Deviation of Mercury's Spin Axis From an Exact Cassini State Induced by Dissipation

Abstract

The spin axis of Mercury is in a Cassini state (Figure 1). The latter describes a configuration in which the planet's spin axis and orbit normal remain coplanar to and precess about the normal to the Laplace plane (Colombo, 1966;Peale, 1969Peale, , 2006. The precession is retrograde, and the latest estimate of its period is 325, 513 ± 10, 713 years (Baland et al., 2017). Figure 2 shows the orientation in space of the spin axis reported in several recent studies, expressed at the J2000 epoch as is the usual convention. A visual inspection of Figure 2 reveals that within measurement errors, Mercury's spin axis aligns with the plane defined by the Laplace pole and orbit normal, a plane which we refer to as the Cassini plane, confirming that Mercury occupies a Cassini state.The retrograde precession of the Cassini plane implies that the line that depicts its location in Figure 2 is displaced toward the bottom left as a function of time. Hence, a spin pole located to the top right (bottom left) with respect to this line is behind (ahead of) the expected Cassini state orientation and corresponds to a phase lag (phase lead). We denote the offset from the Cassini plane by an angle ζ m , defined positive for a phase lag (see Figure 1b). Table 1 gives the spin pole orientations from the recent measurements that are plotted in Figure 2 as well as their phase lag angles ζ m , calculated by the method described in Appendix A. For all spin pole measurements, the 1σ error on the phase lag is either larger than the phase lag itself, or of similar magnitude. This confirms that within measurement errors, Mercury's spin pole indeed occupies a Cassini state. The magnitude of the phase lags in Table 1 provides a quantitative measure of the deviation from an exact Cassini state. For all spin pole

The Gravity Signal of Mercury's Inner Core

“…However, if present, its size is not known. Several studies have attempted to place bounds on the inner core size, either by investigating its dynamical influence on the librations (Dumberry, 2011;Dumberry et al, 2013;Koning & Dumberry, 2013;Peale et al, 2002;Van Hoolst et al, 2012;Veasey & Dumberry, 2011;Yseboodt et al, 2013) and the mantle obliquity (Dumberry, 2021a;MacPherson & Dumberry, 2022;Peale et al, 2016), or by constructing interior models that are consistent with the observed amplitude of librations and mantle obliquity (Dumberry & Rivoldini, 2015;Genova et al, 2019;Hauck et al, 2013;Knibbe et al, 2021;Knibbe & Van Westrenen, 2015;Steinbrügge et al, 2021). While no general consensus has emerged from these, they all point to an inner core that cannot be too large.…”

“…We do not have direct observations of the orientation of the spin axis of the fluid core, nor that of the inner core if present. However, we expect that they should also be in a Cassini state, and their orientations should differ from that of the mantle (Dumberry, 2021a;MacPherson & Dumberry, 2022;Peale et al, 2014Peale et al, , 2016. Their misalignment angles depend on the elliptical shapes of the core-mantle boundary (CMB) and inner core boundary (ICB)-which in turn depend on the interior structure, including the size of the inner core and its density contrast with the fluid core.…”

“…The objective of our study is to present plausible predictions of the amplitude of this internal gravity signal in order to establish the observational precision that would be required to detect it. To do so, we use the rotational model of the Cassini state of Mercury presented in Dumberry (2021a) and further developed in MacPherson and Dumberry (2022), which are henceforth referred to as D21 and MD22, respectively. The presence and size of an inner core is an important diagnostic of the thermal evolution of a planetary body.…”