of this or any other extrapolation method using the electric current density as a lower boundary condition must be done cautiously, with the current magnetography.     

Helicity Patterns of the Active Regions Connected by Transequatorial Loops

Using photospheric vector magnetograms of the Huairou Solar Observing Station and coronal X-ray images from the Yohkoh Soft X-Ray Telescope, we calculate the helicity patterns of 43 pairs of active regions and the chirality of 50 pairs of opposite magnetic polarity regions that are connected by transequatorial loops (TLs). To make the results more convincing, two helicity proxies including the local current helicity h _c and the force-free factor α _best are computed. The results, which are similar for both parameters, are as follows: (1) Current helicity of the active regions pairs connected by transequatorial loops have no obvious regularity: About 50% of the active region pairs carry the same current helicity sign and about 50% of them have the opposite. (2) If we consider the magnetic polarity pairs connected by the TLs, the result is almost the same as that for the active region pairs, with a little more than half of them showing the same chirality. We also make linear force-free extrapolations for 33 TLs and determine their force-free parameter α by comparing extrapolated field lines to X-ray images of the TLs. Out of the 19 cases when the footpoints of the TLs have the same current helicity sign, we find that the sign of α of the TLs is the same as the sign of the current helicity in the footpoints in 12 cases, whereas it is of opposite sign in 4 cases, and in 3 cases the TLs were found to be potential.     

Constraining the cosmological time variation of the fine - structure constant

The variation of the fine-structure constant α = e ² / ħc can be probed by comparing the wavelength of atomic transitions from the redshift of quasars in the Universe and laboratory over cosmological time scales t ~ 10¹⁰ yr. After a careful selection of pairs of lines, the Thong method with a derived analytical expression for the error analysis was applied to compute the α variation. We report a new constraint on the variation of the fine-structure constant based on the analysis of the C_IV, N_V, Mg_II, Al_III, and Si_IV doublet absorption lines. The weighted mean value of the variation in α derived from our analysis over the redshift range 0.4939 ≤ z ≤ 3.7 is = ( 0.09 ± 0.07)×10⁻⁵. This result is three orders of magnitude better than the results obtained by earlier analysis of the same data on the constraint on Δα/α .     

Radio, Hard X-Ray, EUV and Optical Study of September 9, 2002 Solar Flare

The multi-wavelength analysis is performed on a flare on September 9, 2002 with data of Owens Valley Solar Arrays (OVSA), Big Bear Solar Observatory (BBSO), Ramaty High Energy Solar Spectroscopic Imager (RHESSI), and Extreme UV Imager Telescope (EIT), and The Michelson Doppler Imager (MDI) on board of the Solar and Heliospheric Observatory (SOHO). The radio sources at 4.8 and 6.2 GHz located in the intersection of two flaring loops at 195 of SOHO/EIT respectively with two dipole magnetic fields of SOHO/MDI, in which one EIT loop was coincident with an X-ray loop of RHESSI at 12–25 keV, and two H_αbright kernels a1 and a2 of BBSO, respectively at the two footpoints of this loop; the second EIT loop connected another two H_αkernels b1 and b2 and radio sources at 7.8 and 8.2 GHz of OVSA. The maximum phase of microwave bursts was evidently later than that of hard X-ray bursts and H_αkernels a1 and a2, but consistent with that of H_αkernels b1 and b2. Moreover, the flare may be triggered by the interaction of the two flaring loops, which is suggested by the cross-correlation of radio, optical, and X-ray light curves of a common quasi-periodic oscillation in the rising phase, as well as two peaks at about 7 and 9 GHz of the microwave spectra at the peak times of the oscillation, while the bi-directional time delays at two reversal frequencies respectively at 7.8 and 9.4 GHz (similar to the peak frequencies of the microwave spectra) may indicate two reconnection sites at different coronal levels. The microwave and hard X-ray footpoint sources located in different EUV and optical loops may be explained by different magnetic field strength and the pitch angle distribution of nonthermal electrons in these two loops.     

Counterstreaming in a Large Polar Crown Filament

The motion of small-scale structures is well resolved in high-resolution filament images that were observed on 19 June 1998 with the Swedish Vacuum Solar Telescope, La Palma. The filament was between 80 000 and 100 000 km high. The study is based on two hours of narrow-band observations at three wavelength positions in Hα. Velocities along the line of sight and in the transverse direction, respectively, V _los and V _tr, were measured for a large number of individual small-scale filament structures. Small features are all moving along nearly parallel threads, some in one direction along the threads and the remainder in the other direction, a pattern of motion known as counterstreaming. The net flow velocities in the two directions are about 8 km s⁻¹ and both are tilted by an angle δ≃16° relative to the plane of the sky. This angle is less than expected, by factors between 2.0 and 2.5, relative to the local horizontal plane. We believe that V _los is underestimated by these factors due to a line-shift reducing effect by the underlying Hα absorption line of the chromosphere. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1026150809598     

Cosmic behavior, statefinder diagnostic and w?w′ analysis for?interacting new agegraphic dark energy model in non-flat universe

We investigate the interacting NADE model in non-flat universe. The effects of spatial curvature Ω _k , interaction coefficient α and the main parameter of NADE, n, on EoS parameter w _d and deceleration parameter q are studied. We obtain a minimum value for n in both early and present time, in order to that our DE model crosses the phantom divide. Also in a closed universe, changing the sign of q is strongly dependent on α. It has been shown that the quantities w _d and q have a different treatment for various spatial curvature. At last, we calculate the statefinder diagnostic and w−w ^′ analysis in non flat universe. In non flat universe, the statefinder trajectories are discriminated by both n and α.     

Shear-free homogeneous cosmological model with heat flux

We present the condition of vanishing shear in a spatially homogeneous spacetime in terms of the Ricci rotation co-efficients corresponding to an orthonormal tetrad (ν ^α. _A η ^α) (whereν ^α is the unit vector along the time axis and _A η ^α are the three independent reciprocal group vectors). Assuming that the velocity vector can be expanded in the direction ofν ^α and any one of the _A η ^α’s it is shown that shear-free motion is possible only in case of some special Bianchi types, and these cases are studied assuming the velocity vector to be geodetic and that there may be a nonvanishing heat flux term.     

Analysis of the properties of galaxy clusters in the Leo supercluster region

We analyze the properties of galaxy clusters in the region of the Leo supercluster using observational data from the SDSS and 2MASS catalogs. We have selected 14 galaxy clusters with a total dynamical mass of 1.77 × 10¹⁵ M _⊙ in the supercluster region 130 by 60 Mpc in the plane of the sky (z ≃ 0.037). The composite luminosity function of the supercluster is described by a Schechter function with parameters that, within the error limits, correspond to field galaxies and does not differ from the luminosity function of the richer Ursa Major (UMa) supercluster for the same luminosity range (the bright end). The luminosity functions of early-type and late-type galaxies in Leo at the faint end are characterized by a sharp decrease (α = −0.60±0.08) and a steep increase (α = −1.44± 0.10) in the number of galaxies, respectively. In the virialized cluster regions, the fraction of early-type galaxies selected by the u-r color, bulge contribution, and concentration index among the galaxies brighter than M _K ^* + 1 is, on average, 62%. This fraction is smaller than that in the UMa supercluster at a 2–3σ level. The near-infrared luminosities of galaxy clusters down to a fixed absolute magnitude correlate with their masses almost in the same way as for other samples of galaxy clusters (L _200,K ∝ M ₂₀₀^0.63±0.11)).     

Comparison of long-term trend of solar radius with sunspot activity and flare index

Results are presented from a study of solar radius measurements taken with the solar astrolabe at the TUBITAK National Observatory (TUG) over seven years, 2001–2007. The data series with standard deviation of 0.35 arcsec shows the long-term variational trend with 0.04 arcsec/year. On the other hand, the data series of solar radius are compared with the data of sunspot activity and H-α flare index for the same period. Over the seven year trend, we have found significant linear anti-correlations between the solar radius and other indicators such as sunspot numbers, sunspot areas, and H-α flare index. While the solar radius displays the strongest anti-correlation (−0.7676) with sunspot numbers, it shows a significant anti-correlation of −0.6365 with sunspot areas. But, the anti-correlation between the solar radius and H-α flare index is found to be −0.4975, slightly lower than others. In addition, we computed Hurst exponent of the data sets ranging between 0.7214 and 0.7996, exhibiting the persistent behavior for the long term trend. In the light of the strong correlations with high significance, we may suggest that there are a causal relationship between the solar radius and solar time series such as sunspot activity and H-α flare index.     

STEREO SECCHI COR1-A/B Intercalibration at 180° Separation

The twin Solar Terrestrial Relations Observatory (STEREO) spacecraft reached a separation angle of 180° on 6 February 2011. This provided a unique opportunity to test the intercalibration between the Sun–Earth Connection Coronal and Heliospheric Investigation (SECCHI) telescopes on both spacecraft for areas above the limb. So long as the corona is optically thin, at 180° separation each spacecraft sees the same corona from opposite directions. Thus, the data should appear as mirror images of each other. We report here on the results of the comparison of the images taken by the inner coronagraph (COR1) on the STEREO-Ahead and -Behind spacecraft in the hours when the separation was close to 180°. We find that the intensity values seen by the two telescopes agree with each other to a high degree of accuracy. This validates both the radiometric intercalibration between the COR1 telescopes, and the method used to remove instrumental background from the images. The relative error between COR1-A and COR1-B is found to be less than 10⁻⁹ B/B _⊙ over most of the field-of-view, growing to a few ×10⁻⁹ B/B _⊙ for the brighter pixels near the edge of the occulter. The primary source of error is the background determination. We also report on the analysis of star observations which show that the absolute radiometric calibration of either COR1 telescope has not changed significantly since launch.     

On most general exact solution for Vaidya-Tikekar isentropicsuperdense star

The energy density of Vaidya-Tikekar isentropic superdense star is found to be decreasing away from the center, only if the parameter K is negative. The most general exact solution for the star is derived for all negative values of K in terms of circular and inverse circular functions. Which can further be expressed in terms of algebraic functions for K = 2-(n/δ)² < 0 (n being integer andδ = 1,2,3 4). The energy conditions 0 ≤ p ≤ αρc ², (α = 1 or 1/3) and adiabatic sound speed conditiondp dρ ≤ c ², when applied at the center and at the boundary, restricted the parameters K and α such that .18 < −K −2287 and.004 ≤ α ≤ .86. The maximum mass of the star satisfying the strong energy condition (SEC), (α = 1/3) is found to be3.82 Mq_· at K=−2/3, while the same for the weak energy condition (WEC), (α =1) is 4.57 M_ _⊙ atK=−>5/2. In each case the surface density is assumed to be 2 × 10¹⁴ gm cm^-3. The solutions corresponding to K>0 (in fact K>1) are also made meaningful by considering the hypersurfaces t= constant as 3-hyperboloid by replacing the parameter R ² by −R² in Vaidya-Tikekar formalism. The solutions for the later case are also expressible in terms of algebraic functions for K=2-(n/δ² > 1 (n being integer or zero and δ =1,2,3 4). The cases for which 0 < K < 1 do not possess negative energy density gradient and therefore are incapable of representing any physically plausible star model. In totality the article provides all the physically plausible exact solutions for the Buchdahl static perfect fluid spheres. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeled soft X-ray solar irradiances

Solar soft X-rays have historically been inaccurately modeled in both relative variations and absolute magnitudes by empirical solar extreme ultraviolet (EUV) irradiance models. This is a result of the use of a limited number of rocket data sets which were primarily associated with the calibration of the AE-E satellite EUV data set. In this work, the EUV91 solar EUV irradiance model has been upgraded to improve the accuracy of the 3.0 to 5.0 nm relative irradiance variations. The absolute magnitude estimate of the flux in this wavelength range has also been revised upwards. The upgrade was accomplished by first digitizing the SOLRAD 11 satellite 4.4 to 6.0 nm measured energy flux data set, then extracting and extrapolating a derived 3.0 to 5.0 nm photon flux from these data, and finally by performing a correlation between these derived data and the daily and 81-day mean 10.7 cm radio flux emission using a multiple linear regression technique. A correlation coefficient of greater than 0.9 was obtained between the dependent and independent data sets. The derived and modeled 3.0 to 5.0 nm flux varies by more than an order of magnitude over a solar cycle, ranging from a flux below 1×10⁸ to a flux greater than 1×10⁹ photons cm^–2 s^–1. Solar rotational (27-day) variations in the flux magnitude are a factor of 2. The derived and modeled irradiance absolute values are an order of magnitude greater than previous values from rocket data sets related to the calibration of the AE-E satellite.     

Optical imaging and spectroscopic observation of the galactic supernova remnant G85.9-0.6

Optical CCD imaging with Hα and [SII] filters and spectroscopic observations of the galactic supernova remnant G85.9-0.6 have been performed for the first time. The CCD image data are taken with the 1.5 m Russian-Turkish Telescope (RTT150) at TüBİTAK National Observatory (TUG) and spectral data are taken with the Bok 2.3 m telescope on Kitt Peak, AZ. The images are taken with narrow-band interference filters Hα, [SII] and their continuum. [SII]/Hα ratio image is performed. The ratio obtained from [SII]/Hα is found to be ∼0.42, indicating that the remnant interacts with HII regions. G85.9-0.6 shows diffuse-shell morphology. [SII]λ λ6716/6731 average flux ratio is calculated from the spectra, and the electron density N _e is obtained to be 395 cm⁻³. From [OIII]/Hβ ratio, shock velocity has been estimated, pre-shock density of n _c =14 cm⁻³, explosion energy of E=9.2×10⁵⁰ ergs, interstellar extinction of E(B−V)=0.28, and neutral hydrogen column density of N(HI)=1.53×10²¹ cm⁻² are reported.     

A New Forecasting Index for Solar Wind Velocity Based on EIT 284 Å Observations

Various solar wind forecasting methods have been developed during the past decade, such as the Wang?–?Sheeley model and the Hakamada?–?Akasofu?–?Fry Version 2 (HAFv2) model. Also, considerable correlation has been found between the solar wind speed v and the coronal hole (CH) area A _M on the visible side of the Sun, showing quantitative improvement of forecasting accuracy in low CME activity periods (e.g., Vr?nak, Temmer, and Veronig, Solar Phys. 240, 315, 2007a). Properties of lower layers of the solar atmosphere are good indications of the subsequent interplanetary and geomagnetic activities. We analyze the SOHO/EIT 284 Å images and construct a new forecasting factor (Pch) from the brightness of the solar EUV emission, and a good correlation is found between the Pch factor and the 3-day-lag solar wind velocity (v) probed by the ACE spacecraft. The main difference between the Pch and A _M factor is that Pch does not depend on the CH-boundary estimate and can reflect both the area and brightness of CH. A simple method of forecasting the solar wind speed near Earth in low CME activity periods is presented. Between Pch and v from 21 November until 26 December 2003, the linear correlation coefficient is R=0.89. For comparison we also analyze the data in the same period (DOY 25?–?125, 2005) as Vr?nak, Temmer, and Veronig (Solar Phys. 240, 315, 2007a), who used the CH areas A _M for predicting the solar wind parameters. In this period the correlation coefficient between Pch and v is R=0.70, whereas for A _M and v the correlation coefficient is R=0.62. The average relative difference between the calculated and the observed values is $\overline{|\delta|}\approx 12.15\%Various solar wind forecasting methods have been developed during the past decade, such as the Wang – Sheeley model and the Hakamada – Akasofu – Fry Version 2 (HAFv2) model. Also, considerable correlation has been found between the solar wind speed v and the coronal hole (CH) area A _M on the visible side of the Sun, showing quantitative improvement of forecasting accuracy in low CME activity periods (e.g., Vršnak, Temmer, and Veronig, Solar Phys. 240, 315, 2007a). Properties of lower layers of the solar atmosphere are good indications of the subsequent interplanetary and geomagnetic activities. We analyze the SOHO/EIT 284 ? images and construct a new forecasting factor (Pch) from the brightness of the solar EUV emission, and a good correlation is found between the Pch factor and the 3-day-lag solar wind velocity (v) probed by the ACE spacecraft. The main difference between the Pch and A _M factor is that Pch does not depend on the CH-boundary estimate and can reflect both the area and brightness of CH. A simple method of forecasting the solar wind speed near Earth in low CME activity periods is presented. Between Pch and v from 21 November until 26 December 2003, the linear correlation coefficient is R=0.89. For comparison we also analyze the data in the same period (DOY 25 – 125, 2005) as Vršnak, Temmer, and Veronig (Solar Phys. 240, 315, 2007a), who used the CH areas A _M for predicting the solar wind parameters. In this period the correlation coefficient between Pch and v is R=0.70, whereas for A _M and v the correlation coefficient is R=0.62. The average relative difference between the calculated and the observed values is . Furthermore, for the ten peaks during the analysis period, Pch and v show a correlation coefficient of R=0.78, and the average relative difference between the calculated and the observed peak values is . Moreover, the Pch factor can eliminate personal bias in the forecasting process, which existed in the method using CH area as input parameter, because CH area depends on the CH-boundary estimate but Pch does not. Until now the CH-boundary could not be easily determined since no quantitative criteria can be used to precisely locate CHs from observations, which led to differences in forecasting accuracy.     

Molecular systems in a strong magnetic field

Brief overview of one-two electron molecular systems made out of protons and/or α-particles in a strong magnetic field B≤4.414×10¹³ G is presented. A particular emphasis is given to the one-electron exotic ions H₃⁺⁺(pppe), He₂³⁺(α α e) and to two-electron ionsH₃⁺(pppee), He₂⁺⁺(α α ee). Quantitative studies in a strong magnetic field are very complicated technically. Novel approach to the few-electron Coulomb systems in magnetic field, which provides accurate results, based on variational calculus with physically relevant trial functions is briefly described.      

An Attempt to Detect Coronal Mass Ejections in Lyman-α Using SOHO Swan

In this study, the possibility that coronal mass ejections (CMEs) may be observed in neutral Lyman-α emission was investigated. An observing campaign was initiated for SWAN (Solar Wind ANisotropies), a Lyman-α scanning photometer on board the Solar and Heliospheric Observatory (SOHO) dedicated to monitoring the latitude distribution of the solar wind from its imprints on the interstellar sky background. This was part of SOHO Joint Observing Program (JOP) 159 and was an exploratory investigation as it was not known how, or even if, CMEs interact with the solar wind and interstellar neutral hydrogen at this distance (≈60 and 120 R _S). The study addresses the lack of methods for tracking CMEs beyond the field-of-view of current coronagraphs (30 R _S). In our first method we used LASCO, white-light coronagraphs on SOHO, and EIT, an extreme ultraviolet imaging telescope also on SOHO, to identify CME candidates which, subject to certain criteria, should have been observable in SWAN. The criteria included SWAN observation time and location, CME position angle, and extrapolated speed. None of the CME candidates that we discuss were identified in the SWAN data. For our second method we analyzed all of the SWAN data for 184 runs of the observing campaign, and this has yielded one candidate CME detection. The candidate CME appears as a dimming of the background Lyman-α intensity representing ≈10% of the original intensity, moving radially away from the Sun. Multiple candidate CMEs observed by LASCO and EIT were found which may have caused this dimming. Here we discuss the campaign, data analysis technique and statistics, and the results.     

Evidence of Traveling Waves in Filament Threads

High-resolution Hα filtergrams (0.2″) obtained with the Swedish 1-m Solar Telescope resolve numerous very thin, thread-like structures in solar filaments. The threads are believed to represent thin magnetic flux tubes that must be longer than the observable threads. We report on evidence for small-amplitude (1 – 2 km s⁻¹) waves propagating along a number of threads with an average phase velocity of 12 km s⁻¹ and a wavelength of 4″. The oscillatory period of individual threads vary from 3 to 9 minutes. Temporal variation of the Doppler velocities averaged over a small area containing a number of individual threads shows a short-period (3.6 minutes) wave pattern. These short-period oscillations could possibly represent fast modes in accordance with numerical fibril models proposed by Díaz et al. (Astron. Astrophys. 379, 1083, 2001). In some cases, it is clear that the propagating waves are moving in the same direction as the mass flows.     

Analytical Reference Functions <Emphasis Type="Italic">F</Emphasis>(λ) for the Sun's Limb Darkening and Its Absolute Continuum Intensities (λλ 300 to 1100 m)

It is shown (1) that the coefficients A_i of the limb darkening functions I(μ)/I_center = P₅ (μ) = ∑A_i μⁱ (i = 0... 5; μ = cos ϑ), which had been published by Neckel and Labs (Solar Phys. 153, 91, 1994), can well be approximated by analytical functions of wavelength λ, and (2) that at first sight purely formal extrapolation of the functions P₅(μ) to the very limb (μ = 0.0) is not meaningless: in combination with absolute intensities for the disk center these functions yield ‘limb intensities’ which all correspond to almost the same ‘limb temperature’, T_limb≈4746 K. Together these results lead to ‘reference functions’ which can quickly yield rather reliable values of the Sun's continuum intensities, for any values of μ and λ.     

Planar electron-acoustic solitary waves and double layers in a two-electron-temperature plasma with nonthermal ions

A rigorous theoretical investigation of nonlinear electron-acoustic (EA) waves in a plasma system (containing cold electrons, hot electrons obeying a Boltzmann distribution, and hot ions obeying a nonthermal distribution) is studied by the reductive perturbation method. The modified Gardner (MG) equation is derived and numerically solved. It has been found that the basic characteristics of the EA Gardner solitons (GSs), which are shown to exist for α around its critical value α _c [where α is the nonthermal parameter, α _c is the value of α corresponding to the vanishing of the nonlinear coefficient of the Korteweg-de Vries (K-dV) equation, e.g. α _c ≃0.31 for μ=n _h0/n _i0=0.5, σ=T _h /T _i =10, n _h0, n _i0 are, respectively, hot electron and nonthermal ion number densities at equilibrium, T _h (T _i ) is the hot electron (ion) temperature], are different from those of the K-dV solitons, which do not exist for α around α _c , and mixed K-dV solitons, which are valid around α∼α _c , but do not have any corresponding double layers (DLs) solution. The parametric regimes for the existence of the DLs, which are found to be associated with positive potential, are obtained. The present investigations can be observed in various space plasma environments (viz. the geomagnetic tail, the auroral regions, the cusp of the terrestrial magnetosphere, etc.).     

Solar quadrupole moment and purely relativistic gravitation contributions to Mercury's perihelion advance

The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones for testing General Relativity (G.R.).The main goal of this paper is to discuss how, presently, observational and theoretical constraints may challenge Einstein's theory of gravitation characterized by β=γ=1. To achieve this purpose, we will first recall the experimental constraints upon the Eddington-Robertson parameters γ,β and the observational bounds for the perihelion advance of Mercury, Δω_obs. A second point will address the values given, up to now, to the solar quadrupole moment by several authors. Then, we will briefly comment why we use a recent theoretical determination of the solar quadrupole moment, J ₂=(2.0 ± 0.4) 10^-7, which takes into account both surfacic and internal differential rotation, in order to compute the solar contribution to Mercury's perihelion advance. Further on, combining bounds on γ and J ₂ contributions, and taking into account the observational data range for Δω_obs,we will be able to give a range of values for β. Alternatively, taking into account the observed value of Δω_obs, one can deduce a dynamical estimation of J ₂ in the setting of G.R. This point is important as it provides a solar model independent estimation that can be confronted with other determinations of J ₂ based upon solar theory and solar observations (oscillation data, oblateness...). Finally, a glimpse at future satellite experiments will help us to understand how stronger constraints upon the parameter space (γω J ₂) as well as a separation of the two contributions (from the quadrupole moment, J ₂, or purely relativistic, 2α²+2αγ–β) might be expected in the future. This revised version was published online in July 2006 with corrections to the Cover Date.