Apse-alignment in narrow-eccentric ringlets and its implications for the epsilon-ring of Uranus and the ring system of (10199) Chariklo

MELITA, M.D.; PAPALOIZOU J.C.B.

ICARUS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2019 vol. 335

0019-1035

The discovery of ring systems around objects of the outer Solar Systemprovides a strong motivation to apply theoretical models in order to betterestimate their physical and orbital parameters, which can constrain scenariosfor their origin.We review the criterion for maintaining apse-alignment across a ring andthe balance between the energy input rate provided by a close by satelliteand the internal dissipation rate occurring through ring particle collisionsthat is required to maintain ring eccentricity, as derived from the equationsof motion governing the Lagrangian-displacements of the ring-particle orbits.We use the case of the ǫ-ring of Uranus, to calibrate our theoretical discussionand illustrate the basic dynamics governing these types of ring.In the case of the ring system of (10199) Chariklo, where the evidencethat the rings are eccentric is not conclusive, we apply the theory of apse-alignment to derive information about the most plausible combination of val-ues of the surface density and eccentricity-gradient, as well as the masses andlocations of their postulated but -presently undetected- shepherd-satellites.When the balance conditions that we predict are applied to the ringsystem of (10199) Chariklo, we are able to estimate the minimum mass of ashepherd satellite required to prevent eccentricity decay, as a function of itsorbital location, for two different models of dissipation. We conclude thatthe satellite mass required to maintain the m = 1 eccentric mode in the ring,would be similar or smaller than that needed to confine the rings radially.Our estimation of the most plausible combinations of eccentricity gradientand surface density consistent with apse-alignment are based on a standardmodel for the radial form of the surface density distribution, which approx-imately agrees with the optical depth profile derived by the stellar occulta-tions. We find a diverse range of solutions, with combinations of eccentricitygradient and surface mass density that tend to minimize required enhancedcollisional effects, having adopted estimated values of the form factor of thesecond degree harmonic of the gravitational potential.