Modelling the inner disc of the Milky Way with manifolds – I. A first step

Mon. Not. R. Astron. Soc. 418, 1176–1193 (2011) doi:10.1111/j.1365-2966.2011.19569.x Modelling the inner disc of the Milky Way with manifolds – I. A first step M. Romero-Gómez,1 E. Athanassoula,2 T. Antoja3 and F. Figueras1 1 Dept. d’Astronomia i Meteorologia, Institut de Ciències del Cosmos (ICC), Universitat de Barcelona (IEEC-UB), Martı́ i Franquès 1, E08028 Barcelona, Spain 2 Laboratoire d’Astrophysique de Marseille (LAM), UMR6110, CNRS/Université de Provence, Technopôle de Marseille Etoile, 38 rue Frédéric Joliot Curie, 13388 Marseille Cédex 20, France 3 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, the Netherlands ABSTRACT We study the bar-driven dynamics in the inner part of the Milky Way by using invariant manifolds. This theory has been successfully applied to describe the morphology and kinematics of rings and spirals in external galaxies, and now, for the first time, we apply it to the Milky Way. In particular, we compute the orbits confined by the invariant manifolds of the unstable periodic orbits located at the ends of the bar. We start by discussing whether the COBE/Diffuse Infrared Background Experiment (DIRBE) bar and the Long bar compose a single bar or two independent bars and perform a number of comparisons which, taken together, argue strongly in favour of the former. More specifically, we favour the possibility that the so-called COBE/DIRBE bar is the boxy/peanut bulge of a bar whose outer thin parts are the so-called Long bar. This possibility is in good agreement both with observations of external galaxies, with orbital structure theory and with simulations. We then analyse in detail the morphology and kinematics given by five representative Galactic potentials. Two of these have a Ferrers bar, two have a quadrupole bar and the last one a composite bar. We first consider only the COBE/DIRBE bar and then extend it to include the effect of the Long bar. We find that the large-scale structure given by the manifolds describes an inner ring, whose size is similar to the near and far 3-kpc arm, and an outer ring, whose properties resemble those of the Galactic Molecular Ring. We also analyse the kinematics of these two structures, under the different Galactic potentials, and find they reproduce the relevant overdensities found in the galactic longitude–velocity CO diagram. Finally, we consider for what model parameters, the global morphology of the manifolds may reproduce the two outer spiral arms. We conclude that this would necessitate either more massive and more rapidly rotating bars, or including in the potential an extra component describing the spiral arms. Key words: Galaxy: bulge – Galaxy: disc – Galaxy: evolution – Galaxy: kinematics and dynamics – Galaxy: structure – galaxies: spiral. 1 I N T RO D U C T I O N The large-scale structure of the Milky Way (MW) disc has been under study for many years. The COBE/Diffuse Infrared Background Experiment (DIRBE; Weiland et al. 1994) and Spitzer/Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE; Churchwell et al. 2009) missions provided infrared information on the global structure of the inner Galaxy. Even though these studies have provided some light, the large-scale structure of the MW disc proves to be highly complex. Near- and mid-infrared (IR) lowresolution images detected the COBE/DIRBE bar (Weiland et al. 1994), also referred to as the triaxial bulge or the COBE/DIRBE bar.  E-mail: Near-IR red clump giants of the mid-plane revealed the existence of a second bar (Hammersley et al. 2000; López-Corredoira et al. 2007; Cabrera-Lavers et al. 2008), and confirmed by GLIMPSE (Benjamin et al. 2005), usually referred to as the Long bar. Observations suggest two other large-scale structures towards the inner parts of the Milky Way, namely the near and far 3-kpc arms (Kerr 1964; Dame & Thaddeus 2008) and the Galactic Molecular Ring (GMR; Clemens, Sanders & Scoville 1988). Although their characteristics or even their existence are currently being under debate (Dame & Thaddeus 2011), here we aim to bring some light given the observed characteristics up-to-date. The near and far 3-kpc arms were detected using the H I 21-cm line and CO emission surveys and extend roughly parallel to the COBE/DIRBE bar, whereas the position of the GMR is not so well determined. Clemens et al. (1988) suggested it is located at ∼5.5 kpc from the Galactic Centre, while  C 2011 The Authors C 2011 RAS Monthly Notices of the Royal Astronomical Society  Accepted 2011 August 2. Received 2011 August 2; in original form 2011 April 11 Manifolds in the inner disc of the Milky Way  C 2011 The Authors, MNRAS 418, 1176–1193 C 2011 RAS Monthly Notices of the Royal Astronomical Society  potentials to the COBE/DIRBE bar, and we use the same set of parameters as they do. The paper is organized as follows. In Section 2, we discuss whether our Galaxy has a single or a double bar, using arguments from the morphology of external galaxies, from orbital structure theory and from N-body simulations. We also describe the models and compare them in detail in terms of forces. In Section 3, we give a brief summary of the dynamics driven by the unstable Lagrangian points and, in particular, the definition of the invariant manifolds. We also give a brief summary of the main relevant results found in Papers I–V. In Section 4, we compute the invariant manifolds for the selected models and we analyse them in terms of morphology and kinematics. The results are compared to the observables in Section 4.3. In Section 5, we explore the parameter space and determine in which cases the manifolds could reproduce outer spiral arms. Finally, we give a short summary and conclusions in Section 6. In the appendix, we describe in detail the analytical models and give the default parameters used. 2 M O D E L L I N G T H E G A L AC T I C P OT E N T I A L 2.1 Analytical models There are several analytical models in the literature used to model the MW Galaxy. They essentially consist of an axisymmetric plus a one-bar component. Each model has been constructed to model the MW and in the appendix of this paper we give a brief description of the potentials used and their default parameters. We want to stress here that we will consider the same parameters as these studies. The axisymmetric component describes the disc, halo and bulge of the Galaxy and in each model it is modelled in a different way. The models considered in this paper are the following. (i) Melnik & Rautiainen (2009, hereafter MR09) and Gardner & Flynn (2010, hereafter GF10) both use a Ferrers bar (Ferrers 1877), though the purpose of each of the papers is very different. The former uses the bar potential in test particle simulations to model the kinematics of the outer rings and spirals of the Galaxy and to compare it with the residual velocities of OB associations in the Perseus and Sagittarius regions. The latter studies the (...truncated)