Constraining the Angular Momentum of the Sun with Planetary Orbital Motions and General Relativity

The angular momentum of a star is an important astrophysical quantity related to its internal structure, formation, and evolution. Helioseismology yields $S_{\odot}= 1.92\times10^{41}\ \mathrm{kg\ m^{2}\ s^{-1}}$ for the angular momentum of the Sun. We show how it should be possible to constrain it in a near future by using the gravitomagnetic Lense?CThirring effect predicted by General Relativity for the orbit of a test particle moving around a central rotating body. We also discuss the present-day situation in view of the latest determinations of the supplementary perihelion precession of Mercury. A fit by Fienga et al. (Celestial Mech. Dynamical Astron. 111, 363, 2011) of the dynamical models of several standard forces acting on the planets of the solar system to a long data record yielded milliarcseconds per century. The modeled forces did not include the Lense?CThirring effect itself, which is expected to be as large as from helioseismology-based values of S _??. By assuming the validity of General Relativity, from its theoretical prediction for the gravitomagnetic perihelion precession of Mercury, one can straightforwardly infer $S_{\odot}\leq0.95\times10^{41}\ \mathrm{kg\, m^{2}\, s^{-1}}$ . It disagrees with the currently available values from helioseismology. Possible sources for the present discrepancy are examined. Given the current level of accuracy in the Mercury ephemerides, the gravitomagnetic force of the Sun should be included in their force models. MESSENGER, in orbit around Mercury since March 2011, will collect science data until 2013, while BepiColombo, to be launched in 2015, should reach Mercury in 2022 for a year-long science phase: the analysis of their data will be important in effectively constraining S _?? in about a decade or, perhaps, even less.