Arm morphology in off-centre barred galaxies

Many barred galaxies, including the Large Magellanic Cloud (LMC), display strong lopsidedness and off-centre bars. The dynamical connection between bar–disc misalignments, internal-mass asymmetries, and arm morphology has not yet been fully characterised. We aim to investigate how internal-mass imbalances within the bar and global offsets between the bar and the centre of mass (CM) of the system modify the equilibrium-point structure and the invariant manifolds that organise arms. We constructed a barred galaxy model that includes an off-centred and asymmetrically shaped bar. Using numerical continuation, we tracked the position, stability, and bifurcations of the Lagrangian equilibrium points as functions of the displacement of the asymmetric mass component along the bar and of the offset between the bar and the system’s CM. For representative configurations we computed the invariant manifolds of planar Lyapunov orbits around unstable points and analysed the resulting arm structures. Internal bar lopsidedness and modest bar–disc offsets that keep the CM inside the bar preserve the classical configuration with five equilibrium points, but strongly distort the associated invariant manifolds, producing two arms with different densities and shapes. The bar–disc offset reaches a threshold at the point at which the galactic CM exits the bar ellipsoid, in which a pitchfork bifurcation removes the collinear unstable points and the system transitions to a three-equilibrium-point configuration; there, a single unstable point and its associated manifold support one arm. Internal inhomogeneities in the bar's density and modest bar–disc offsets dynamically support two asymmetric arms, while larger offsets drive a transition to one-armed structures. This framework is compatible with the observed correlation between off-centre bars and photometric lopsidedness, and it provides a dynamical explanation for the strongly asymmetric arm morphology of galaxies such as the LMC.