RESPONSE OF GALACTIC GAS DISK TO A SPIRAL POTENTIAL

1. RESPONSE OF GALACTIC GAS DISK TO A SPIRAL POTENTIAL H.H. Wang13, Chi Yuan13 and David Yen12 1Institute of Astronomy and Astrophysics, Academia Sinica, Taiwan, R.O.C. 2Department of Mathematics, Fu-Jen Catholic University, Hinchuang, Tapei Hsien, Taiwan, R.O.C. 3Department of Physics, National Taiwan University Abstract We use the gasdynamic simulations to investigate the response of a gaseous disk to the logarithmic spiral potential without self-gravity in disk galaxies. Our simulations are performed on the Cartesian coordinate version of the Antares codes, the codes we have recently developed by using finite volume scheme and Godnov’s method. The results show the distinct difference between waves generated by the resonance excitation and the forced oscillation. Logarithmic spiral potentials are adopted and are arranged into two cases: (1) It covers from the inner Lindblad resonance (ILR) to the outer Lindblad resonance (OLR) and (2) from ILR to the co-rotation. To avoid the confusion of mixing waves generated from resonance excitation and from forced oscillation by the imposed spiral potential, we substantially reduce the strength of the spiral potential near the resonances. In the case (1), the result shows the shock wave solution ceases to exist near the co-rotation as expected by the asymptotic analysis. The shock waves formed inside the co-rotation radii lies in the inner side of the spiral potential, and those formed outside the co-rotation radii lies outside the spiral potential. In the case (2), we identify the four-armed structure formed in the central part of the galaxies as the first ultra-harmonic excitation waves. However, the overall pattern soon is dominated by the spill-over (spur-like) phenomenon, which can be identified as the crowding of the streamlines. The results are different from the work of Chakrabarti; Laughlin and Shu, F. H. (2003), which does not distinguish the effects from resonance excitation and forced oscillation. (f) gas density distribution (a) turn 1 (b) turn 4 (c) turn 7 (d) turn 10 (e) spiral potential Fig. 1. Sequential snapshots of the gas response to the spiral potential at different turns. The locations of ILR, CR and OLR are at 3kpc, 12kpc and 22kpc, respectively. The imposed periodic spiral stretches from 6 kpc to 10 kpc as shown in (e). The evolution of gas density distribution in radial direction at different turns is shown in (f). From left to right, clear four arms are formed in the central part of the galaxy, and the spur-like structure protruding from the main spiral manifests the streamlines of the gas. (c) turn 7 (a) turn 1 (b) turn 4 (d) turn 10 (e) spiral potenrial (f) gas density distribution Fig. 2. Sequential snapshots of the gas response to the spiral potential at different turns. The locations of ILR, CR and OLR are at 3kpc, 12kpc and 22kpc, respectively. The imposed periodic spiral stretches from 6 kpc to 18 kpc as shown in (e). The evolution of gas density distribution in radial direction at different turns is shown in (f). From (a) to (d), the spiral shocks break around the radii of corotation. (a) turn 1.5 (b) turn 3 ( c) turn 6 Fig. 3. Snapshots as the instability occur, left, surface density and right, vorticity divided by surface density. In (a), wiggles appear at the spiral shock region and move in along the main spiral. At the shock, vorticity divided by surface density has local extreme, which gives rise to a Rayleigh-type shear instability. In (b) and (c ), the instability apparently is associated with the the streamlines, along which the value of vorticity divided by surface density is supposed to remain constant in the rotating frame of the imposed spiral potential, and the local unstable regions eventually form a ring. Concluding Remark (1) The grid number used in Fig. 1. and Fig. 2 are 512 x 512. While simulations in lower resolution are stable, higher resolution, say 1024 x 1024 as shown in Fig. 3., however, are unstable. We believe that it belongs to the Rayleigh’s shear instability. For compressible fluid, the vorticity divided by surface density plays the role of vorticity. Once it has an extremum, the instability results, according to Rayleigh. (2) The phenomenon of discontinuity of the shock solution near the corotaion radii is different from the work of Chakrabarti; Laughlin and Shu, F. H. (2003). We suspect that their spiral waves are mainly excited at the Lindblad resonance by the periodic spiral forcing, not the forced oscillation waves studied by Roberts (1969).