Analysis of a Precambrian Resonance-Stabilized Day Length

Abstract:

Calculations indicate the average rate of decrease of Earth's angular momentum must have been less than its present value in the past; otherwise, the Earth should have a longer day length. Existing stromatolite data suggests the Earth's rotational frequency would have been near that of the atmospheric resonance frequency toward the end of the Precambrian era, approximately 600Ma. The semidiurnal atmospheric tidal torque would have reached a maximum near this day length of 21hr. At this point, the atmospheric torque would have been comparable in magnitude but opposite in direction to the lunar torque, creating a stabilizing effect which could preserve a constant day length while trapped in this resonant state, as suggested by Zahnle and Walker (1987). We examine the hypothesis that this resonant stability was encountered and sustained for a large amount of time during the Precambrian era and was broken by a large and relatively fast increase in global temperature, possibly in the deglaciation period following a snowball event. Computational simulations of this problem were performed, indicating that a persistent increase in temperature larger than around 10K over a period of time less than 10⁷ years will break resonance (though these values vary with Q), but that the resonant stability is not easily broken by random high-amplitude high-frequency atmospheric temperature fluctuation or other forms of thermal noise. Further work also indicates it is possible to escape resonance simply by increasing the lunar tidal torque on the much longer timescale of plate tectonics, particularly for low atmospheric Q-factors, or that resonance could have never formed in the first place, had the lunar torque been very high or Q been very low when the Earth's rotational frequency was near the atmospheric resonance frequency. However, the need to explain the present day length given the current lunar torque favors the interpretation we offer, in which Earth's length of day was stabilized for hundreds of millions of years, escaping this stability in the aftermath of a sudden global temperature change.