Ellipsoidal halo finders and implications for models of triaxial halo formation

We describe an algorithm for identifying ellipsoidal haloes in numerical simulations, and quantify how the resulting estimates of halo mass and shape differ with respect to spherical halo finders. Haloes become more prolate when fit with ellipsoids, the differ-ence being most pronounced for the more aspherical objects. Although the ellipsoidal mass is systematically larger, this is less than 10 % for most of the haloes. However, even this small difference in mass corresponds to a significant difference in shape. We quantify these effects also on the initial mass and deformation tensors, on which most models of triaxial collapse are based. By studying the properties of protohaloes in the initial conditions, we find that models in which protohaloes are identified in Lagrangian space by three positive eigen-values of the deformation tensor are tenable only at the masses well-above M∗. The overdensity δ within almost any protohalo is larger than the critical value associated with spherical collapse (increasing as mass decreases); this is in good qualitative agree-ment with models which identify haloes requiring that collapse have occured along