1. Does the Fornax dwarf spheroidal have a central cusp or core? Collaborators: Justin Read, Ben Moore, Joachim Stadel, Marcel Zemp and George Lake Tobias Goerdt Universität Zürich

2. Outline: 1.Problem 2.Dynamical friction: Chandrasekhar 3.N-body simulations 4.Our analytical calculations 5.Implications on CDM

3. The Fornax dwarf spheroidal Most dark matter dominated object in the universe Five globular clusters Projected distances between 240 pc and 1.6 kpc Why are they not at the centre?

4. Barred galaxies: Why does the bar survive?

5. Dynamical friction:

6. Chandrasekhar dynamical friction: Would let GCs / bars spiral in Perturbative approach: Timescale about 5 Gyr Shorter than age of Fornax

8. N-body simulations: Equilibrium dark matter haloes: –(i) cusped (NFW) (ii) cored –M vir = 2 x 10 9 M sun –~10 7 particles, shell model, effective 10 9 Distribute 5 GCs within haloes: –1 particle 20 pc softening –M GC = 2 x 10 5 M sun –Circular + eccentric orbits

9. Halo models Core size

10. Results: Cusp: –GC sink-in, as expected

11. Results: Cusp: –GC sink-in, as expected –Chandrasekhar: very good estimate

12. Results: Cusp: –GC sink-in, as expected –Chandrasekhar: very good estimate –DM-particles are expelled from the centre

13. Core: –GC sink towards core radius as expected –Unexpected behaviour: Super-Chandrasekhar sinking GCs stop at the core radius => solution to timing problem

14. Core: –GC sink towards core radius as expected –Unexpected behaviour: GCs stop at the core radius => solution to timing problem Deviation from Chandrasekhar

15. Why deviation from Chandrasekhar? Orbit-resonance scattering Particles are scattered out of the phase- space region, which is responsible for dynamical friction Harmonic core => No phase mixing Analytical phaselag {particles / GC} =  / 4 Semianalytic or N-body: good agreement

16. 2D density contours Slice through halo in plane of GC’s orbit Only coplanar orbiting particles shown GC orbits anti- clockwise Solid lines: N-body Dashed: Semianalytic

17. Histogram of  - velocities Solid line: GC

18. CDM N-body simulations uniquely predict cuspy haloes e.g: Diemand et al. 2005

19. Summary Core natural explanation for position of the inner GC’s in Fornax Cores contradict CDM We propose a core of  240 pc Corresponds to m WDM  0.5 keV Would solve substructure problem

20. Any questions?