A plausible Galactic spiral pattern and its rotation speed

Mon. Not. R. Astron. Soc. 350, L47–L51 (2004) doi:10.1111/j.1365-2966.2004.07850.x A plausible Galactic spiral pattern and its rotation speed M. Martos,1 X. Hernandez,1 M. Yáñez,1 E. Moreno1 and B. Pichardo2 1 Instituto de Astronomı́a, Universidad Nacional Autónoma de México A. P. 70–264, México 04510 D.F., Mexico of Wisconsin, Department of Astronomy 475 N. Charter St. Madison, WI 53706, USA 2 University Accepted 2004 March 17. Received 2004 March 12; in original form 2004 January 27 ABSTRACT Key words: ISM: structure – Galaxy: fundamental parameters – Galaxy: kinematics and dynamics – Galaxy: structure – galaxies: spiral. 1 INTRODUCTION The comparison of near-infrared and optical images of external galaxies reveals interesting differences. Striking examples are M81 and NGC 2997 [see pictures in Elmegreen (1981) and Block et al. (1994), respectively]. It is common to observe a smooth, simple two-armed K-band pattern but a more complex pattern in the optical blue band, often suggesting more arms and bifurcations (segments of arms that appear to be connected to a K-band arm but are not detectable in the infrared). A two-armed smooth structure underlying a more complex morphology also appeared in the work of Grosbøl, Pompei & Patsis (2002); in a K-band study of 53 nearby spirals, most galaxies displayed a grand-design, two-armed, symmetric pattern in their inner regions which often breaks up into tighter-wound, multiple arms further out. Non-linear effects were invoked to explain such morphology.  E-mail:  C 2004 RAS In recent work, data from COBE-DIRBE have shed light into the Milky Way spiral pattern. Drimmel (2000) and Drimmel & Spergel (2001) have presented a comprehensive picture of what this pattern is like, presenting emission profiles of the Galactic plane in the K band and at 240 µm. The former data set, which suffers little absorption and traces density variation in the old stellar population, is dominated by a two-armed structure with a minimum pitch angle of 15.5◦ . At 240 µm, the pattern is consistent with the standard fourarmed model, that corresponding to the distribution of the youngest stellar populations delineated by H II regions. The conventional picture of the spiral pattern of our Galaxy maps at least four arms, named Norma, Crux–Scutum, Carina–Sagittarius and Perseus (for a recent review, see Vallée 2002, who also reports a likely pitch angle of 12◦ for this pattern). Additionally, features such as the Orion spur at the solar neighbourhood have been revealed (Georgelin & Georgelin 1976). Drimmel (2000) laid down, from the comparison, the hypothesis that the four-armed structure is the gas response to the two-armed ‘stellar’ pattern. Assuming that indeed the K-band data is by far a better tracer of mass than the optical data of spiral structure, in this work we We report calculations of the stellar and gaseous response to a Milky Way mass distribution model including a spiral pattern with a locus as traced by K-band observations, superimposed on the axisymmetric components in the plane of the disc. The stellar study extends calculations from previous work concerning the self-consistency of the pattern. The stellar response to the imposed spiral mass is studied via computations of the central family of periodic and nearby orbits as a function of the pattern rotation speed,  p , among other parameters. A fine grid of values of  p was explored, ranging from 12 to 25 km s−1 kpc−1 . Dynamical self-consistency is highly sensitive to  p , with the best fit appearing at 20 km s−1 kpc−1 . We give an account of recent independent pieces of theoretical and observational work that are dependent on the value of  p , all of which are consistent with the value found here: the recent star formation history of the Milky Way, local inferences of cosmic ray flux variations and Galactic abundance patterns. The gaseous response, which is also a function of  p , was calculated via 2D hydrodynamic simulations with the ZEUS code. For  p = 20 km s−1 kpc−1 , the response to a two-armed pattern is a structured pattern of four arms, with bifurcations along the arms and interarm features. The pattern qualitatively resembles the optical arms observed in our Galaxy and other galaxies. The complex gaseous pattern appears to be linked to resonances in stellar orbits. Among these, the 4:1 resonance plays an important role, as it determines the extent of the stellar spiral pattern in the self-consistency study presented here. Our findings seemingly confirm predictions by Drimmel & Spergel (2001), based on K-band data. L48 M. Martos et al. corotation and the outer Lindblad resonance (OLR). For galaxies with a bar perturbation, the extent of the main spiral was better fitted assuming it is limited by corotation and the OLR. Using H 0 = 75 km s−1 Mpc−1 , the pattern speed was found to be for the entire sample of the order of 20 km s−1 kpc−1 and, remarkably, was not a sensitive function of morphological type or total mass. In the following section, we describe our results for the stellar orbital response to the imposed spiral pattern, through which  p is determined. 2 O R B I TA L S E L F - C O N S I S T E N C Y M O D E L L I N G , I N F E R R I N G Ωp As in P1, our axisymmetric Galactic model is that of Allen & Santillán (1991), which includes a bulge and a flattened disc proposed by Miyamoto & Nagai (1975), together with a massive spherical dark halo. We coupled to this mass distribution a spiral pattern modelled as a superposition of inhomogeneous oblate spheroids along a locus that fits the K-band data of Drimmel (2000), with a pitch angle of 15.5◦ . P1 describes in detail the parameters of the spheroids, which briefly are that the minor axis of the spheroids is perpendicular to the Galactic plane and its length is 0.5 kpc, and that the major semi-axes have a length of 1 kpc. Each spheroid has a similar mass distribution. Different density laws, linear and exponential, were analysed, finding no important differences. The total mass in the spiral is fixed such that the local ratio of spiral to background (disc) force have a prescribed value. Seeking sensible values for this ratio, we used the empirical result of Patsis, Contopoulos & Grosbøl (1991), where self-consistent models for 12 normal spiral galaxies are presented, a sample including Sa, Sb and Sc galaxies. Their fig. 15 shows a correlation between the pitch angle of the spiral arms and the relative radial force perturbation. The forcing, proportional to the pitch angle, is increasing from Sa to Sc types in a linear fashion. For our pitch angle of 15.5◦ , the required ratio for self-consistency is between 5 and 10 per cent. As shown in P1, the ratio is a function of galactocentric distance R. The authors consider strong spirals to be those in which the ratio is 6 per cent or more. We found that, in order to obtain relative force perturbations in the 5 to 10 per cent range, our model requires a (...truncated)