Updated values of solar gravitational moments $J_{2n}$ using HMI helioseismic inference of internal rotation

TL;DR

This study calculates updated solar gravitational moments $J_{2n}$ using helioseismic data from SDO/HMI and SoHO/MDI, confirming their sensitivity to internal solar rotation and aligning with recent astronomical measurements.

Contribution

It introduces a new integral approach to determine $J_{2n}$ from helioseismic rotation data, improving the precision of solar gravitational moment estimates.

Findings

Computed $J_{2}$ aligns with Mercury's perihelion precession measurements.

High order moments are sensitive to the solar rotation profile.

Results agree with space-based measurements of solar oblateness.

Abstract

The solar gravitational moments $J_{2n}$ are important astronomical quantities whose precise determination is relevant for solar physics, gravitational theory and high precision astrometry and celestial mechanics. Accordingly, we propose in the present work to calculate new values of $J_{2n}$ (for $n$=1,2,3,4 and 5) using recent two-dimensional rotation rates inferred from the high resolution SDO/HMI helioseismic data spanning the whole solar activity cycle 24. To this aim, a general integral equation relating $J_{2n}$ to the solar internal density and rotation is derived from the structure equations governing the equilibrium of slowly rotating stars. For comparison purpose, the calculations are also performed using rotation rates obtained from a recently improved analysis of SoHO/MDI heliseismic data for solar cycle 23. In agreement with earlier findings, the results confirmed the sensitivity of high order moments ($n>1$) to the radial and latitudinal distribution of rotation in the convective zone. The computed value of the quadrupole moment $J_{2}$ ($n=1$) is in accordance with recent measurements of the precession of Mercury's perihelion deduced from high precision ranging data of the MESSENGER spacecraft. The theoretical estimate of the related solar oblateness $\Delta_{\odot}$ is consistent with the most accurate space-based determinations, particularly the one from RHESSI/SAS.