The Astrophysical Journal, 615:758–766, 2004 November 10 # 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A. THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC MODELING OF THE GASEOUS STRUCTURE OF THE GALAXY: SYNTHETIC OBSERVATIONS Gilberto C. Go´mez1 Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706; [email protected] and Donald P. Cox Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, WI 53706; [email protected] Receivved 2003 October 9; accepted 2004 July 15 ABSTRACT We generate synthetic observations from the four-arm model we presented previously for the Galactic ISM in the presence of a spiral gravitational perturbation. We find that velocity crowding and diffusion have a strong effect in the longitude-velocity (l-v) diagram. The velocity-latitude (v-b) diagram presents structures at the ex- pected spiral arm velocities, which can be explained by the off-the-plane structure of the arms presented in previous papers of this series. Such structures are observed in the Leiden/Dwingeloo H i survey. The rotation curve, as measured from the inside of the modeled galaxy, shows similarities with the observed one for the Milky Way, although it has large deviations from the smooth circular rotation corresponding to the background potential. The magnetic field inferred from a synthetic synchrotron map shows a largely circular structure but with interesting deviations in the midplane due to distortion of the field from circularity in the interarm regions. Subject headings:g galaxies: spiral — galaxies: structure — ISM: kinematics and dynamics — ISM: magnetic fields — MHD 1. INTRODUCTION tion in the midplane. As it shocks, the gas shoots up to higher z Our position inside the Milky Way allows us to make ob- in a way similar to water jumping over an obstacle in a river- servations at a much higher spatial resolution that we could bed. The gas then accelerates as it runs over the arm and falls do in other disk galaxies. But that same fact makes it much down behind it, generating a secondary set of shocks. In the more difficult to infer the large-scale characteristics of our two-arm cases, the gas bounces back up, generating interarm home Galaxy. A lot of the current questions of the spiral struc- structures that mimic the ones found at the arms. ture of the Milky Way could be resolved if we knew the po- In this work we focus on the four-arm case, designed to have sition and full velocity vector of the observed gas. Numerical spiral arms similar to those traced by Georgelin & Georgelin studies of large-scale Galactic structure have proved to be very (1976) as modified by Taylor & Cordes (1993). In Figure 1 valuable in discerning the sought-after characteristics. Never- we show the surface density of the four-arm model from theless, this is a very complicated problem, and so far, it is Paper II, along with the aforementioned arm pattern and the impossible to include all the physics involved. Therefore, mod- corresponding position of the Sun. Note that the scale of the elers must decide which parts of the problem are not going to spiral arms has been reduced so that the distance from the Sun be considered, in the hope that those neglected will have little to the Galactic center is 8 kpc, as in our model. In x 2wepre- influence in the overall conclusions. The models presented sent all-sky column-density maps in radial velocity ranges; in here do not include self-gravity of the gas, supernova explo- x 3 we present synthetic longitude-velocity diagrams; in x 4we sions, or other energetic events and have uncomfortably low present velocity-latitude diagrams, which we believe have a spatial resolution. They include a substantial magnetic field, a definite signature of these models; in x 5 we present the rota- high thermal pressure (to represent tangled fields, cosmic rays, tioncurvethatwouldbemeasuredinthisGalaxyasaffected and subgrid turbulence), and the extra degree of freedom of by the spiral arms; in x 6 we analyze the arm’s effect on the three dimensions. We believe these are definitive factors that measured kinematic distances in the Galactic plane; in x 7we have not been sufficiently explored. The thermal pressure was examine the rotation of gas above the midplane; in x 8we also adjusted to drop sharply at high densities to encourage the present an all-sky synchrotron map; and in x 9 we present our formation of denser structures. conclusions. In the first two papers of this series (Go´mez & Cox 2002, 2. ALL-SKY MAPS 2004, hereafter Papers I and II, respectively), we presented the results of our simulations of the ISM response to a spiral Figure 2 shows a map of the integrated column density of the gravitational perturbation. We showed that the extra stiffness simulation, as seen from the position of the observer marked in that the magnetic field adds to the gas makes it develop a Figure 1, in Galactic coordinates. The gray scale shows the combination of a shock and a hydraulic jump with significant column density, with contours in a geometric sequence and la- 3 complications added by vertical bouncing. This jump/shock beled in units of kpc cmÀ . (The reader should keep in mind leans upstream above the plane (more so in the two-arm models that our model spans only from 3 through 11 kpc in radius and than in the four-arm ones), ahead of the main gas concentra- up to 1 kpc in z. The hatched region in the Galactic center di- rection shows the angular extent of the central ‘‘hole’’ in our 1 Current address: Department of Astronomy, University of Maryland, simulation grid. In addition, the full strength of the perturba- College Park, MD 20742; [email protected]. tion is applied only for r > 5 kpc, and therefore, the useful part 758 GALAXY GASEOUS STRUCTURE: SYNTHETIC OBSERVATIONS 759 Fig. 2.—Column density of the gas for a region around the Galactic plane. The contours are in geometric sequence and labeled in units of kpc cmÀ3. The hatched region marks the inner limit of the simulation domain. velocities in the general direction of the Galactic anticenter (positive in the second quadrant, negative in the third). In ad- dition, the gas in the anticenter direction has a positive mean velocity, while the envelope of the emission averages to zero at l 170. These characteristics depend strongly on the chosen Fig. 1.—Surface density of the simulation, compared with the Milky Way’s position for the observer. Features similar to these are observed spiral arms as traced by Georgelin & Georgelin (1976) modified by Taylor & in l-v diagrams from Milky Way H i surveys, although details Cordes (1993). The position chosen for the observer in the following syn- (like the longitude of the zero velocity around the anticenter) thetic maps is also presented. The galactocentric distance for the Sun was cho- do not necessarily coincide with our model. The proximity of sen to be 8 kpc. our outer boundary (3 kpc in the anticenter direction) might have some influence on this. of the grid extends from r ¼ 5 11 kpc.) Two vertical protu- Ridges and intensity enhancements in this diagram are berances are clear in this figure, corresponding to the directions usually interpreted as spiral arms. Since in our model we have tangent to the Sagittarius arm, at l 60o and l À75.Imprints the advantage of knowing exactly where the material is and corresponding to other arms are also present; they are harder with which velocity it is moving, we can trace the gaseous to pick up in this figure but become evident when we restrict spiral arms into the simulated l-v diagram. We found the po- the line-of-sight integration to certain velocity ranges, as in sition of the spiral arms by fitting, for each radius in the sim- Figure 3. (A map with the line-of-sight component of the ulation grid, a sinusoidal function along azimuth to the vertical velocities, vlos, for the midplane is presented in Fig. 4). The column density of the gas. Figure 6 presents the result of the fit, Perseus arm appears in all the velocity ranges, but it is more while Figure 7 traces the spiral arms into the l-v diagram. Most prominent in l > 90 at negative velocities and l < À90 at of the ridges in Figure 7 correspond to spiral arms, although À1 vlos > 20 km s . Other features are also prominent: a super- the relation is not one-to-one. For example, around l ¼ 120 ,at position of the Perseus, Scutum, and Norma arms between the Perseus arm, the line of sight goes through a large velocity À1 l 0 and À60 at vlos < À20 km s ; the Sagittarius arm from gradient, which spreads the arm in velocity and diffuses the l À60 90 at intermediate negative velocities, with a very ridge. The converse also happens: lower intensity ridges that large vertical extension; and a superposition of the Sagittarius are not related to spiral arms are generated when the velocity and Scutum arms from l 0 60 for large positive velocities. gradient is small, and large spatial extents condense into a À1 À1 The diagram for 0 < vlos < 20 km s features three large small velocity range, for example, at (l; v) (À90 ; 30 km s ). column-density elements. The one at l À75 corresponds to The capacity of the velocity field to create or destroy structures the Sagittarius arm. At l 0 30 weseeanarrowstripeof in this diagram with little regard to the underlying gas density the whole inner Galaxy, including the Perseus, Scutum, and has been long known (Burton 1971; Mulder & Liem 1986).