The Orbital Structure of Triaxial Galaxies With Figure Rotation

Abstract

We survey the properties of all orbit families in the rotating frame of a family of realistic triaxial potentials with central supermassive black holes (SMBHs). In such galaxies, most regular box orbits (vital for maintaining triaxiality) are associated with resonances which occupy two-dimensional surfaces in configuration space. For slow figure rotation all orbit families are largely stable. At intermediate pattern speeds a significant fraction of the resonant box orbits as well as inner long-axis tubes are destabilized by the "envelope doubling" that arises from the Coriolis forces and are driven into the destabilizing center. Thus, for pattern rotation periods 2×10 8 yr T p 5×10 9 yr, the two orbit families that are most important for maintaining triaxiality are highly chaotic. As pattern speed increases there is also a sharp decrease in the overall fraction of prograde short-axis tubes and a corresponding increase in the retrograde variety. At the highest pattern speeds (close to that of triaxial bars), box-like orbits undergo a sudden transition to a new family of stable retrograde loop-like orbits, which resemble orbits in three-dimensional bars, and circulate about the short axis. Our analysis implies that triaxial systems (with central cusps and SMBHs) could either be very rapidly rotating like fast bars or slowly rotating like triaxial elliptical galaxies or dark matter halos found in N-body simulations. Collisionless triaxial systems that remain in stable dynamical equilibrium are unlikely to have intermediate pattern speeds which produce a high level of stochasticity in both the box and inner long-axis tube orbit families.

A Unified Framework for the Orbital Structure of Bars and Triaxial Ellipsoids

“…We find no prograde z-tubes parented by x2 orbits in the pure bar model (Model A) and only a small fraction of retrograde z-tubes (parented by x4 orbits) ( Figure 6). This is consistent with the behavior of short-axis tubes found in rotating triaxial potentials-retrograde members of the family dominate at high pattern speeds (Martinet & de Zeeuw 1988;Deibel et al 2011). However, in Model B, which has a central point mass representing a 0.2% SMBH, a significant fraction of the x1 and x-tube orbits are destroyed and replaced by prograde z-tube orbits (parented by x2 orbits).…”

“…Similarly, when we discuss shortaxis(long-axis) tubes, anticlockwise motion about the z-axis (x-axis) corresponds to positive angular momentum J z (J x ). Deibel et al (2011) ( ) ( ) = --= and a weak cusp (γ=0.1). This shape is quite close to that of the bars in our N-body simulations.…”

“…This results in a higher central stellar density in the bar than in the axisymmetric model. The differences between Model A and Model B arise as a result of two effects: (a) elongated orbits, e.g., x1 orbits and x-tubes are unable to survive the growth of the central point mass, which makes the potential more axisymmetric (Deibel et al 2011); and(b) inflow of matter from large radii with positive angular momentum results in the formation of prograde z-tube orbits seen in the SoS, which did not exist in the original bar. …”

“…Finally, while short-axis tubes remain stable under figure rotation, the phase space occupied by prograde short-axis tubes decreases dramatically with increasing pattern speed, and theyare increasingly replaced by retrograde short-axis tubes (Martinet & de Zeeuw 1988;Deibel et al 2011).…”

“…Since the loop orbits circulating around the long axis are the parents of the long-axis tube family in a stationary triaxial potential, it follows that the stable anomalous orbits parent the long-axis tube families in a rotating triaxial potential. Consequently, long-axis tube orbits are also tipped about the intermediate axis in a rotating system (Deibel et al 2011).…”