Hydrodynamical simulations of the barred spiral galaxy NGC 6782

1. Hydrodynamical simulations of the barred spiral galaxy NGC 6782 Lien-Hsuan Lin1,2 , Chi Yuan1,2, and R. Buta3 1Department of Physics, National Taiwan University, Taiwan, R.O.C. 2Institute of Astronomy and Astrophysics, Academia Sinica, Taiwan, R.O.C 3Department of Physics and Astronomy, University of Alabama, Alabama, U.S.A. Abstract NGC 6782 is a type (R1R2’)SB(r)a galaxy with multiple ring patterns. It has a nearly circular bright nuclear ring connected with a pair of almost straight dust lanes, the other ends of which attach to a diamond-shaped (or pointy oval) inner ring. Two faint arms in turn extend from the two tips of the inner ring to the outermost parts of the galaxy, forming a faint double outer ring-pseudoring morphology. In this study we use numerical simulations to show that such striking features can be reproduced by imposing a strong bar to a gaseous disk system. Since strong bar potentials may, through instabilities, lead to chaotic sub-structures, they present challenging problems to the numerical simulations. Our simulations are performed with our own Antares code, which employs Cartesian coordinates and the higher-order Godunov scheme with unsplit flux calculated from the exact Riemann solver. Calculations are carried out with and without self-gravitation, which produce similar results. In both cases, the bar is able to drive spiral density waves simultaneously at both the outer Lindblad resonance (OLR) and the inner Lindblad resonance (ILR). When the bar potential is strong enough, 4:1 higher harmonic spiral density waves are excited, which interact with waves excited at the ILR and give rise to the diamond-shaped structure. All the essential features are in excellent agreement with observations. Our work is in part supported by National Science Council, Taiwan, NSC95-2752-M-001-009-PAE, and by NSF grant AST050-7140. Observations Fig. 1 is a multicolor optical image of NGC 6782 released by Space Telescope Science Institute in 2002. Fig. 2 is a B-band image and Fig. 3 is the 2D Fabry-Perot velocity field which is observed by R. Buta using the CTIO 4-m telescope. The detector scale is 0.349 arcsec/pixel corresponding to a field of view of about 3.6 x 3.6 arcminutes. These images have north at top, east to left. The PA of the major bar of the galaxy is 177°. The IA of the galaxy is 27° and the PA of the line of nodes is 35°. Fig. 4 is the rotation curve derived from the velocity field of Fig. 3. Fig. 1 Fig. 2 Fig. 3 Numerical method and simulations We use the higher-order Godunov method with 2nd-order accuracy which employs the exact Riemann solver on Cartesian coordinates, so the problem with the inner boundary conditions is avoided. Cases involving self-gravitation are solved by FFT Poisson solvers. The initial conditions are a bell-shaped surface density distribution and a circular motion corresponding to the nearly flat rotation curve (green line in Fig. 4) which is fitted from the observed rotation curve. From this fitted rotation curve, we obtain the angular velocity curves plotted in Fig. 5. The bar potential adopted is shown in Fig. 6 and the angular speed of the bar is chosen to be 25 km/s/kpc. Fig. 4 Fig. 5 Fig. 6 Simulations vs Observations Fig. 7 is the projected density distribution of the simulation result. Its superimpositions onto Figs. 1 and 2 are shown in Figs. 8 and 9 respectively. Fig. 8 shows that for the nuclear ring, the dust lanes, as well as the pointy oval inner ring, Fig. 7 Fig. 8 Fig. 9 simulation results match well with observations. At the northwestern outer arm in Fig. 2, there are two faint branches near the tip of the inner ring, which are also reproduced by our simulation. The only part our simulation cannot fit well is the outer part of the outer arms. The arms in our simulation are much broader than those in observation. Fig. 10 is the velocity field of the simulation result. Fig. 11 shows the superposition of its contours and the observation. It is particular noteworthy that at the southeastern part of the inner ring, the contours bend outwards along the spiral arms for both simulation and observation. It is one of the distinct features for the density waves excited at the ILR. Self-gravitation Figs. 12 and 13 are the results for our simulations in the absence and presence of self-gravitation respectively. They are almost identical except for a slight difference around the very high-density nuclear rings. Fig. 10 Fig. 11 Conclusions In this study, we successfully use a simple model to explain almost all the striking features of NGC 6782.  We confirm it to be a moderately strong barred galaxy, in agreement with Buta and Block 2001. To obtain the good fit with observations, the pattern speed of the bar has to be slow, which is consistent with the view of Byrd et al. 1994 that NGC 6782 is a slow pattern speed barred galaxy. Moreover, we believe self-gravitation of the gas disk is unimportant in this case. Fig. 12 Fig. 13