NUMERICAL STABILITY OF A FAMILY OF OSIPKOV-MERRITT MODELS

We have investigated the stability of a set of nonrotating anisotropic spherical models with a phase-space distribution function of the Osip kov-Merritt type. The velocity distribution in these models is isotrop ic near the center and becomes radially anisotropic at large radii. Th e models are special members of the family studied by Dehnen and by Tr emaine et al. in which the mass density has a power-law cusp rho propo rtional to r(-gamma) at small radii and decays as rho proportional to r(-4) at large radii. The radial-orbit instability of models with gamm a = 0, 1/2, 1, 3/2, and 2 was studied using an N-body code written by one of us and based on the ''self-consistent field'' method developed by Hernquist & Ostriker. These simulations have allowed us to delineat e a boundary in the (gamma, r(a))-plane that separates the stable from the unstable models. This boundary is given by 2T(r)/T-t = 2.31 +/- 0 .27 for the ratio of the total radial to tangential kinetic energy. We also found that the stability criterion df/dQ less than or equal to 0 , recently raised by Hjorth, gives lower values compared with our nume rical results. The stability to radial modes of some Osipkov-Merritt g amma-models that fail to satisfy the Doremus-Feix criterion partial de rivative f/partial derivative E < 0 has been studied using the same N- body code but retaining only the l = 0 terms in the potential expansio n. We have found no signs of radial instabilities for these models.