Gasflows in Barred Galaxies with Big Orbital Loops-A Comparative Study of Two Hydrocodes

TL;DR

This study investigates gas dynamics in barred galaxies where big loops in x1 and n:1 periodic orbits create complex orbital backgrounds, focusing on the region between the 4:1 resonance and corotation. By comparing two hydrodynamic codes, SPH and RAMSES, under the same rotating-bar potential, the authors show that gas shocks avoid large x1 loops and instead develop angled extensions with Gamma-like features, accompanied by dense tails toward the shocks. The results reveal complementary insights: SPH provides fine-grained velocity fields with replenishment-driven stationarity, while RAMSES exposes a quasi-periodic cycle with a mean morphology and sensitivity to resolution and sound speed. The findings tie gas morphology directly to the underlying orbital structure, including a chaotic envelope around the x1 bar, and have implications for interpreting dust lanes and gas flows in real barred galaxies.

Abstract

We study the flow of gas in a barred-galaxy model, in which a considerable part of the underlying stable periodic orbits have loops where, close to the ends of the bar, several orbital families coexist and chaos dominates. Such conditions are typically encountered in a zone between the 4:1 resonance and corotation. The purpose of our study is to understand the gaseous flow in the aforementioned environment and trace the morphology of the shocks that form. We use two conceptually different hydrodynamic schemes for our calculations, namely, the mesh-free Lagrangian SPH method and the adaptive mesh refinement code RAMSES. This allows us to compare responses by means of the two algorithms. We find that the big loops of the orbits, mainly belonging to the x1 stable periodic orbits, do not help the shock loci to approach corotation. They deviate away from the regions occupied by the loops, bypass them and form extensions at an angle with the straight-line shocks. Roughly at the distance from the center at which we start to observe the big loops, we find characteristic "tails" of dense gas streaming towards the straight-line shocks. The two codes give complementary information for understanding the hydrodynamics of the models.

Figures (18)

• Figure S1: The circular speed $v_c=\sqrt{r \frac{d\Phi_0}{dr}}$ (a) and the k = 2 (b), k = 4 (c) and k = 6 (d) components of the potential, normalized by $\Phi_0$, as a function of the radius $r$. From (b--d), magenta curves refer to the cosine and green to the sine terms.
• Figure S2: (a--h): Successive snapshots of the stellar response model. Lighter regions correspond to denser regions, according to the logarithmic color bar at the bottom of the panels. The number of pattern rotations is given at the upper-left corner of the frames. The red dots indicate the location of L$_1$ (top), L$_2$ (bottom), L$_4$ (right) and L$_5$ (left) of the bar. The bar rotates counterclockwise.
• Figure S3: Characteristics of the main families of POs, x1 and f, projected in the ($E_J$, $x_0$) plane. Stable parts of these curves are plotted with black, while unstable with red, color. The zero-velocity curve is the thick green curve, having at its local maximum the L$_4$ point. The area between the $E_J$'s of L$_1$ and L$_4$ is shaded with cyan color. In the embedded frame, we give an enlargement of the characteristics of all main families close to the center of the system (see text). The x2-x3 loop is plotted with magenta, the x1 characteristic with balck and that of x4 with blue color.
• Figure S4: Periodic orbits with loops. (a) Stable orbits of x1 are plotted with black and an unstable f with pairs of loops at its apocenters is plotted with grey. (b) Two stable f orbits (black and cyan) and an unstable in grey. (c) POs with loops beyond the 4:1 resonance. The grey belongs to f, while the two others (black and cyan) to x1.
• Figure S5: (a) Three orbits with loops, plotted with black, green and red color) that follow different paths and eventually cross the corotation region $((x_{L_{1,2}}, y_{L_{1,2}}) = (\pm1.21, \pm9.65))$. (b) The central part of the $(x,\dot{x})$ surface of section at $E_J=-$111,723. The location of x1 and f are indicated with a green and magenta dot, respectively. The left empty part (roughly for $x<-0.5$) is occupied by invariant curves around x4 (not plotted), while the empty part for $x>-0.5$ is due to the fact that orbits with initial conditions in this region are practically escape orbits (they intersect the surface of section at large distances, outside the frame of panel).