Letter to the Editor

Phase-space distortion as a key to unraveling galactic bar buckling

¹ St. Petersburg State University, Universitetskij Pr. 28, 198504 St. Petersburg, Stary Peterhof, Russia
² Central (Pulkovo) Astronomical Observatory of RAS, Pulkovskoye Chaussee 65/1, 196140 St. Petersburg, Russia

^⋆ Corresponding author: n.sotnikova@spbu.ru

Received: 28 March 2025
Accepted: 30 May 2025

Abstract

For the first time, we investigate the resonant structure of N-body galactic bar at the stage of buckling using action-angle variables. We studied the evolution of vertical actions (J_z) and angles associated with vertical resonance (θ_res = θ_z − θ_R) for all orbits in the bar. For this purpose, we divided the orbits into types according to the behavior (libration or circulation) of their resonant angle with respect to fixed points θ_res = 0 and π (vertical resonance). We show that during buckling, flat bar orbits circulating with increasing θ_res transformed into banana-shaped librating orbits (resonant capture) or circulating orbits with decreasing θ_res (resonant heating). The orbital transformation is accompanied by an increase in J_z and the formation of a boxy- or peanut-shaped bulge. During buckling, the phase space J_z − θ_res undergoes a distortion creating an asymmetry in the position of the fixed points θ_res = 0 and π and in banana-shaped orbits near these points. The fixed point θ_res = 0 may disappear completely. This also breaks the symmetry between the orbits, which are captured into resonance or go into circulation with decreasing θ_res near θ_res = 0 and π. At the same time, near θ_res = 0, banana-shaped orbits with low vertical action J_z appear. This reopens the path of orbital transformation through the fixed point, θ_res = 0. The phase space transformation and orbit transformation occur in a coordinated manner and lead to the smoothing of phase space perturbations and restoration of symmetry between orbits.