It has been shown by Binney (1980a), Kormendy (1980), Illingworth and Schechter (1981), and KI, that if one kinematical quantity characterises the rotation of a galaxy, it is V (0)/o
m 0 5 the ratio of the peak rotation velocity on the major axis to the central line-of-sight velocity dispersion. In the interest of demonstrating conclusively that all bulges of disc galaxies are
rotationally flattened, it is useful to measure this quantity in as many disc galaxies as possible. Pursuant to this aim, the kinematical properties of a further four galaxies were observed, NGC 128, 4762, 4179 and Ham I.
However, before these quantities were determined, it was necessary to have an understanding of which easily observed kinematical quantity best describes the degree of rotational support for the bulge. The most popular method to date of achieving this is to determine the domain (or line) in the (0) / v s maximum ellipticity (emax) plane, where a bulge with known ellipticity, Vffl( 0) / 0Q, and flattened only by rotation would lie. It is not clear however, how these dynamical quantities should be measured. For example, there has been some confusion in the literature as to whether the central velocity dispersion o q or a "mean dispersion", <cj> should be used. Binney (1978 and 1980a)computed theoretical lines in the <V>/ <o> ^ e plane where <V> and <a> are the mean rotation velocity and velocity dispersions respectively for models having different amounts of velocity anisotropy. However, these same predictions have been used when e ( where to define this is largely arbitrary) has been plotted against ^m (0)/ ^ (eg Capaccioli, 1979) and Vm (0)/ <a> (eg KI, 1981). KI used <a> and found their points lie close to the theoretical line of Binney. If c was adopted instead, most of their points fall below this line (see also Kormendy 1980). This is interesting in view of Binney (1979) finding that for bulges of constant ellipticity and isotropic velocity distribution, <V> / <o> - ( 0 ) / to good accuracy.
In order partially to resolve this situation, the bulge dynamical models were used to construct their own domain in this
velocity on the major axis, V ^ Q ) to the central velocity dispersion The observed value of V_. (0 ) / o could then be
--- o m o
unambiguously compared with the theoretical value. Observation- ally, is best defined by extrapolating the run of o on the
minor axis back to the centre. Some ambiguity also exists as to where the ellipticity e should be measured. For example, should £ be taken to be the maximum observed ellipticity, the value at the radius where Vm (o) occurs, or mean ellipticity to some radius? For this work, the maximum ellipticity e is used. This should
be a suitable quantity because it is readily measured and for bright galaxies occurs at a surface brightness well above the threshold of the photometry. In practice, it should not matter too much how vm , o and e are defined, except that when comparing theory with
observation, the same definition should be used.
Using the above definitions for V , a and e , two sets of
models were constructed. The first set consisted of a grid of models in which the bulge was rotationally flattened with no externally applied potential field. Models so constructed inhabit the horizontally hatched area (Region 1) of Figure 4.24. The upper and lower bounds defining this area are not intended to suggest strict limits to ^m (0)/Qo , but merely to indicate the region in which most models fall for edge-on models. The vertically hatched area (Region 2) is defined by the locus of models with a disc included. The disc-to-bulge mass ratio was kept constant with Md/Mb = 0.25. Also, the disc scale lengths were held constant at a=10 and b=l. Both hatched regions were produced by changing and y only. Region 2 is the relevant region to use here
parameters. The models were found to have the property that the radius at which V
(o)occured was always less than the radius at which £max occured. Moreover, a systematic equalising of the radii at which these occur, resulted when the models were more highly rotated. With the generation of regions 1 and 2, the data could then be plotted in the V (o)/a 'v e plane and
m o max r
compared with the theoretical predictions to gauge the importance of rotational support and flattening in real bulges.
(ii) NGC 4762
NGC A762 is an edge-on galaxy classified as S0^ by Sandage (1961) and S(r)B0° by de Vaucouleurs and de Vaucouleurs (1964) - see Figure 4.14. Surface photometry has been performed by van Houten (1961), Tsikoudi (1977) and Burstein (1979) among others. It is this galaxy in which Burstein first identified the thick disc component (see Chapter VI). The purpose here is to derive an observed ^m (0)/ao value for the bulge. Previous determinations of a have been made by Minkowski (1962) who found Oq = 195 km.s~^> and Faber and Jackson (1976) who give an upper limit less than 150 km.s-'*-. No direct measurements of rotation in the bulge alone have been made; Bertola and Capaccioli (1978) have measured the rotation along the major axis and find V^(o) = 165 km.s although this is likely to be effected by the disc.
A total exposure of 4000s was made with the IPCS slit displaced 6" north-west and parallel with the major axis. The rotation curve is tabulated in Table 4.10 and plotted in Figure 4.15. The systemic radial velocity corrected for solar motion with
Figure 4.14 Upper Panel The galaxy NGC 4762 from a five hour J band (IIIa-J+GG385) exposure taken at the f/8 focus of the 1.0 m telescope. The major axis is at a position angle of 30.5°. The white line is a plate flaw.
Lower Panel Pseudo isodensity contours of the above plate to accentuate the structure of the galaxy. Note the faint warped disc.
OBSERVED ROTATION CURVE OF NGC 4762 6"NW |
r (arc sec) V (NE)b r (arc sec) V (SW)
0.5 25.0 3.1 43.3 2.0 74.7 5.6 8.4 4.6 96.8 8.1 - 55.1 7.1 27.8 10.7 - 24.7 9.7 38.8 13.2 - 46.8 12 80.2 15.7 - 77.2 15 110 18.2 - 93.7 17 121 20.8 - 71.6 20 122 23.4 - 79.9 22 138 25.9 - 129 25 110 28.4 - 132 27 113 31.0 - 115 30 188 33.5 - 171 33 204 36.0 - 104 35 102 41.1 - 132 38 100 48.7 - 85 40 199 43 107 a b
relative to corrected systemic velocity of 925 km.s 1 units in km.s“l.
Figure 4.15 Observed optical rotation curve of NGC 4762, with the slit 6" NW and parallel to the major axis. The data have been plotted relative to a corrected systemic velocity of 925 km.s The error associated with each observation is also shown. The open circle shows the measured velocity dispersion and its error on the minor axis at z=6", taken from Figure 4.16.