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In the past two decades it has become clear that spiral galaxies are embedded in massive dark-matter halos. A recent study of two dozen galaxies of different morphological type and luminosity has shown that more luminous, early-type galaxies contain relatively less dark matter than later types. The sample is too small to separate the trend in either a luminosity or a morphological type effect.
To investigate this problem in more detail we set out to study the kinematics of stars and gas within a sample of Sa galaxies. Sa's lie at one of the two extreme ends of the dark-matter content vs. morphological type relation and have been relatively understudied as a class. Besides, by a variety of criteria Sa galaxies seem to form a more heterogeneous group than their later spiral counterparts.
Here we report on VLA-H{\sc I} observations of the Sa galaxy NGC~4138, the first H{\sc I} observation in this project. The spatial distribution of neutral hydrogen is regular and the size of the gas disk is more than twice that of the optical disk. Beyond the optical edge of the galaxy the radial velocities along the major axis drop by more that $80\,{\rm km\,s^{-1}}$. If the inclination in the outer regions is about the same as in the inner regions, then the rotation curve shows a Keplerian decline beyond two optical scale lengths. In this case the observed rotation curve can be fitted very well by a mass-model consisting only of the luminous components. Unfortunately, the observed velocity field is also in agreement with a more-or-less flat rotation curve and a strongly warped disk, with inclination angles decreasing from 46 to 25 degrees. However, even in this case a maximum-disk fit shows that the relative amount of dark matter is less than the average amount in later spiral types.
