Self-consistent Models for Triaxial Galaxies with Flat Rotation Curves: The Disk Case

We examine the possibility of constructing scale-free triaxial logarithmic potentials self-consistently, using Schwarzschild's linear programing method. In particular, we explore the limit of nonaxisymmetric disks. In this case it is possible to reduce the problem to the self-consistent reconstruction of the disk surface density on the unit circle, a considerably simpler problem than the usual two- or three- dimensional one. Models with surface densities of the form {SIGMA} = [x^n^ + (y/q)^n^]^-1/n^ with n = 2 or 4 are investigated. We show that the complicated shapes of the "boxlet" orbit families (which replace the box orbit family found in potentials with smooth cores) limit the possibility of building self-consistent models, though elliptical disks of axis ratio above 0.7 and a restricted range of boxier models can be constructed. This result relies on using sufficiently fine bins, smaller than the 10^deg^ bins commonly used in two- or three-dimensional investigations. It also indicates the need for caution in interpreting N- body models of triaxial halos in which the core of the potential is numerically smoothed.