Numerical Stability of a Family of Osipkov‐Merritt Models

Abstract

We have investigated the stability of a set of nonrotating anisotropic spherical models with a phasespace distribution function of the Osipkov-Merritt type. The velocity distribution in these models is isotropic near the center and becomes radially anisotropic at large radii. The models are special members of the family studied by Dehnen and by Tremaine et al. in which the mass density has a power-law cusp o P r~c at small radii and decays as o P r~4 at large radii.The radial-orbit instability of models with c \ 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 Ðeld ÏÏ method developed by Hernquist & Ostriker. These simulations have allowed us to delineate a boundary in the (c, that separates r a )-plane the stable from the unstable models. This boundary is given by for the ratio of the 2T r /T t \ 2.31^0.27 total radial to tangential kinetic energy. We also found that the stability criterion df/dQ ¹ 0, recently raised by Hjorth, gives lower values compared with our numerical results.The stability to radial modes of some Osipkov-Merritt c-models that fail to satisfy the Doremus-Feix criterion Lf/LE \ 0 has been studied using the same N-body code but retaining only the l \ 0 terms in the potential expansion. We have found no signs of radial instabilities for these models.

The Hernquist model revisited: Completely analytical anisotropic dynamical models

“…The study of the stability of anisotropic stellar systems is difficult, and a satisfactory criterion can not easily be given. For stability against radial perturbations, we can apply the sufficient criterions of Antonov (1962) or Dorémus & Feix (1973), but numerical simulations have shown that these criteria are rather crude (Dejonghe & Merritt 1988;Meza & Zamorano 1997). Moreover, the only instability that is thought to be effective in realistic galaxies is the so-called radial orbit instability, an instability that drives galaxies with a large number of radial orbits to forming a bar (Hénon 1973;Palmer & Papaloizou 1987;Cincotta et al 1996).…”

Stability of rotating spherical stellar systems

“…For example, models dominated by stars on radial or eccentric orbits can be unstable to forming a triaxial bar (Polyachenko 1981;Merritt & Aguilar 1985;Meza & Zamorano 1997), while models e-mail: ameza@uvic.ca Present Address: Department of Physics and Astronomy, University of Victoria, Victoria BC, V8P 1A1, Canada. composed mainly of stars on circular orbits can exhibit quadrupole-mode oscillations (Barnes et al 1986).…”

Two-component Jaffe models with a central black hole – I. The spherical case

“…From its definition Ξ → 1 for sa → ∞ (globally isotropic models), while Ξ → ∞ for sa → 0 (fully radially anisotropic models). Numerous investigations of one-component systems have confirmed that the onset of ROI is in general prevented by the empirical requirement that Ξ < 1.7 ± 0.25; the exact value of the limit is model dependent (see, e.g., Merritt & Aguilar 1985;Bertin & Stiavelli 1989;Saha 1991Saha , 1992Meza & Zamorano 1997;Nipoti, Londrillo & Ciotti 2002). Here we are considering two-component systems, however N-body simulations have shown that the presence of a DM halo does not change very much the situation with respect to the one-component systems (e.g., see Stiavelli & Sparke 1991, Nipoti et al 2002.…”