Mass modelling of dwarf spheroidal galaxies

1. Mass modelling of dwarf spheroidal galaxies Ewa L. Łokas Copernicus Center, Warsaw

2. Collaborators • Jarosław Klimentowski (Copernicus Center, Warsaw) • Stelios Kazantzidis (Ohio State) • Gary Mamon (IAP, Paris) • Lucio Mayer (Zurich) • Francisco Prada (IAA, Granada)

3. The method of velocity moments • Measure positions and velocities of stars in the galaxy • Determine the profiles of velocity moments • Make assumptions about the model for the mass distribution and anisotropy of stellar orbits (e.g. mass follows light, β = const) • Fit the solutions of the Jeans equations to the observed velocity moments • Adjust the free parameters (total mass, anisotropy)

4. Velocity moments • The second-order velocity moment σ is obtained • from the lowest-order Jeans equation • The fourth-order moment is governed by thehigherorderJeans equation, which for β = const reads

5. Line-of-sight moments For comparison with observations we need to project the solutions along the line-of-sight

6. The simulation • The simulation traced the evolution of a two-component dwarf galaxy on an eccentric orbit in a static Milky Way potential for 10 Gyrs • The dwarf initially had a stellar disk and an NFW-like dark matter halo • The dwarf was modelled with 106 stellar and 4 x 106 dark matter particles • The progenitor had an initial mass of 4 x 109M • 99% of the mass is lost Klimentowski et al. 2007

7. Observing the dwarf Depending on the angle of view the measurements will be different

8. Simulated data Very strong contamination for observation along the tidal tails  unbound accepted rejected

9. Contaminated velocity dispersion • For observation along the tails the dispersion shows a secondary increase • After cleaning the data of interlopers the dispersion decreases with radius and traces well the profile for bound particles

10. Two sources of contamination • The kinematic samples can be contaminated by tidal tails • Additional source of contamination are the stars of the Milky Way + MW stars  unbound

11. Application to Fornax Kinematic dataset of 202 stars for the Fornax dwarf from Walker et al. (2006)

12. Sample selection members interlopers

13. Velocity dispersion profilesfor Fornax Models with M/L=const

14. Constraints on the parameters Models with M/L=const

15. Summary of M/L=const models

16. Additional constraints from kurtosis σlosσlos + κlos M/LV =11.3 M/L β= –0.17 χ2/N=3.4/4 M/LV =11.4 M/L β= –0.03 χ2/N=10.9/10

17. Tidal tails in Fornax? If tidal tails are visible then they are probably not along the line of sight (Coleman et al. 2005)

18. Contamination from the MW The rejected stars in Fornax have velocities consistent with the population expected from the MW according to the Besancon model (Robin et al. 2003)

19. Application to Draco Kinematic sample for 207 stars from Wilkinson et al. (2004) ● accepted ° rejected

20. Velocity moments for Draco • Velocity moments were calculated for the sample of 194 stars cleaned of interlopers • The interlopers most likely some from the tidal tails since no contamination from MW stars is expected at the velocity range of Draco stars

21. Distribution of dark matter Small dark matter haloes orbiting bigger ones get tidally stripped, but their inner slope remains cuspy (Kazantzidis et al. 2004), Klimentowski et al. 2007) and is well fitted by

22. Dark matter distribution in Draco

23. Application to Leo I • Kinematic sample of 328 stars from Mateo et al. (2007) • The secondary increase of dispersion disappears after removal of interlopers

24. Constraints on parameters If kurtosis is included or analysis restricted to inner points the data are consistent with isotropy or weakly tangential orbits

25. Constraints on parameters If the data are cleaned of interlopers the agreement with isotropy or weakly tangential orbits is even better

26. Weakly tangential orbits Weakly tangential orbits are expected for dwarfs not strongly dominated by dark matter

27. Conclusions • Removal of unbound stars from the tidal tails and/or Milky Way is essential in modelling dwarfs • The kinematic data for Fornax and Leo I are consistent with mass following light and weakly tangential orbits • Fornax and Leo I are not strongly dark matter dominated with M/L=11 and 7 solar units • Draco is poorly fitted by mass-follow-light models and has M/L>100

28. References • Łokas, E. L., Mamon, G. A., Prada, F., 2005, Dark matter distribution in the Draco dwarf from velocity moments, MNRAS, 363, 918 • Klimentowski, J., Łokas, E. L., Kazantzidis, S., Prada, F., Mayer, L., Mamon, G. A., 2007, Mass modelling of dwarf spheroidal galaxies: the effect of unbound stars from tidal tails and the Milky Way, MNRAS, 378, 353 • Sánchez-Conde, M. A., Prada, F., Łokas, E. L., Gómez, M. E., Wojtak, R., Moles, M., 2007, Dark matter annihilation in Draco: New considerations of the expected gamma flux, Physical Review D, 76, 123509 • Łokas, E. L., Klimentowski, J., Wojtak, R., 2007, The effect of unbound stars on the mass modelling of the Fornax dwarf, arXiv:0712.2372