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1 Probes of Dark Matter on Galaxy Scales Monterey, CA July 15, 2013 The Diversity of Dark Matter Profiles in the Milky Way s dsphs John Jardel, University of Texas

2 Dark Matter & Galaxy Formation Lots of substructure Springel+(2008) Universal density profiles

3 Modeling Dark Matter in Dwarf Spheroidals Multiple Populations WP11 WP11 Review by Battaglia, Helmi, & Breddels (2013) Found cored profile Found cuspy profile Results not conclusive

4 Local Group dsphs Why study Local Group dsphs? DM dominated Lowest mass products of galaxy formation Large public data sets Individual stars resolved Unanswered questions: Cores, cusps, or something else? Challenge to CDM? New details about galaxy formation? Fornax Draco

5 How I m doing this Data Publicly available individual radial velocities from multi-fiber spectroscopy (Walker+ 2009) Individual radial velocities taken with VIRUS-W (a handful in Draco) Surface brightness profiles from star counts Models Orbit-based models (Gebhardt+ 2003) but with the added d feature of specifying a density profile nonparametrically (JJ+ 2013) Usually used in big elliptical galaxies (integrated light kinematics, not individual velocities)

6 Data What form are the data in? fraction of stars r (pc) Walker+ (2009) Murphy+ (2011)

7 From RVs to LOSVDs Individual Radial Velocities * Fitting can also be done to the individual velocities (Maarten Breddels thesis) Line-of-sight Velocity Distributions (LOSVDs) Kernel Density Estimation ion of stars fracti Silverman (1986) JJ+ (2013)

8 Models How do the models work? How do they fit to the data? (courtesy J. Kormendy)

9 Why Schwarzschild modeling? Other forms of modeling subject to massanisotropy degeneracy Schwarzschild modeling picks up extra information in the LOSVD to constrain the orbits Wolf+ (2010) fraction of st tars van der Marel & Franx (1993) JJ & Gebhardt (2012)

10 Non-Parametric Schwarzschild hild Modeling (courtesy M. Cappellari) This is where the non-parametric part comes in r

11 Draco: A test case Input age and metallicity of best-fitting isochrone to SSP models (Maraston+ 2005) to get stellar density JJ usually small

12 Results for 5 dsphs Points w/error bars are point-wise 1σ density Gray band is joint 1σ profile Red band in Fornax is stellar density (only galaxy where stellar density DM density)

13 A common halo? Rescale each density profile to a common normalization and see what happens.

14 V c profiles Boylan-Kolchin, Bullock & Kaplinghat (2012)

15 Anisotropy is mildly radial Radial orbits are a generic prediction of tidal stirring formation method for dsphs

16 Summary/Conclusions There are a variety of different profile types in real galaxies. Future Work: Detailed comparison of modeled d profiles to simulations How does DM profile change with stellar mass? Unleash Non-Parametric Schwarzschild Modeling on more massive galaxies

17 Extra Slides

18 Density estimation Histogram: Kernel Density Estimator: Silverman (1986) How to choose the smoothing size h?

19 Next steps: Feedback from baryons THINGS: HI survey of late-type type field dwarfs Simulations: Governato+ (2012) N- body/hydro cosmological simulations of THINGS-like lk dwarfs core How do DM profiles change in simulations that include baryons? cusp Do more stars = more ( ) p feedback? Governato+ (2012) with dsphs added

20 Anisotropy in Draco Find orbits are mostly radial radial tangential Consistent with tidal stirring scenario for formation of dsphs (Łokas+ 2010, Kazantzidis+ 2011)

21 Draco: A test case New VIRUS-W IFU observations (55 x 105 ) Data from literature JJ+ (2012) JJ+ (2012) New observations Kleyna+ (2002) 158 (from literature) + 12 (new) radial velocities 8 LOSVDs binned in annuli from 8 pc to 500 pc

22 How does Draco compare to ΛCDM simulations? JJ+ (2012) Boylan-Kolchin, Bullock, & Kaplinghat (2012)

23 Draco velocities from VIRUS-W Iterative sigma-clipping Hard cut at 30 km/s from systemic Both methods give same 12 stars as members

24 Draco Photometry in inner region JJ+ (2012)

25 Line-of-sight Velocity Distributions (LOSVDs) LOSVDs contain information about what types of orbits the stars are on van der Marel l& Franx (1993) They are the kinematics input in our models JJ & Gebhardt (2012)

26 Maximum Entropy Regularization Typical models have >10,000 orbits and only 20 LOSVDS with 15 velocity bins (300 observables) bl Thomas et al. (2005)

27 Calculating Phase Space Volumes Evaluating the integral Voronoi Tessellation Enclose each point (site) in SOS inside a polygon Area contains all points which lie closer to site in consideration than another Thomas et al. (2004)

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