The distance to external galaxies makes it difficult to resolve them into stars, and hence the motions of their stars have been but poorly studied. In the nearby Magellanic Clouds, such studies are quite possible in principle; in fact, however, in important regions the stars are so close together in the sky that it becomes very difficult to obtain separated spectra from which to determine individual radial velocities. As planetary nebulae are relatively rare and obvious objects, they are not subject to this crowding. By a survey of their radial velocities it has been determined that the inner 2kpc of the LMC rotate like a solid body, revolving once in a few hundred million years. Towards the outer parts, the rotation curve flattens, and at 4kpc distance from the centre the tangential velocity is about 30kms-1. The latter value is not the true value because the rotation axis of the LMC is inclined to the line of sight at an angle somewhere between 25° and 45°. This lack of precision leads to an uncertainty in the mass, which probably is about six billion solar masses. In the SMC, no reliable observations of this kind have been made.

The stellar motions in the dwarf elliptical galaxy M 32 have been studied in some detail. Since it is at present out of the question to measure the velocities of individual stars in such a densely-packed faint object, a spectrum had to be taken of the light of all stars together, thus measuring the average Doppler effect. From this it appears that M 32 has a nucleus with a diameter of eight parsecs, which rotates as a solid body with a tangential velocity of about lOOkms-1, thus revolving once in half a million years. Outside this nuclear region, the rotation curve drops rapidly to zero velocity at a radius of 30 pc. This indicates that the outer regions of the centre of M32 rotate at best very slowly. The mass within 30 pc is 18 mil¬lion solar masses, equivalent to a mean distance between stars of
1.9pc.

In a similar way, the nuclear region of the Andromeda Nebula was analysed. It is of interest to present this in detail, because the nuclei of some galaxies are the site of puzzling and highly energetic phenomena. As we have seen in the case of our Galaxy, the central clouds of gas and stars may well be considered as a giant galactic thundercloud, and we should like to know the behaviour and especially the origin of its outbreaks.

Spectra taken through the nucleus with the slit parallel to the major axis of the galaxy yield a strange rotation curve. It rises from zero velocity straight to 200 km s-1 at a radius of 200 pc, which implies that this part of the stellar cloud rotates as a solid body with a period of six million years. Between 200 and 400 pc from the nucleus, the curve shows a sharp dip with a minimum of 100 km s-1. Thereafter, it decreases from 200 km s-1 at 400 pc to 100 km g-1 (perhaps even to 50kms-1) at 1600pc.

These two features are very surprising, although the latter effect is not unlike the rapid decrease in the rotation curve of M 32. An explanation for this behaviour might be that the stellar orbits are not on the average circular, but instead show systematic motions away from the galactic nucleus. Indeed, spectra taken with the spectroscope slit parallel to the minor axis show radial motions up to 100kms-1. It is an unsolved puzzle how these systematic motions are created and maintained in the central region. The problem is that a star moves once around the nucleus in 10 million years or so, whereas the age of most, of these stars is about four billion years: in their lifetime they have orbited the nucleus 400 times, so that all systematic motions present at their formation should have been smeared out, long ago.

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