Triaxial versus Spherical Dark Matter Halo Profiles

When analyzing dark matter halos forming in cosmological n-body simulations, it is common practice to obtain the density profile utilizing spherical shells. However, it is also known that the systems under investigation are far from spherically symmetric but, rather, follow a triaxial mass distribution. In this study we present an estimator for the error introduced by spherically averaging an elliptical mass distribution. We systematically investigate the differences arising when using a triaxial density profile under the assumption of spherical symmetry. We show that the variance in the density can be as large as 50% in the outer parts of dark matter halos for extreme (but still credible) axis ratios of 0.55:0.67:1. The inner parts are less affected but still show a scatter at the 16% level for these prolate systems. For more moderate ellipticities, i.e. axis ratios of 0.73:0.87:1, the error is smaller but still as large as 10-20% depending on distance. We further provide a simple formula that allows estimation of this variance as a function of radius for arbitrary axis ratios. We conclude that highly prolate and/or oblate systems are better fit by analytical profiles that take into account the triaxial nature of cosmological objects.