The Chandler wobble — the free Eulerian wobble of a planet's rotation pole — was detected for Mars in 2020 from 18 years of spacecraft radio tracking, with a period of 206.9 ± 0.5 days and an amplitude of about 10 cm at the surface: the first detection of a free polar wobble on any planetary body other than Earth. Because the Martian mantle is anelastic, the wobble should decay with an e-folding time of only 7–63 years, so an ongoing process must continually re-excite it. Atmospheric angular-momentum variations are the leading candidate, but the source paper could not exclude core–mantle coupling or marsquakes, and no quantitative excitation budget has been closed since. The problem is to identify, quantitatively, the mechanism(s) that sustain the observed amplitude, determining whether the atmosphere (its matter and wind contributions to the angular momentum) suffices at the now-constrained mantle quality factor and bounding any residual role of interior sources.

Background

Polar motion is the motion of a planet's rotation axis relative to its crust, and the Chandler wobble (CW) is its free component: the torque-free wobble of the rotation pole of a deformable, rotating body (for Earth, a ~433-day circular motion of the pole with a 3–6 m amplitude). Polar motion is governed by the Liouville equations, in which mass redistribution and winds within the fluid layers enter through an excitation function; for Earth this function is dominated by the atmospheric angular momentum (conventionally split into a matter term from pressure and mass redistribution and a wind term from atmospheric motion), together with oceanic and hydrological contributions, which quantitatively explain the maintenance of Earth's CW against its damping (Gross, 2000). For a planet with a deformable mantle the free wobble is damped by anelastic dissipation, parameterized by a quality factor QQ: the smaller QQ, the faster the amplitude decays.

Mars has no oceans, and its main fluid reservoir is a thin CO2_2 atmosphere whose seasonal condensation and sublimation at the polar caps drives a large annual mass exchange. Pre-detection modeling established that the Martian CW should have a period near 200 days (Van Hoolst et al., 2000; Zharkov & Gudkova, 2009) and that the atmosphere could stochastically excite it: Dehant et al. (2006), using output of the LMD (Laboratoire de Météorologie Dynamique) Mars general circulation model, estimated atmospheric-noise-excited CW amplitudes between 10 cm and 1.1 m for mantle QQ between 80 and 200, while marsquakes — with expected seismic moments up to ~101610^{16} N·m, about 10710^{7} times smaller than Earth's largest events — were judged unable to excite observable polar motion.

Konopliv et al. (2020) detected the Martian CW for the first time from Doppler tracking of the Mars Odyssey, Mars Reconnaissance Orbiter, and Mars Global Surveyor orbiters, obtaining a period of 206.9 ± 0.5 days and an amplitude of ~10 cm (6.1 milliarcseconds). Combining the CW period with the precession rate and the tidal Love number k2k_2 (a measure of the planet's deformation response to tidal forcing), they constrained the frequency dependence of Martian mantle rheology, with a CW quality factor QQ between about 40 and 350, implying an e-folding decay time of only 7–63 years. The observed amplitude sits at the lower extreme of the Dehant et al. (2006) predictions. Since the wobble must be continually re-excited on geologically short timescales, the source paper states that the principal excitation mechanism is likely of atmospheric origin, whereas excitations produced by core–mantle interactions or marsquakes are unlikely but cannot be excluded — leaving the excitation of the first planetary free wobble detected beyond Earth unidentified.

Problem Statement

Identify, quantitatively, the mechanism or mechanisms that excite and sustain the Chandler wobble of Mars — the free wobble of its rotation pole, observed at a period of 206.9 ± 0.5 days with an amplitude of ~10 cm (6.1 milliarcseconds) — against anelastic mantle damping with quality factor Q≈40Q \approx 40–350350 (e-folding decay time 7–63 years). It remains to be determined whether the atmospheric excitation function for Mars (matter and wind terms of the angular momentum) sustains, for the admissible range of mantle QQ and rheology, a wobble consistent with the observed amplitude and, where the data allow, its phase and amplitude evolution; whether the competing candidate sources named in the detection paper (Konopliv et al., 2020) — core–mantle coupling and marsquake excitation — can be quantitatively bounded; and which mechanism(s) dominate within quantified uncertainties. The problem is solved when the excitation budget of the observed wobble is closed: the dominant source is identified and the predicted equilibrium amplitude and behavior of the damped, excited wobble match the observed ~10-cm amplitude within quantified uncertainties.

References

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