Helioseismic determination of the solar gravitational quadrupole moment

Pijpers, F. P.

doi:10.1046/j.1365-8711.1998.01801.x

Cited by 140 publications

(133 citation statements)

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“…The present total solar angular momentum is about 10 48 g cm 2 s −1 (Pijpers 1998;Antia et al 2000;Komm et al 2003). Thus, the mean angular momentum loss rate is not less than 10 40 g cm 2 s −1 yr −1 .…”

Section: Hydrodynamical Instabilitiesmentioning

confidence: 85%

Angular momentum transport and element mixing in the stellar interior

Yang

2006

A&A

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Aims. The purpose of this work was to obtain diffusion coefficient for the magnetic angular momentum transport and material transport in a rotating solar model. Methods. We assumed that the transport of both angular momentum and chemical elements caused by magnetic fields could be treated as a diffusion process. Results. The diffusion coefficient depends on the stellar radius, angular velocity, and the configuration of magnetic fields. By using of this coefficient, it is found that our model becomes more consistent with the helioseismic results of total angular momentum, angular momentum density, and the rotation rate in a radiative region than the one without magnetic fields. Not only can the magnetic fields redistribute angular momentum efficiently, but they can also strengthen the coupling between the radiative and convective zones. As a result, the sharp gradient of the rotation rate is reduced at the bottom of the convective zone. The thickness of the layer of sharp radial change in the rotation rate is about 0.036 R in our model. Furthermore, the difference of the sound-speed square between the seismic Sun and the model is improved by mixing the material that is associated with angular momentum transport.

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Section: Hydrodynamical Instabilitiesmentioning

confidence: 85%

Angular momentum transport and element mixing in the stellar interior

Yang

2006

A&A

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“…We adopt the value of  =´-S 190 10 kg m s 39 2 1 from helioseismology (Pijpers 1998;Mecheri et al 2004), which gives a Mercury perihelion precession rate of about −0 002/century for γ=1 (Iorio 2005). For earlier theoretical calculation of the LT effect on the perihelion precession of Mercury based on previous estimates of Mercury's orbit and the Sun's angular momentum (see de Sitter 1916;Barker & O'Connell 1970;Cugusi & Proverbio 1978;Soffel 1989).…”

Section: Dynamical Effects On Precession Of Mercury's Perihelionmentioning

confidence: 99%

“…The Earth-induced LT effect has been detected for the LAGEOS satellites in Earth orbit (with 10% stated uncertainty, but with ongoing evaluation; Ciufolini & Pavlis 2004;Ciufolini et al 2011;Iorio 2011b;Renzetti 2014) and contributed to the precession of gyroscopes measured by Gravity Probe B (19%) (Everitt et al 2011). Instead of estimating the LT effect, which is linearly proportional to S e , we consider the effect of an uncertainty of´-15 10 kg m s 39 2 1 in the estimation process (Bierman 1977), which is 10 times the reported uncertainty from helioseismology (Pijpers 1998). This constrains the value of S e , but includes its uncertainty in the estimated solution.…”

Section: Dynamical Effects On Precession Of Mercury's Perihelionmentioning

confidence: 99%

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

et al. 2017

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The perihelion of Mercury's orbit precesses due to perturbations from other solar system bodies, solar quadrupole moment (J 2 ), and relativistic gravitational effects that are proportional to linear combinations of the parametrized post-Newtonian parameters β and γ. The orbits and masses of the solar system bodies are quite well known, and thus the uncertainty in recovering the precession rate of Mercury's perihelion is dominated by the uncertainties in the parameters J 2 , β, and γ. Separating the effects due to these parameters is challenging since the secular precession rate has a linear dependence on each parameter. Here we use an analysis of radiometric range measurements to the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) spacecraft in orbit about Mercury to estimate the precession of Mercury's perihelion. We show that the MESSENGER ranging data allow us to measure not only the secular precession rate of Mercury's perihelion with substantially improved accuracy, but also the periodic perturbation in the argument of perihelion sensitive to β and γ. When combined with the γ estimate from a Shapiro delay experiment from the Cassini mission, we can decouple the effects due to β and J 2 and estimate both parameters, yielding ( ) ( ) b -= -´-1 2.7 3.9 10 5 and J 2 =(2.25±0.09)×10 −7. We also estimate the total precession rate of Mercury's perihelion as 575.3100±0.0015″/century and provide estimated contributions and uncertainties due to various perturbing effects.

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“…Preliminary calculations [5] reveal that the major planets of the solar system are sufficiently massive to pull photons by their gravitational fields, which have significant multipolar structures [6], in contrast with the Sun whose quadrupole moment is only J 2 2:3 10 ÿ7 [7,8]. Moreover, in the case of a photon propagating near the planet the interaction between the gravitational field and the photon can no longer be considered static, because the planet moves around the Sun as the photon traverses through the solar system [9,10].…”

Section: Introductionmentioning

confidence: 99%

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

2007

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General-relativistic deflection of light by mass, dipole, and quadrupole moments of the gravitational field of a moving massive planet in the solar system is derived in the approximation of the linearized Einstein equations. All terms of order 1 as are taken into account, parametrized, and classified in accordance with their physical origin. The monopolar light-ray deflection, modulated by the radial Doppler effect, is associated with the total mass and radial velocity of the gravitating body. It displaces the apparent positions of stars in the sky plane radially away from the origin of the celestial coordinates associated with the planet. The dipolar deflection of light is due to a translational mismatch of the center of mass of the planet and the origin of the planetary coordinates caused by the inaccuracy of planetary ephemeris. It can also originate from the difference between the null cone for light and that for gravity that is not allowed in general relativity but can exist in some of the alternative theories of gravity. The dipolar gravity field pulls the apparent position of a star in the plane of the sky in both radial and orthoradial directions with respect to the origin of the coordinates. The quadrupolar deflection of light is caused by the physical oblateness, J 2 , of the planet, but in any practical experiment it will have an admixture of the translation-dependent quadrupole due to inaccuracy of planetary ephemeris. This leads to a bias in the estimated value of J 2 that should be minimized by applying an iterative data reduction method designed to disentangle the different multipole moments and to fit out the translation-dependent dipolar and quadrupolar components of light deflection. The method of microarcsecond interferometric astrometry has the potential of greatly improving the planetary ephemerides, getting unbiased measurements of planetary quadrupoles, and of thoroughly testing the null-cone structure of the gravitational field and the speed of its propagation in the near-zone of the solar system. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole, and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. We discuss the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by Jupiter and Saturn.

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Helioseismic determination of the solar gravitational quadrupole moment

Cited by 140 publications

References 11 publications

Angular momentum transport and element mixing in the stellar interior

Angular momentum transport and element mixing in the stellar interior

Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

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