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

Abstract

We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these bars are classified both visually and with a new automated orbit classification method based on frequency analysis. The well-known prograde x1 orbit family originates from the same parent orbit as the box orbits in stationary and rotating triaxial ellipsoids. However, only a small fraction of bar orbits (∼4%) have predominately prograde motion like their periodic parent orbit. Most bar orbits arising from the x1 orbit have little net angular momentum in the bar frame, making them equivalent to box orbits in rotating triaxial potentials. In these simulations a small fraction of bar orbits (∼7%) are long-axis tubes that behave exactly like those in triaxial ellipsoids: they are tipped about the intermediateaxis owingto the Coriolis force, with the sense of tipping determined by the sign of their angular momentum about the long axis. No orbits parented by prograde periodic x2 orbits are found in the pure bar model, but a tiny population (∼2%) of short-axis tube orbits parented by retrograde x4 orbits are found. When a central point mass representing a supermassive black hole (SMBH) is grown adiabatically at the center of the bar, those orbits that lie in the immediate vicinity of the SMBH are transformed into precessing Keplerian orbits thatbelong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH,the inflow of mass and outward transport of angular momentum transformsome x1 and long-axis tube orbits into prograde short-axis tubes. This study has important implications for future attempts to constrain the masses of SMBHs in barred galaxies using orbit-based methods like the Schwarzschild orbit superposition scheme and for understanding the observed features in barred galaxies.

The chemistry of stars in the bar of the Milky Way

“…These pencil thin bar orbits cover a galactocentric radial velocity range -80 km s −1 to 80 km s −1 in steps of 20 km s −1 . As expected, the model bar orbits lie in the region of these pencil thin orbits with a scatter due to the width of the bar and its underlying orbits (Valluri et al 2016).…”

Orbital classification in anN-body bar

“…Both of them have been successfully applied to various potential systems (e.g. Papaphilippou & Laskar 1998;Valluri et al 2010;Bryan et al 2012;Valluri et al 2016). …”

“…An alternative route, much nearer to the N-bodies, is to freeze the simulation potential at a representative time and then follow in it orbits with initial conditions obtained from the positions and velocities of the simulation particles at that chosen time (Athanassoula 2002(Athanassoula , 2003(Athanassoula , 2005Martinez-Valpuesta et al 2006;Voglis et al 2007;Wozniak & Michel-Dansac 2009;Valluri et al 2012Valluri et al , 2016. This approach has a number of advantages.…”

Anatomy of a buckling galactic bar

“…Combes et al (1990) and Pfenniger & Friedli (1991) were the first to propose that the instability results from trapping x1 orbits of the bar at vertical resonances. However, such resonances are expected to apply only to banana-like orbits that have been shown to contribute only a little to the final boxy/peanut shape (Patsis et al 2002;Portail et al 2015;Valluri et al 2016;Abbott et al 2017;Patsis & Harsoula 2018). An alternative hypothesis for the origin of the instability involves the ratio of the vertical to horizontal velocity dispersion of the stars in the bar and relates it to the fire-hose instability (Toomre 1966;Raha et al 1991;Merritt & Hernquist 1991;Merritt & Sellwood 1994).…”