Mapping the Milky Way’s halo with BHB and K giant stars

1. Mapping the Milky Way’s halo with BHB and K giant stars Xiangxiang Xue (Max-Planck-Institute for Astronomy) collaborators: Hans-Walter Rix, Heather Morrison, Paul Harding, Real(Zhibo) Ma, Bill Janesh, Timothy C. Beers, Young Sun Lee, Eric F. Bell, Constance Rockosi, Brian Yanny, James S. Bullock and Kathryn Johnston

2. Exploring the MW’s stellar halo need kinematic tracers with r(α,δ,D), vlos and [Fe/H] to • trace the MW halo mass Mvir (Halo) vs. e.g. Mstar -->> baryon fraction in stars Scale expected number of dark matter sub-halos Dynamics of the local group -->> M31 infall, LMC bound? • see and quantify position-velocity substructure Signposts of hierarchical formation for that, we need tracers which are luminous and have good distances: BHB stars(Mg~0.7) have good distances, but are very old. K-giants (-3<Mr<1) are more representative, but distances are less precise.

3. BHB stars in SDSS （Xue et al. 2008, 2011,Deason et al. 2012) • are luminous enough to be observed in distant halo (d~60kpc); • have nearly constant absolute magnitude (Mg~0.7); So, they have precise distances ~ 5%, but metallicities are only approximate.

4. SEGUE K giant stars SEGUE K giants Giant stars • are luminous to visible to >100kpc • have well-defined ntracer/M*(tot) • are present at all (old) ages and [Fe/H] • (K-)giant stars (in SEGUE) • but have wide luminosity range -3<Mr<1 • How to get good distances for giant stars?

5. A ‘clean’ K-giant sample in SEGUEMa, Morrison et al 2012 • The SSPP slightly overestimates the [Fe/H], but they are consistent with GCs’ [Fe/H] within 0.2 dex. • The SSPP underestimates the log g, so it will introduce some dwarfs if only use log g as a cut. • Mg lines are used to double check!

6. How to get distances? • [Fe/H] from SEGUE spectra • (g-r) from SDSS photometry • DM = mr-Mr( g-r, [Fe/H]) • But!!! • How to incorporate [Fe/H] and g-r errors? • p(L)~L-2  more likely to over-estimate L  over-estimate DM • Very high/low [Fe/H] values are rare  systematic errors • Set up probabilistic framework, including prior (i.e. external) information through Bayes’ theorem observables priors with Gaussian errors

7. Applications in practice: Prior (=external) information Results for 3 stars L(DM) Luminosity prior no [Fe/H] prior no lum. prior • Get L(DM) for each star, which depends on: • [Fe/H] errors, magnitude errors, g-r errors • Mr, [Fe/H]: priors, and shape of isochrones

8. Results: How good are the distances? The impact of priors • We get for 9000 halo giant stars: • Unbiased distance estimates to giant stars • We get distance errors (full pdf) • 5000 K giants with r>15kpc and Mr<0.5 (previous samples: 200) • Distances good to ~15% • Distances most precise at ~100kpc • tip of the giant branch

9. Estimate the MW dark matter halo mass Basic approach: • Assemble a large and well defined set of distant kinematic tracers from SDSS BHBs with distance precision of 5% r~60 kpc, δv~7 km/s, [Fe/H] • Compare to Kinematics in the simulated halos that have been scaled to different halo mass derive p(vlos) at different r model it to get Vcir(r) • Fit Vcir(r) to the NFW DM halo+ Hernquistbulge+exponential disk Mvir=1.0±0.3×1012M⊙

10. Estimate the MW dark matter halo mass Results:(Xue, Rix et al 2008) • Robust measurement M(r<60kpc)=4.0±0.7×1011M⊙ • Vcir(r) is not constant but gently falling. • If DM halo is NFW then Mvir=1.0±0.3×1012M⊙ • Imply (high) 40% of baryons end up as stars. • LMC and other satellites marginally bound.

11. Velocity dispersion of the K giant sample r>15kpc r>15kpc Xue et al 2012 (in prep) • K giants show consistent velocity dispersion profile to BHB etc. by X08 and Deason et al. 2012. • 700 tracers R>40kpc  far smaller error bars • dispersion drops to 65km/s at 100 kpc • new Mvir model ongoing no Sgr stream r>15kpc

12. Quantify the substructure in the stellar halo 4-distance is defined as distance between two stars in 4-dimension space (α,δ,d,vlos)(Starkenburg et al. 2009) Compare to smooth model to quantify the substructure. Results: (Xue, Rix et al. 2011) • Very clear position-velocity substructure signal seen in BHB sample. • The outer halo of the Milky Way exhibits a stronger kinematic substructure signal than the inner halo. • Quantitatively, most simulations produce a stronger substructure signal. BHB stars are overrepresented in the oldest sub-populations of the stellar halo turn to K giants !! log(4distance) log(4distance) log(4distance)

13. Substructure seen in K giant sample (Janesh, Morrison, Ma, Xue et al in prep) stronger substructure in less metal poor stars stronger substructure in K giants (vs BHB) stronger substructure in distant halo Sgr dominates substructure signal

14. Summary • BHB stars have showed that • Vcir(r) is not constant but gently falling • the mass of the dark matter halo is 1.0±0.3×1012M⊙ • obvious substructure signal, more distant more substructure, but weaker than models, which we attribute to BHB stars being overrepresented in the oldest sub-populations • So, we turn to more representative tracers – K giants. • ~5000 K giants with distances good to 15% • more precise at larger distances • 700 K giants with r>40kpc. • Preliminary results from SEGUE K giants show that • the radial velocity dispersion profile σlos(r) is falling with the distance  low-mass halo(?) • K giants show stronger substructure signal than BHBs (metallicity?) • more distant & more metal rich giants show more substructure Thank you!