The IAU 2006 precession quantities with an improved Earth’s J2 long-term variation

In 2006, the IAU adopted a standard precession theory, the IAU2006 model, in which the time variation of the Earth's dynamical flattening J2 has an important contribution to the precession rate in longitude. However, a linear J2 trend, which was valid at that time, is no longer a good approximation and may limit the accuracy of the theory. In this work, we use the most recent satellite laser ranging (SLR) data to model the Earth's J2 long-term variation with a parabola. It was then implemented in calculating the polynomial expressions for precession quantities with a method similar to the IAU2006 approach. The new precession solution, named IAU2006J2, is checked against high accurate VLBI data over 45 years. It is clearly more consistent with observations: the overall difference between the observed and modeled positions decreases by about 20%, and most of the curvature signals in the CPO series are reduced. Besides the basic precession parameters, the full set of precession-nutation quantities (X, Y, s, EO ...) compatible with the IAU2006J2 model are developed, for both classical and CIO-based transformation from the GCRS to the ITRS. Considering its significant improvement, we propose that the IAU2006J2 precession model be considered in the update of the IERS Conventions which is currently in progress.