Triaxial Galaxies with Central Density Cusps
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**Session 51 -- Galaxies**
*Oral presentation, Thursday, June 15, 1995, 10:00am - 11:30am*

## [51.02] Triaxial Galaxies with Central Density Cusps

*T.Fridman, D.Merritt (Rutgers University)*

We present numerical models for triaxial galaxies with central
density cusps. The mass-density distribution is $\rho \propto
m^{- \gamma}(1+m)^{-(4-\gamma)}$, $ m^{2} =\frac {x^{2}} {a^{2}} + \frac
{y^{2}} {b^{2}}+ \frac {z^{2}} {c^{2}} $, which
is an ellipsoidal generalization of the $\eta$-models of Tremaine *et
al.*
(1993). Such a distribution has the important properties that it
resembles the de Vaucouleurs profile at large radii, while
providing flexibility of the slope of the central cusp in
accordance with recent data from HST.

Here we present results for triaxial models with $\gamma=2$ (``strong
cusp''), similar to the observed luminosity density in $M32$, and
for $\gamma = 1$ (``weak cusp''), similar to M87.
We discuss the structure and stability of orbits in the potentials
generated by the two mass-density distributions.
A large fraction of the phase-space for both models is occupied by
stochastic orbits.
Self-consistent models were constructed using quadratic programming.

We constructed models in two ways. 1. Treating the stochastic orbits like
regular ones; and 2. Assuming that the model is fully mixed, i.e.
calculating the time-independent average density of stochastic orbits
as the ensemble average.
Quasi-equilibrium solutions, in which the stochastic orbits were treated
like
the regular orbits, exist for both mass models.
However these models would evolve near the center due to the slow
diffusion of the stochastic orbits through phase space.
Fully mixed models exist for the weak-cusp
model but not for the strong-cusp model.
This result suggests that galaxies like M32 that have strong cusps
must either be axisymmetric, or slowly evolving.

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