Gas dynamics in the Milky Way: second pattern speed and large-scale morphology

Nicolai Bissantz 0 Peter Englmaier Ortwin Gerhard Astronomisches Institut Universitat Basel Venusstrasse CH- Binningen Switzerland Max-Planck Institut fur extraterrestrische Physik Garching Germany 0 Now at: Institut fur Mathematische Stochastik der Universitat Gottingen , Lotzestr. 13, 37083 Gottingen, Germany A B S T R A C T We present new gas flow models for the Milky Way inside the solar circle. We use smoothed particles hydrodynamics (SPH) simulations in gravitational potentials determined from the near-infrared (NIR) luminosity distribution of the bulge and disc, assuming a constant NIR mass-to-light ratio, with an outer halo added in some cases. The luminosity models are based on the COBE/DIRBE maps and on clump giant star counts in several bulge fields and include a spiral arm model for the disc. Gas flows in models that include massive spiral arms clearly match the observed 12CO (l, v) diagram better than if the potential does not include spiral structure. Furthermore, models in which the luminous mass distribution and the gravitational potential of the Milky Way have four spiral arms are better fits to the observed (l, v) diagram than two-armed models. Besides single-pattern speed models we investigate models with separate pattern speeds for the bar and spiral arms. The most important difference is that in the latter case the gas spiral arms go through the bar corotation region, keeping the gas aligned with the arms there. In the (l, v) plot this results in characteristic regions that appear to be nearly devoid of gas. In single-pattern speed models these regions are filled with gas because the spiral arms dissolve in the bar corotation region. Comparing with the 12CO data we find evidence for separate pattern speeds in the Milky Way. From a series of models the preferred range for the bar pattern speed is p = 60 5 Gyr1, corresponding to corotation at 3.4 0.3 kpc. The spiral pattern speed is less well constrained, but our preferred value is sp 20 Gyr1. A further series of gas models is computed for different bar angles, using separately determined luminosity models and gravitational potentials in each case. We find acceptable gas models for 20 bar 25. The model with (bar = 20, p = 60 Gyr1, sp = 20 Gyr1) gives an excellent fit to the spiral arm ridges in the observed (l, v) plot. - Observations of cold gas in the Milky Way (MW) have contributed substantially to our understanding of MW structure. No other tracer is observed in as large a part of the MW as are gas clouds. Longitudevelocity (lv) diagrams (Hartmann & Burton 1997; Dame, Hartmann & Thaddeus 2001) show the distribution of gas velocities as a function of galactic longitude l, integrated over some range in latitude b. By observing the MW in different spectral lines, this gas can be traced at substantially different densities. The largest absolute velocity as a function of l defines the terminal velocity curve (TVC). In an axisymmetric galaxy, the gas at these velocities is found at the tangent point where the line of sight is tangential to a circle around the Galactic Centre. From this the rotation curve can be determined. However, owing to the bar and spiral perturbations in the MW potential, the gas has substantial non-circular velocities, which are most evident in the central 1020, owing to the bar, but also as bumps in the TVC where spiral arm tangents perturb the gas flow by 1020 km s1. At subTVC velocities, crowding in both position and in velocity produces ridge-like structures in the (l, v) diagram. The Galactic spiral arms are visible as straight or curved such ridges. A number of attempts have been made to model these observations. One group is formed by analytic models of spiral structure. The first exhaustive analytical formulation of a spiral arm theory was developed by Lin & Shu (1964) and applied to the MW by Lin, Yuan & Shu (1969). They proposed a two-armed model with a pitch angle of 6 and a pattern speed for the spiral structure sp 13.5 km s1 kpc1. Amaral & Lepine (1997) fitted the rotation curve of the MW to an analytic mass model and found a self-consistent solution with a combined two- and four-armed spiral structure. In Lepine, Mishurov & Dedikov (2001) they extended this model to allow for a phase difference between the two- and the four-armed spiral pattern. The second group, numerical simulations of the Galactic gas flow, also have a long tradition. A recent example is the smoothed particles hydrodynamics (SPH) models of Fux (1999), who evolved a gas disc inside a self-consistent N-body model scaled to the COBE/DIRBE K-band map of the MW and the radial velocity dispersion of M giants in Baades window. The resulting gas flow was transient, but at specific times closely resembled a number of observed arms and clumps in the bar region. Weiner & Sellwood (1999) compared predictions from fluid dynamic simulations for analytic mass densities with the observed outer velocity contours of the H I (l, v) diagram to constrain the pattern speed and bar angle. Englmaier & Gerhard (1999) (hereafter, Paper I) computed gas flows in the gravitational potential of the near-infrared (NIR) luminosity distribution of Binney, Gerhard & Spergel (1997), assuming a constant NIR mass-to-light ratio (M/L). Their best SPH gas flow models reproduced quantitatively a number of observed gas flow features, including the positions of the five main spiral arm tangents at |l| 60 and much of the terminal velocity curve. An important feature of all of these gas flow models is the pattern speed of the non-axisymmetric component. Englmaier & Gerhard found a best pattern speed for the bar p 60 km s1 kpc1. Weiner & Sellwood derived a bar pattern speed of 42 km s1 kpc1, whereas Fux determined 50 km s1 kpc1 from his models. Dehnen (2000) used resonant features in the Hipparcos stellar velocity distribution to argue that the Sun is located just outside the OLR of the exciting quadrupole perturbation, giving a pattern speed of 51 km s1 kpc1 for solar constants R0 = 8 kpc and v0 = 220 km s1. For their spiral structure model, Amaral & Lepine (1997) and Lepine et al. (2001) found sp 2035 Gyr1. Fernandez, Figueras & Torra (2001) obtained a somewhat higher sp 30 km s1 kpc1 from Hipparcos data for OB stars and Cepheids. Debattista, Gerhard & Sevenster (2002) used the TremaineWeinberg method on a sample of intermediate age to 8-Gyr old OH/IR-stars in the inner Galactic disc. They found a pattern speed of 59 5 10 (systematic) km s1 kpc1, which may be driven by the bar in the centre of the MW. Thus the bar and spiral arms in the MW may not rotate with the same pattern speed. For a fast bar, a single p would imply that the spiral arms are entirely outside their corotation radius. Observations of external galaxies (see, e.g., the Hubble Atlas of Galaxies, Sandage 1961) suggest that galaxies exist with dust lanes on the inner (concave) edges of their spiral arms. For a trailing spiral pattern, these arms would be in (...truncated)