# Paper No. 09-47

**D Chakrabarty**

**Different Traces give Different Gravitational Mass Distributions**

**Date: **December 2009

**Abstract:** Charting the extent and amount of dark matter (DM) in the Universe is highly appealing but is equally hard since it is only through the interpretation of its effect that we can track the DM distribution, i.e. the problem is fundamentally inverse. Given the implementational problems, it is non-trivial to quantify the effects of DM on the motion of individual test particles in an elliptical galaxy, with the aim of identifying itstotal gravitational (i.e. luminous+dark) mass distribution; expectedly, this has caused controversy. Aims. Leaving such technical details aside, in this article we report on the danger of the very notion that test particle velocities can reliably imply total mass distribution in galaxies. Methods. We expose the fallibility of this mass determination route, by undertaking a non-parametric Bayesian analysis (using the algorithm CHASSIS) of the observed line-of-sight velocities of individual test particles belonging two distinct particle (or mass tracer) populations: planetary nebulae (PNe) and globular clusters (GCs) that span the outskirts of the galaxy NGC 3379. Results. The PNe and GC data are shown to be drawn from independent phase space density distributions and total gravitational mass density distributions that are derived from implementation of the two kinematic data sets are found to be significantly different, leading to significant (at 1-¾ level) differences in the corresponding solutions for the gravitational potential. CHASSIS currently assumes isotropy in phase space, so this assumption is tested with a robust Bayesian hypothesis test; the GC velocities are found to be more supportive of the assumption of isotropy than are the PNe data. We find that this recovered difference in the state of isotropy between the phase space distributions that the data are drawn from, cannot be used to reconcile the differences in the recovered gravitational mass density distributions. Conclusions. This recovered dichotomy in the potential structure of the galaxy is indicative of the multistability of the dynamical system at hand, i.e. the galaxy. In light of this, we advance the risk involved in the interpretation of gravitational mass distributions obtained from individual tracer samples, as equivalent to the mass distribution of the whole galaxy.

**Keywords: **Galaxies: kinematics and dynamics, dark matter; Methods: Bayesian, hypothesis testing