| 22 Dec 2025
Effect of a non-hydrostatic core-mantle boundary on the nutations of Mars
Abstract. Dynamic loads in planetary mantles have the potential to deform the core-mantle boundary (CMB). On Earth, subducting slabs primarily induce a degree 2–order 2 deformation of the CMB in the spherical harmonic (SH) reference system. On Mars, the presence of the dichotomy and of the Tharsis region could produce loading across multiple degrees and orders, including degree-1, degree 2–order 2, degree 2–order 0, and degree 3–order 3 components. Thanks to the InSight (Interior exploration using Seismic Investigations, Geodesy, and Heat Transport) mission’s radio science experiment, observations of Mars' nutations are now available. Periodic length-of-day (LOD) variations of Mars have been detected first by radio tracking the Viking landers, and InSight data have indicated the presence of a secular trend in LOD. In the case of nutations, the Martian core’s non-hydrostatic flattening plays a first-order role in determining nutation amplitudes. In this study, we explore second-order effects arising from dynamic topography at the CMB. We compute the pressure exerted on the CMB topography inside Mars' liquid core and evaluate the resulting topographic pressure torque acting on the boundary, which can influence both nutations and LOD variations. Our results show that, albeit at microarcsecond level—well below current observational thresholds, the most significant contribution to nutations arises from degree 2–order 2 component. As for LOD variations, while Earth exhibits notable contributions from inertial wave resonances, the situation on Mars is different. The planet’s tidal LOD variations have periods that are either too long or too far apart from those of inertial waves. Consequently, the associated contributions fall below the level of detectability.
Given my area of expertise, my ability to review that paper is limited to anything that relates to mantle dynamics and than is not much, unfortunately. The one part I am familiar with is on the Green's functions. On the whole, in the absence of further information, I think the approach taken - converting geoid coefficients to CMB topography coefficients assuming amplitudes of mantle loads are independent of depth - is reasonable, but of course the sensitivity kernels and hence the conversion depend on viscosity structure, and I would have preferred if that was a bit discussed, perhaps elaborating on uncertainties depending on viscosity structure, or variability for the range of possible viscosity structures.
Line 53: on degree-1 gravity: In center of mass coordinates, this is required to be zero, as also pointed out by Wieczorek et al. (2019). Also, that would mean that the approach of inferring CMB topography from gravity mentioned in the above point would not work, so it should be clarified how you get degree-1 CMB topography. Relate it to degree-1 surface topography (since that can also be computed from sensitivity kernels) or infer it from Kaula's law?
Line 66/67: "greater than in cases without a post-spinel phase transition" - I don't understand, I think the case with a larger core is the case without a post-spinel phase transition.
Line 67: What is non-hydrostatic equilibrium? Do you mean deviation from hydrostatic equilibrium?
Line 104: You start here with 1, but the introduction is not numbered. I find this a bit confusing.
Figures 1 and 2: These symbols are hard to recognize. It would be helpful to plot that figures bigger. For the Plus-signs on the axis, the horizontal line cannot be seen, so they are especially hard to be recognized. Symbols for prograde and retrograde appear to be identical, so they cannot be distinguished. What is the unit for sigma (frequency)? In Figure 1 sigma goes from 0.99 to 1.01 whereas in Figure 2 it goes from 0 to 0.09. A
Line 290-302: You write microsecond level in lines 293, 296 and 302, and microarcsecond level in line 300. Do you mean microarcsecond level in all cases? I am not sure what microsecond level would mean. Microarcsecond is a small distance, so it seems to me a measure for the size of nutations.
Figure A1: There are supposedly symbols for Earth and Mars but they appear identical, so couldn't be distinguished. Also, on each graph, there is only one symbol of each kind, it seems, whereas it should be two, if it is for Earth and Mars. Also, same comments as in Figure 1 and 2; it would be helpful to plot the figure bigger.
Minor comments:
line 21: "from the degree 2-order 2 component"
Line 65: Not "In a core" but rather "With a core"
Line 169/170: "properties of spherical harmonic properties"