While currently Iapetus is locked into a 1:1 spin-orbit resonance with Saturn, its original state... more While currently Iapetus is locked into a 1:1 spin-orbit resonance with Saturn, its original state was likely one of rapid rotation. Simulations (Aleshkina 2009) have demonstrated that: (1) with a high arbitrariness in the initial conditions, Iapetus had passed without delay through the 5:2, 2:1, and 3:2 spin-orbit commensurabilities, and (2) its tidal-despinning time was about hundred billion years, an unphysical result for a moon in a spin-orbit lock. (For the other large satellites of Saturn these times are shorter by orders of magnitude.) Hence the necessity to seek efficient tidal-despinning mechanisms. One such mechanism was introduced by Castillo-Rogez et al. (2007), who derived accelerated tidal dissipation from the presence of short-lived Al and Fe isotopes. These could have created a warm and low-viscosity interior permitting an initial despinning phase, with the rotation period of 7 hr decreasing to 15-16 hr, while preserving the non-hydrostatic, fossil oblateness. Since the amount of 26Al used in models implies a range of times of formation for Iapetus and thus the Saturnian system, it is crucial to constrain the processes and parameters involved. In Castillo-Rogez et al. (2007), the dynamical equations were simplistic, while the dissipation calculation relied on the Maxwell model, not on laboratory data. Recent developments increase the level of realism in coupled geophysical and dynamical modeling. Efroimsky and Lainey (2008) and Efroimsky and Williams (2009) have improved the theories of tidal lagging and despinning, while the measurements tackled at the JPL (Castillo-Rogez et al. 2009) yield a realistic dissipation model for ices in the conditions relevant to Iapetus. We are exploring if the realistic frequency-dependence of the attenuation rate can lead to efficient tidal despinning. Our purpose is to determine whether or not 26Al is required to achieve synchronous rotation. This will enable us to constrain the time of Iapetus’ formation.
Abstract Gauge freedom emerges when the number of mathematical variables exceeds the number of ph... more Abstract Gauge freedom emerges when the number of mathematical variables exceeds the number of physical degrees of freedom and, thus, generates a continuous group of physically-equivalent reparametrisations of the theory. This internal freedom may be interconnected with freedom of coordinate-frame choice (eg, general relativity) or may be totally independent (eg, electrodynamics and quantum physics). Previously, we explained how gauge-type freedom emerges in ordinary differential equations whenever the ...
Aas Division of Dynamical Astronomy Meeting 39, May 1, 2008
We compare two derivations of a popular formula for the tidal despinning rate, and emphasise that... more We compare two derivations of a popular formula for the tidal despinning rate, and emphasise that both are strongly limited to the case of a vanishing inclination and a certain (sadly, unrealistic) law of frequency-dependence of the quality factor. One method is based on the MacDonald torque, the other on the Darwin torque. Fortunately, the second approach is general enough to accommodate both a finite inclination and the actual rheology. We also address the rheological models with the Q factor scaling as the tidal frequency to a positive fractional power, and disprove the popular belief that these models introduce discontinuities into the equations and thus are unrealistic at low frequencies. Though such models indeed make the conventional expressions for the torque diverge for vanishing frequencies, the emerging infinities reveal not the impossible nature of one or another rheology, but a subtle flaw in the underlying mathematical model of friction. Flawed is the common misassumption that damping merely provides phase lags to the terms of the Fourier series for the tidal potential. A careful hydrodynamical treatment by Sir George Darwin (1879), with viscosity explicitly included, had demonstrated that the magnitudes of the terms, too, get changed -- a fine detail later neglected as ``irrelevant". Reinstating of this detail tames the fake infinities and rehabilitates the ``impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).
While currently Iapetus is locked into a 1:1 spin-orbit resonance with Saturn, its original state... more While currently Iapetus is locked into a 1:1 spin-orbit resonance with Saturn, its original state was likely one of rapid rotation. Simulations (Aleshkina 2009) have demonstrated that: (1) with a high arbitrariness in the initial conditions, Iapetus had passed without delay through the 5:2, 2:1, and 3:2 spin-orbit commensurabilities, and (2) its tidal-despinning time was about hundred billion years, an unphysical result for a moon in a spin-orbit lock. (For the other large satellites of Saturn these times are shorter by orders of magnitude.) Hence the necessity to seek efficient tidal-despinning mechanisms. One such mechanism was introduced by Castillo-Rogez et al. (2007), who derived accelerated tidal dissipation from the presence of short-lived Al and Fe isotopes. These could have created a warm and low-viscosity interior permitting an initial despinning phase, with the rotation period of 7 hr decreasing to 15-16 hr, while preserving the non-hydrostatic, fossil oblateness. Since the amount of 26Al used in models implies a range of times of formation for Iapetus and thus the Saturnian system, it is crucial to constrain the processes and parameters involved. In Castillo-Rogez et al. (2007), the dynamical equations were simplistic, while the dissipation calculation relied on the Maxwell model, not on laboratory data. Recent developments increase the level of realism in coupled geophysical and dynamical modeling. Efroimsky and Lainey (2008) and Efroimsky and Williams (2009) have improved the theories of tidal lagging and despinning, while the measurements tackled at the JPL (Castillo-Rogez et al. 2009) yield a realistic dissipation model for ices in the conditions relevant to Iapetus. We are exploring if the realistic frequency-dependence of the attenuation rate can lead to efficient tidal despinning. Our purpose is to determine whether or not 26Al is required to achieve synchronous rotation. This will enable us to constrain the time of Iapetus’ formation.
Abstract Gauge freedom emerges when the number of mathematical variables exceeds the number of ph... more Abstract Gauge freedom emerges when the number of mathematical variables exceeds the number of physical degrees of freedom and, thus, generates a continuous group of physically-equivalent reparametrisations of the theory. This internal freedom may be interconnected with freedom of coordinate-frame choice (eg, general relativity) or may be totally independent (eg, electrodynamics and quantum physics). Previously, we explained how gauge-type freedom emerges in ordinary differential equations whenever the ...
Aas Division of Dynamical Astronomy Meeting 39, May 1, 2008
We compare two derivations of a popular formula for the tidal despinning rate, and emphasise that... more We compare two derivations of a popular formula for the tidal despinning rate, and emphasise that both are strongly limited to the case of a vanishing inclination and a certain (sadly, unrealistic) law of frequency-dependence of the quality factor. One method is based on the MacDonald torque, the other on the Darwin torque. Fortunately, the second approach is general enough to accommodate both a finite inclination and the actual rheology. We also address the rheological models with the Q factor scaling as the tidal frequency to a positive fractional power, and disprove the popular belief that these models introduce discontinuities into the equations and thus are unrealistic at low frequencies. Though such models indeed make the conventional expressions for the torque diverge for vanishing frequencies, the emerging infinities reveal not the impossible nature of one or another rheology, but a subtle flaw in the underlying mathematical model of friction. Flawed is the common misassumption that damping merely provides phase lags to the terms of the Fourier series for the tidal potential. A careful hydrodynamical treatment by Sir George Darwin (1879), with viscosity explicitly included, had demonstrated that the magnitudes of the terms, too, get changed -- a fine detail later neglected as ``irrelevant". Reinstating of this detail tames the fake infinities and rehabilitates the ``impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).
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