5.1.3. Dynamics of Bars. II. Basic Kinematics of NGC 936
Selected velocity and dispersion profiles in NGC 936 are illustrated in Figure 41. The first result of these data is that the outer disk rotation curve is flat. Similar results have been derived for other barred galaxies, mostly in emission lines and sometimes at much larger radii, by Chevalier and Furenlid (1978); Bosma (1978); Sancisi, Allen and Sullivan (1979); Pence (1981); Illingworth and McElroy (see Illingworth 1981), and Kormendy (1982b). Barred galaxies do not lack massive halos.
All of the measurements of NGC 936 are consistent with circular motions beyond the end of the bar. Between 4 and 7 kpc radius the rotation velocity is V* = 289 ± 11 km s-1 in the disk plane. This is larger than the rotation rate in the same radius range in our Galaxy (Gunn, Knapp and Tremaine 1979), and comparable to or larger than the rotation rate in M31 (Roberts and Whitehurst 1975; Emerson 1978).
Figure 41. Rotation velocity V, dispersion and line strength along several slit positions in NGC 936. Velocities and dispersions are in km s-1; the systemic velocity has been removed. Different symbols represent data from opposite sides of the center. The open symbols for the minor axis represent a different averaging of the data that yielded the closed symbols. The major-axis rotation curve is very similar to that along PA 122°, but slightly less accurate because of a shorter integration time. Note that since a is not negligible, V(r) is not the circular-orbit rotation curve, and so velocities do not directly measure mass. The bar is at position angle 77°. The length rB of the bar is 51" along the major axis, 50" at PA 122°, 42" as measured at PA 77°, and 38" along the minor axis at PA 46°.
The present observations of NGC 936 provide a clear detection of non-circular stellar motions in the bar.
(1) Off-Center Rotation Curve Along the Bar. The rotation curve along the bar is symmetrical about a point displaced by r = 4.8" from the optical center (Fig. 41, bottom panels). Such a shift greatly reduces the scatter of the points. In fact, the details of the rotation curve are precisely reproduced on both sides of the center, although some of this may be fortuitous. Unlike the bar, the bulge appears to rotate about its center. Isodensity tracings show that the bulge and bar are concentric (Fig. 40). The simplest interpretation is then that the bar's velocity field consists of slightly asymmetric, elongated streamlines. If the orbits are elongated, as they are in the gas velocity field of NGC 5383 (Fig. 6b of Peterson et al. 1978a) and in the n-body model of Miller and Smith (1979), then lines of constant velocity are skewed so that they are almost radial (Fig. 44). Then even a small asymmetry, perhaps combined with a small centering error, will produce a large apparent shift of the kinematic center along the slit. I therefore interpret the above shift as a signature of non-circular streaming motions.
(2) Difference Between Major-Axis and Bar Rotation Curves. Another indication of non-circular motions is seen in Fig. 42. This shows that major-axis rotation velocities are larger than those along the bar over precisely the radius range 14" r 42" in which the bar dominates the brightness distribution. The difference is Vmaj - Vbar = 21 ± 5 km s-1. Beyond the end of the bar the data are consistent with circular rotation.
Figure 42. Projection of the major-axis rotation curve of NGC 936 onto that of the bar. The bar radius is 42". Here and in all subsequent discussion results are illustrated with a bar rotation curve derived using r = 4.8". However, all analysis has been repeated assuming r = 0". The two sets of results are consistent. Thus no conclusion except that of point (1), above, depends on the reality or interpretation of a value of r different from zero.
The sense of the non-circular motions is that rotation is slower than circular along the crest of the bar and faster than circular along a line at ' = 66° from the bar. This implies that average orbits are elongated parallel to the bar, in agreement with conclusion (1). The perturbation on the circular velocity V* ~ (Vmaj + Vbar)/2 is not small: since (Vmaj - Vbar) / V* 0.39 ± 0.09, the average non-circular velocity perturbation is ~ 20% of V*.
(3) Minor-Axis Rotation is significantly different from zero in the region of the bar (Fig. 41, upper right). Between 10" and 38" radius, the average rotation rate is 16 ± 4 km s-1, with a maximum of ~ 20 km s-1. (The need for long integration times, here 164 minutes, is clear.) The sense of the rotation is opposite to that along the bar. That is, the zero-velocity line is twisted from the photometric minor axis toward the bar, a behavior also seen in numerical models (Fig. 44) and in emission-line velocity fields (e.g., Peterson et al. 1978a; Pence 1981). The implication is again that the orbits are elongated parallel to the bar.
(4) The Velocity Dispersion along all slit positions through the bar region is ~ 0.5 - 1.0 times as large as the maximum disk rotation rate. The dispersion is largest at small radii, where it is only slightly smaller than in the bulge. At r = rB it has declined to values near the instrumental measuring limit of ~ 60 km s-1. The relative importance of ordered and random motions will be discussed below. However, it is already clear that the bar of NGC 936 shows both significant non-circular streaming motions and large random motions.
The above results are summarized in Figure 43. If various indistinct spiral features in the disk are trailing, then the north-east side is the far side. (If this assumption is wrong, the sense of rotation and circulation is reversed but the behavior is unchanged.)
Figure 43. Schematic velocity field in NGC 936 (cf. Fig. 40). The five slit positions measured are indicated. The dotted line is a schematic average orbit. The dashed line estimates the position of the line of zero velocities.
Since rotation velocities are smaller along the bar than along the major axis, orbits are on average elongated parallel to the bar. The streaming motions are therefore outward along the minor axis, and indeed, minor axis velocities are, e.g., directed away from us on the far (north-east) side of the galaxy. As a result, the line of zero velocities (dashed) is between the bar and the minor axis where the bar dominates the brightness distribution. Rotation in the outer disk is approximately circular. The above is the average behavior of all the stars along any line of sight; since the velocity dispersion is comparable to V*, individual stars depart by large amounts from the average motion.