Dynamically possible pattern speeds of double bars

TL;DR

This paper introduces a new method based on invariant loops to analyze how the orbital structure of double-barred galaxies varies with the pattern speed of the inner bar, revealing constraints on possible speeds and structural changes.

Contribution

A novel, more understandable approach using invariant loops to study the orbital dynamics of double bars and their dependence on pattern speed.

Findings

Not all pattern speeds are feasible for co-rotating inner bars.

Orbital support disappears below a minimum pattern speed.

Higher pattern speeds produce more round loops.

Abstract

The method to study oscillating potentials of double bars, based on invariant loops, is introduced here in a new way, intended to be more intelligible. Using this method, I show how the orbital structure of a double-barred galaxy (nested bars) changes with the variation of nuclear bar's pattern speed. Not all pattern speeds are allowed when the inner bar rotates in the same direction as the outer bar. Below certain minimum pattern speed orbital support for the inner bar abruptly disappears, while high values of this speed lead to loops that are increasingly round. For values between these two extremes, loops supporting the inner bar extend further out as its pattern speed decreases, and they become more eccentric and pulsate more. These findings do not apply to counter-rotating inner bars.