1. A Different Dark Matter Potential for Modeling Cluster Atmospheres Andisheh Mahdavi University of Hawai’i

2. Why are the shapes of cluster potentials so important? N-body simulations predict self-similar dark matter halos Shapes of potentials can constrain dark matter physics Clusters of galaxies probe dark matter potentials at the very largest scales.

3. Mass profiles in common use “  -model” profile NFW profile Not analytic Generalized cusp

4. An invertible potential with variable slope Has finite mass M 0 Invertible: Useful for calculating distribution functions Facilitates stellar dynamics modeling n=1 corresponds to Hernquist’s model; n=2 gives the Plummer sphere.

5. An invertible potential with variable slope Inner slope is 2-n; outer slope is 3+n n~1/2 is close to the highest resolution N-body simulations Generalizes classical mass profiles, but allows a free shape parameter

7. Hydrodynamics with the potential Isothermal solutions:

8. Hydrodynamics with the potential Isothermal solutions:unphysical Equipartition solutions:

9. Hydrodynamics with the potential Equipartition solutions: Isothermal solutions:unphysical Polytropic solutions:

10. Application Are clusters regular outside the very central regions? Many are poorly fit by the standard  -model profile Cooling flows may not always be the cause for the surface brightness peak.

11. Abell 2550

14. Conclusion A new surface brightness formulation is proposed, with an extra free parameter that can be tied to a physical potential This profile can fit clusters with rising SB without the need for a divergent power law The inferred value of n for Abel 2550 is 0.4, close the what high resolution simulations predict for dark matter halos The potential is an invertible generalization of commonly used ones, and so is useful outside X-ray astronomy: