Hybrid methods in planetesimal dynamics (I) : Description of a new composite algorithm

The formation and evolution of protoplanetary systems, the breeding grounds of planet formation, is a complex dynamical problem that involves many orders of magnitudes. To serve this purpose, we present a new hybrid algorithm that combines a Fokker-Planck approach with the advantages of a pure direct-summation N-body scheme, with a very accurate integration of close encounters for the orbital evolution of the larger bodies with a statistical model, envisaged to simulate the very large number of smaller planetesimals in the disc. Direct-summation techniques have been historically developped for the study of dense stellar systems such as open and globular clusters and, within some limits imposed by the number of stars, of galactic nuclei. The number of modifications to adapt direct-summation N-body techniques to planetary dynamics is not undemanding and requires modifications. These include the way close encounters are treated, as well as the selection process for the "neighbour radius" of the particles and the extended Hermite scheme, used for the very first time in this work, as well as the implementation of a central potential, drag forces and the adjustment of the regularisation treatment. For the statistical description of the planetesimal disc we employ a Fokker-Planck approach. We include dynamical friction, high- and low-speed encounters, the role of distant encounters as well as gas and collisional damping and then generalise the model to inhomogenous discs. We then describe the combination of the two techniques to address the whole problem of planetesimal dynamics in a realistic way via a transition mass to integrate the evolution of the particles according to their masses

N-body Models of Rotating Globular Clusters

We have studied the dynamical evolution of rotating globular clusters with direct $N$-body models. Our initial models are rotating King models; we obtained results for both equal-mass systems and systems composed out of two mass components. Previous investigations using a Fokker-Planck solver have revealed that rotation has a noticeable influence on stellar systems like globular clusters, which evolve by two-body relaxation. In particular, it accelerates their dynamical evolution through the gravogyro instability. We have validated the occurence of the gravogyro instability with direct $N$-body models. In the case of systems composed out of two mass components, mass segregation takes place, which competes with the rotation in the acceleration of the core collapse. The "accelerating" effect of rotation has not been detected in our isolated two-mass $N$-body models. Last, but not least, we have looked at rotating $N$-body models in a tidal field within the tidal approximation. It turns out that rotation increases the escape rate significantly. A difference between retrograde and prograde rotating star clusters occurs with respect to the orbit of the star cluster around the Galaxy, which is due to the presence of a ``third integral'' and chaotic scattering, respectively.Comment: 16 pages, 17 figures, accepted by MNRA

A Component of Retinal Light Adaptation Mediated by the Thyroid Hormone Cascade

Analysis with DNA-microrrays and real time PCR show that several genes involved in the thyroid hormone cascade, such as deiodinase 2 and 3 (Dio2 and Dio3) are differentially regulated by the circadian clock and by changes of the ambient light. The expression level of Dio2 in adult rats (2–3 months of age) kept continuously in darkness is modulated by the circadian clock and is up-regulated by 2 fold at midday. When the diurnal ambient light was on, the expression level of Dio2 increased by 4–8 fold and a consequent increase of the related protein was detected around the nuclei of retinal photoreceptors and of neurons in inner and outer nuclear layers. The expression level of Dio3 had a different temporal pattern and was down-regulated by diurnal light. Our results suggest that DIO2 and DIO3 have a role not only in the developing retina but also in the adult retina and are powerfully regulated by light. As the thyroid hormone is a ligand-inducible transcription factor controlling the expression of several target genes, the transcriptional activation of Dio2 could be a novel genomic component of light adaptation