1. The prolate shape of the Galactic halo Amina Helmi Kapteyn Astronomical Institute

2. Motivation Knowledge of distribution of dark matter in our Galaxy is crucial for DM detection experiments Astrophysical observations provide constraints on  the spatial structure (density profile, shape, local density),  velocity distribution function,  substructure This talk: the shape of the Galactic halo

3. The shape of the Galactic halo The shape of the DM halo is sensitive to the nature of the dark-matter particles. Numerical simulations show that –Cold dark-matter: oblate, prolate, triaxial. Minor to major axis ratio: 0.6 – 0.8 (Dubinski 1994; Bullock 2002). –Hot dark-matter (neutrinos): spherical (Mayer et al. 2002) –Self-interacting: close to spherical (Dave et al. 2002; Yoshida et al. 2002)

4. Observational constraints Difficult determination: –most tracers located in the disk, baryon dominated region (Olling & Merrifield 2000) –Inconclusive results, axis-ratio: 0.3 – 1.0 Best tracers: halo stars whose motion is primarily determined by dark halo potential Streams in the halo are excellent probes: groups of stars on parallel orbits

5. Halo streams Recently, streams from Sgr dwarf galaxy discovered all around the sky (360deg) Majewski et al. 2003

6. Modelling the Sgr streams Spherical halo -> motion occurs in a plane Non-spherical -> plane precesses (streams become wider in time, and less well defined on the sky) -> Easy to test N-body simulations of evolution of Sgr-like systems in Galactic potentials with halo of varying shape: from oblate to prolate Initial conditions: set by current position, and motion of the dwarf (some freedom left) Final dwarf is the same -> differences in streams properties due differences in the halo flattening

7. Evolution in spherical halo

8. Debris sky distribution The appearance depends on the dynamical age of the streams Youngest streams ( < 3 Gyr), in black, have the same distribution independently of halo flattening!

9. Spatial distribution Debris discovered so far trace youngest streams Differences in young streams spatial distribution are almost imperceptible… oblate prolate

10. Kinematics of stream stars Black: particles released in the last 1.5 Gyr (models not distinguishable) Magenta: released between 1.5 and 4 Gyr ago Noticeable differences  deg (trailing) and  deg (leading) oblatesphericalprolate

11. Kinematics of stream stars Radial velocities provided by Majewski et al. (2004) Measured kinematics of trailing streams: do not provide strong constraints oblatesphericalprolate

12. Kinematics of stream stars Leading stream velocities from Law et al. (2003) Measured kinematics support prolate halo shape Differences greater than 100 km/s for other shapes!! oblatesphericalprolate

13. Conclusions I The kinematics of the stars in the streams of Sgr provide direct evidence of the prolate shape of the Galactic halo Favoured axis ratio: q ~ 1.25, or q  ~ 5:3 Consistent with expectations for CDM Implications: Lower local value of the dark matter density (for a fixed circular velocity) No streams from Sgr crossing the Solar neighbourhood

14. No nearby streams from Sgr prolate oblate spherical Distance from the Sun Law et al. (2004)

15. Conclusions II The Sgr streams are the most notorious, highest density in the sky Other streams through Solar neighbourhood will have (much) lower density constrast Such streams have been observed (Helmi et al. 1999), but their stellar densities are lower than 5% of the local stellar value. Given segregation of stars and dark matter in the centres of galaxies, dark-matter streams should have even lower contrast Not have a large effect on dark matter detectors