@phdthesis{Seiler2020,
  author    = {Seiler, Michael},
  title     = {The Non-Keplerian Motion of Propeller Moons in the Saturnian Ring System},
  school      = {Universit{\"a}t Potsdam},
  pages     = {127},
  year      = {2020},
  abstract  = {One of the tremendous discoveries by the Cassini spacecraft has been the detection of propeller structures in Saturn's A ring. Although the generating moonlet is too small to be resolved by the cameras aboard Cassini, its produced density structure within the rings, caused by its gravity can be well observed. The largest observed propeller is called Bl{\´e}riot and has an azimuthal extent over several thousand kilometers. Thanks to its large size, Bl{\´e}riot could be identified in different images over a time span of over 10 years, allowing the reconstruction of its orbital evolution. It turns out that Bl{\´e}riot deviates considerably from its expected Keplerian orbit in azimuthal direction by several thousand kilometers. This excess motion can be well reconstructed by a superposition of three harmonics, and therefore resembles the typical fingerprint of a resonantly perturbed body. This PhD thesis is directed to the excess motion of Bl{\´e}riot. Resonant perturbations are a known for some of the outer satellites of Saturn. Thus, in the first part of this thesis, we seek for suiting resonance candidates nearby the propeller, which might explain the observed periods and amplitudes. In numeric simulations, we show that indeed resonances by Prometheus, Pandora and Mimas can explain the libration periods in good agreement, but not the amplitudes. The amplitude problem is solved by the introduction of a propeller-moonlet interaction model, where we assume a broken symmetry of the propeller by a small displacement of the moonlet. This results in a librating motion the moonlet around the propeller's symmetry center due to the non-vanishing accelerations. The retardation of the reaction of the propeller structure to the motion of the moonlet causes the propeller to become asymmetric. Hydrodynamic simulations to test our analytical model confirm our predictions. In the second part of this thesis, we consider a stochastic migration of the moonlet, which is an alternative hypothesis to explain the observed excess motion of Bl{\´e}riot. The mean-longitude is a time-integrated quantity and thus introduces a correlation between the independent kicks of a random walk, smoothing the noise and thus makes the residual look similar to the observed one for Bl{\´e}riot. We apply a diagonalization test to decorrelated the observed residuals for the propellers Bl{\´e}riot and Earhart and the ring-moon Daphnis. It turns out that the decorrelated distributions do not strictly follow the expected Gaussian distribution. The decorrelation method fails to distinguish a correlated random walk from a noisy libration and thus we provide an alternative study. Assuming the three-harmonic fit to be a valid representation of the excess motion for Bl{\´e}riot, independently from its origin, we test the likelihood that this excess motion can be created by a random walk. It turns out that a non-correlated and correlated random walk is unlikely to explain the observed excess motion.},
  language  = {en}
}
@article{Baumgaertel2011,
  author    = {Baumg{\"a}rtel, Hellmut},
  title     = {A Characteristic decay semigroup for the resonances of trace class perturbations with analyticity conditions of semibounded hamiltonians},
  series = {International journal of theoretical physic},
  volume    = {50},
  journal   = {International journal of theoretical physic},
  number    = {7},
  publisher = {Springer},
  address   = {New York},
  issn      = {0020-7748},
  doi       = {10.1007/s10773-010-0533-9},
  pages     = {2002 -- 2008},
  year      = {2011},
  abstract  = {To asymptotic complete scattering systems {M(+) + V, M(+)} on H(+) := L(2)(R(+), K, d lambda), where M(+) is the multiplication operator on H(+) and V is a trace class operator with analyticity conditions, a decay semigroup is associated such that the spectrum of the generator of this semigroup coincides with the set of all resonances (poles of the analytic continuation of the scattering matrix into the lower half plane across the positive half line), i.e. the decay semigroup yields a "time-dependent" characterization of the resonances. As a counterpart a "spectral characterization" is mentioned which is due to the "eigenvalue-like" properties of resonances.},
  language  = {en}
}