Analysis of Radial Velocities of Stars and Nebulae in the Magellanic Clouds

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Abstract
Radial velocities of 61 stars in the LMC are analysed together with Lick measures of nebular velocities. It is pointed out that, in principle, instantaneous measures of radial velocity do not distinguish between the rotation and translation of a solid body. A least squares solution yields a vector 813 ± 65 km/s (corrected for solar motion and galactic rotation) which is held to be mainly due to solid-body rotation of the LMC. The corresponding gradient of radial velocities in the sky is 14.2 km/s/deg in p.a. 171° in which an uncertainty of ±1.7 km/s/deg would be contributed by a translational velocity of 100 km/s. Small departures from this solution in the outer parts indicate some differential rotation. Further analysis, on the basis of de Vaucouleurs' inclined plane model, yields a rotation curve which disagrees with de Vaucouleurs' but which is only slightly steeper than the corrected peak velocities derived from 21 cm profiles. The optical velocities are more symmetrical about the radio centre than about de Vaucouleurs' optical centre. The mass of the LMC is derived from ( a ) a model of a uniform rotating ellipsoid, ( b ) a model of a non-uniform rotating ellipsoid (after Perek) and ( c ) Bottlinger's interpolation formula for differential rotation. The best estimate for the mass within 4°.5 of the centre is 1.0 × 10 10 ⊙. The velocity-dispersion appears to be slightly larger in the inner portions of the LMC and for the brightest stars compared with the faintest observed. SMC stars with known velocities cover too small an area of the sky to deduce optical evidence of the rotation of the system. The velocity-dispersion in the SMC is of order 16 km/s, as in the LMC.

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