NGC 1300 Dynamics: III. Orbital analysis

We present the orbital analysis of four response models, that succeed in reproducing morphological features of NGC 1300. Two of them assume a planar (2D) geometry with $\Omega_p$=22 and 16 \ksk respectively. The two others assume a cylindrical (thick) disc and rotate with the same pattern speeds as the 2D models. These response models reproduce most successfully main morphological features of NGC 1300 among a large number of models, as became evident in a previous study. Our main result is the discovery of three new dynamical mechanisms that can support structures in a barred-spiral grand design system. These mechanisms are presented in characteristic cases, where these dynamical phenomena take place. They refer firstly to the support of a strong bar, of ansae type, almost solely by chaotic orbits, then to the support of spirals by chaotic orbits that for a certain number of pat tern revolutions follow an n:1 (n=7,8) morphology, and finally to the support of spiral arms by a combination of orbits trapped around L$_{4,5}$ and sticky chaotic orbits with the same Jacobi constant. We have encountered these dynamical phenomena in a large fraction of the cases we studied as we varied the parameters of our general models, without forcing in some way their appearance. This suggests that they could be responsible for the observed morphologies of many barred-spiral galaxies. Comparing our response models among themselves we find that the NGC 130 0 morphology is best described by a thick disc model for the bar region and a 2D disc model for the spirals, with both components rotating with the same pattern speed $\Omega_p$=16 \ksk !. In such a case, the whole structure is included inside the corotation of the system. The bar is supported mainly by regular orbits, while the spirals are supported by chaotic orbits.Comment: 18 pages, 32 figures, accepted for publication in MNRA

Instabilities and stickiness in a 3D rotating galactic potential

We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.Comment: 29pages, 25 figures, accepted for publication in the International Journal of Bifurcation and Chao

NGC 1300 Dynamics: II. The response models

We study the stellar response in a spectrum of potentials describing the barred spiral galaxy NGC 1300. These potentials have been presented in a previous paper and correspond to three different assumptions as regards the geometry of the galaxy. For each potential we consider a wide range of $\Omega_p$ pattern speed values. Our goal is to discover the geometries and the $\Omega_p$ supporting specific morphological features of NGC 1300. For this purpose we use the method of response models. In order to compare the images of NGC 1300 with the density maps of our models, we define a new index which is a generalization of the Hausdorff distance. This index helps us to find out quantitatively which cases reproduce specific features of NGC 1300 in an objective way. Furthermore, we construct alternative models following a Schwarzschild type technique. By this method we vary the weights of the various energy levels, and thus the orbital contribution of each energy, in order to minimize the differences between the response density and that deduced from the surface density of the galaxy, under certain assumptions. We find that the models corresponding to $\Omega_p\approx16$\ksk and $\Omega_p\approx22$\ksk are able to reproduce efficiently certain morphological features of NGC 1300, with each one having its advantages and drawbacks.Comment: 13 pages, 10 figures, accepted for publication in MNRA

Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential

This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis and Zachilas 1994] in order to visualize them. As examples we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.Comment: 12 pages,22 figures, Accepted for publication in the International Journal of Bifurcation and Chao

Particle Swarm Optimization: An efficient method for tracing periodic orbits in 3D galactic potentials

We propose the Particle Swarm Optimization (PSO) as an alternative method for locating periodic orbits in a three--dimensional (3D) model of barred galaxies. We develop an appropriate scheme that transforms the problem of finding periodic orbits into the problem of detecting global minimizers of a function, which is defined on the Poincar\'{e} Surface of Section (PSS) of the Hamiltonian system. By combining the PSO method with deflection techniques, we succeeded in tracing systematically several periodic orbits of the system. The method succeeded in tracing the initial conditions of periodic orbits in cases where Newton iterative techniques had difficulties. In particular, we found families of 2D and 3D periodic orbits associated with the inner 8:1 to 12:1 resonances, between the radial 4:1 and corotation resonances of our 3D Ferrers bar model. The main advantages of the proposed algorithm is its simplicity, its ability to work using function values solely, as well as its ability to locate many periodic orbits per run at a given Jacobian constant.Comment: 12 pages, 8 figures, accepted for publication in MNRA

Dark matter within high surface brightness spiral galaxies

We present results from a detailed dynamical analysis of five high surface brightness, late type spirals, studied with the aim to quantify the luminous-to-dark matter ratio inside their optical radii. The galaxies' stellar light distribution and gas kinematics have been observed and compared to hydrodynamic gas simulations, which predict the 2D gas dynamics arising in response to empirical gravitational potentials, which are combinations of differing stellar disk and dark halo contributions. The gravitational potential of the stellar disk was derived from near-infrared photometry, color-corrected to constant (M/L); the dark halo was modelled by an isothermal sphere with a core. Hydrodynamic gas simulations were performed for each galaxy for a sequence of five different mass fractions of the stellar disk and for a wide range of spiral pattern speeds. These two parameters mainly determine the modelled gas distribution and kinematics. The agreement between the non-axisymmetric part of the simulated and observed gas kinematics permitted us to conclude that the galaxies with the highest rotation velocities tend to possess near-maximal stellar disks. In less massive galaxies, with v_max<200 km/s, the mass of the dark halo at least equals the stellar mass within 2-3 R_disk. The simulated gas morphology provides a powerful tool to determine the dominant spiral pattern speed. The corotation radius for all galaxies was found to be constant at R_corotation ~ 3 R_disk and encloses the strong part of the stellar spiral in all cases.Comment: 28 pages, 7 figures; to appear in the Astrophysical Journal, Vol. 586, March 200