INSTABILITIES OF A FAMILY OF OBLATE STELLAR SPHEROIDS

We have examined the stability of a sequence of oblate elliptical gala xy models having the Stackel form suggested by Kuz'min & Kutuzov, Pie have employed the two-integral distribution functions given by Dejongh e & de Zeeuw, for which flattened non-rotating models are characterize d by counter-streaming motion and are radially cool; we introduce net rotation in some models by changing the sign of the z-component of ang ular momentum for a fraction of the particles, We have found that all non-rotating and slowly rotating members of this sequence rc,under tha n E7 are stable, and that even maximally rotating models rounder than E4 are stable. In the absence of strong rotation the most disruptive i nstability, and the last to be stablized by increasing thickness, is a lopsided (m = 1) mode. This instability appears to be driven by count er-rotation in radially cool models, Its vigour is lessened as rotatio n is increased, but it remains strong even in models with net angular momentum 90 per cent of that of a maximally rotating model before fina lly disappearing in maximally rotating models. Strongly rotating model s are more unstable to bar-forming modes which afflict maximally rotat ing models willi c/a less than or similar to 0.5, but these modes are quickly stabilized by moderate fractions al counter-rotating particles . Bending instabilities appear not to be very important; they are dete ctable in the inner parts of the flatter models, but are less vigorous and mori, easily stabilized than the lopsided or bar modes in every c ase. We briefly discuss the possible relevance of the lopsided instabi lity to the existence of many lopsided disc galaxies.