Bar Force

1. Evolution of Bar-driven Disks under the Influence of the Interaction between Two Inner Lindblad Resonances Chi Yuan1 and David C.C. Yen1,2 1Institute of Astronomy and Astrophysics, Academia Sinica, Taiwan, R.O.C. 2Department of Mathematics, Fu-Jen Catholic University, Hinchuang, Taipei Hsien, Taiwan, R.O.C. Abstract The presence of both the inner inner Lindblad resonance (IILR) and the outer inner Lindblad resonance (OILR) in a bar-driven galactic disk highly complicates the gas-dynamical processes in the disk and greatly affects its structure and evolution. In this study, we use the Antares codes to simulate the evolution of the such disks. The Antares codes are higher order Godunov codes we have developed, which are featured with exact Riemann solver, the self-gravitation of the disk, and the non-reflection boundary conditions. There are three important results: (1) The resonance effect spreads substantially beyond the maximum pattern speed, which is tangent to the curve, and hence beyond which there is no resonance. (2) For the case of self-gravitation, structural features in close resemblance with x1 and x2 orbits appear. (3) But in the case without self-gravitation, no x1 and x2 orbital features. The interaction of IILR and OILR produces a gas bar aligned with and therefore reinforcing the imposed bar. We will show results in movies. The work is in parts supported by a grant from National Science Council, Taiwan, NSC94-2752-M-001-002-PAE. Antares CodeTwo-dimensional high-order Godunov codes based on the exact Riemann solver, and featured with second order Poisson solver for disk self-gravitation and with characteristics decomposition to guarantee no reflection on the boundary. Axisymmetric Model We adopt the Elmegreen rotation curve, with which the angular velocity curve is depicted below. The curve has a plateau, under which there are two Lindblad resonances, the outer inner and the inner inner (OILR and IILR) and above which no resonance in the computing domain. The bar force and initial density of the gas are also depicted. Rotation Curve Lindblad Resonance Bell-Shape Density Bar Force Bar Orientation Case of no resonance Bar speed from left to right 25,30,35,40,50 km/s-kpc Resonance effect remains despite of no resonance, tapering off at high speeds. Evolution IILR-OILR inter-action, 1-5 turns, bar speed 15 km/s-kpc. No self-gravity. Gas forms a bar aligning with the imposed bar, eventually concentrated in the center. Evolution IILR-OILR inter- action at 1-5 turns of the bar, rotating speed 21 km/s-kpc, no self-gravitation. Gas spirals turn from leading to trailing. Gas bar parallel to the imposed bar. Double Ring & Instability Same as above, except self- gravity for the disk. Double rings form in resemblance to x1 & x2 orbits. Toomre instability results after 4 turns of the bar. Conclusion IILR adds amazing changes to the case of single resonance at OILR. The interaction results in bar-type responses aligned the imposed bar. (1) When the two resonances are more separate, like the case =15 km/s-kpc, a large gas bar forms, similar to the case of major bar galaxies. (2) When IILR & OILR are close, =21 km/s-kpc, the last two cases, there are major differences between with and without self-gravity. For the without, it is similar to case (1). But for the case with self-gravity, double rings form, in resemblance to x1 and x2 orbits in stellar dynamics. The outer ring x1 displays Toomre type of instability. (3) Resonance effect spreads beyond the resonance point. For the case of no resonance, as long as the bar speed is not too large, the gas response remains similar to the resonance case.