5. Spiral structure
As Fig. 13 shows, segments of spiral arms are readily identified in H I , CO, and optical maps of M 31, but there has been little agreement among numerous studies as to how - or even if - these features join up into an overall spiral pattern. The high inclination of the disk and the apparent small pitch angle of the arms are difficulties that might have been overcome if the disk were flat, but apparently it is not. Numerous authors starting with Arp (1964; see also Byrd 1977, Henderson 1979, Brinks & Burton 1984, Braun 1991) have been compelled to incorporate disk distortions in their spiral models. The companion galaxy M 32 is a possible cause for such distortions, which can grossly modify the apparent spiral pattern in a galaxy as highly inclined as M 31.
Although molecular clouds are generally an excellent tracer of spiral structure, owing to the CO radial distribution (Sect. 3.3) the outer arm S5 is more obvious in H I (Fig. 13b) and the inner arm S3 more obvious in dust lanes silhouetted against the bulge (Fig. 13c). We will therefore focus our attention here on the arm S4, which is extremely well defined in CO both spatially (Fig. 13a) and in velocity (Fig. 11). One way of circumventing the confusing influence of disk distortions is to study the spiral structure in X-v diagrams, which remain largely unaffected by small distortions; in such diagrams logarithmic spirals appear as loops. In order to study the velocity structure of S4, we masked from the CO survey all emission outside that arm (Fig. 14a) and then integrated over all Y to produce a full X-v diagram of S4 only (Fig. 14b). The spiral features in the Xv and XY diagrams were fit by eye with a logarithmic spiral parameterized by a pitch angle and position of the major axis intercept. We assumed a flat rotation curve ( = 256 km s-1) for radii greater than 5.2 kpc, a systemic velocity of = -315 km s-1, and initially, a constant inclination angle of 13o. The best-fit model, shown as the loop in Fig. 14b, has a pitch angle of 12o and major axis intercept at X = -48.5´. In fitting this arm, no weight was given to the branch of emission running parallel to the lower portion of S4 (labeled A in Fig. 14b); the corresponding feature in H I has been modeled by Byrd (1977) as an inner arm warped out of the plane by a recent passage of M 32 through the disk in this vicinity.
As the dotted curve in Fig. 14a demonstrates, the 12o pitch angle determined for S4 from the X-v diagram fits the spatial map poorly. This inconsistency, true also to some extent for S3 and S5, has been noticed many times before and is one of the motivations for introducing disk distortions into spiral model fits: the velocity structure of these arms and the offsets of their tangents above the major axis suggest significant pitch angles, but they appear to be nearly circular in spatial maps (e.g., Neininger et al. 1998 fit all three of these arms in their CO spatial map with ellipses slightly rotated from the major axis). We found that a 12o pitch angle can be made to fit the spatial map (solid line in Fig. 14a) by introducing a linear change in the disk inclination with Y: from 15o at Y = -10´ to 11o at Y = 10´. This model suggests that the disk of M 31 is slightly convex from our perspective, but other models of the disk warping might fit as well.
A fuller discussion of the spiral structure of M 31 in CO will be presented in a later paper, when our on-going mapping of the disk of M 31 with the FCRAO telescope is complete.
© European Southern Observatory (ESO) 1999
Online publication: November 16, 1999