Symplectic Mappings of Co-orbital Motion in the Restricted Problem of Three Bodies

The dynamics of co-orbital motion in the restricted three-body problem are investigated by symplectic mappings. Analytical and semi-numerical mappings have been developed and studied in detail. The mappings have been tested by numerical integration of the equations of motion. These mappings have been proved to be useful for a quick determination of the phase space structure reflecting the main characteristics of the dynamics of the co-orbital problem.     

The Difference between the α-disks of Seyfert 1 Galaxiesand Quasars

In a previous paper, it was suggested that contamination of the nuclear luminosity by the host galaxy plays an important role in determining the parameters of the standard a disk of AGNs. Using the nuclear absolute B band magnitude instead of the total absolute B band magnitude, we have recalculated the central black hole masses, accretion rates and disk inclinations for 20 Seyfert 1 galaxies and 17 Palomar-Green (PG) quasars. It is found that a small value of a is needed for the Seyfert 1 galaxies than for the PG quasars. This difference in a possibly leads to the different properties of Seyfert 1 galaxies and quasars. Furthermore, we find most of the objects in this sample are not accreting at super-Eddington rates if we adopt the nuclear optical luminosity in our calculation.     

Evolution of cold shock-bounded slabs

The stability and evolution of cold, shock-bounded slabs is studied using numerical hydrodynamic simulations. We confirm the analysis of Vishniac (1994) [ApJ, 428, 186], who showed that such slabs are unstable if they are perturbed by a displacement larger than their width. The growth rate of this nonlinear thin shell instability (NTSI) is found to increase with decreasing wavelength, in qualitative agreement with Vishniac's analysis. The NTSI saturates when the bending angle becomes large and the growth in the width of the slab pinches off the perturbation. After saturation, the slab remains greatly extended with an average density much less than the original slab density, supported primarily by supersonic turbulence within the slab. Linear perturbations are also found to be unstable in that they can lead to turbulent flow within the slab, although this response to linear perturbations is distinct from, and much less violent than the NTSI.Richard McCray