1. Probing the dark matter distribution in the Milky Way with tidal streams Monica Valluri Kavli Institute for Cosmological Physics University of Chicago University of Michigan This work forms part of the PhD. Thesis of graduate student: Jennifer Siegal-Gaskins (University of Chicago, KICP) Siegal-Gaskins et al. 2007 (in preparation) Thanks to Andrey Kravtsov, Brant Robertson & Stelios Kazantzidis

2. Outline Goals –Simulate the effects of dynamic subhalos on the properties of tidal streams to derive generic features that can be uniquely attributed to subhalos independent of shape of the DM halo Importance of resonant orbits in halos GADGET 2 Simulations of tidal disruption –of NFW satellites (with “stars” in a Hernquist profile) –Disk+bulge+NFW halo (oblate/prolate/spherical) –two different subhalo distributions drawn from cosmological simulations (Kravtsov et al. 2004) Results

3. 2002: “Dark subhalos will be detectable from future observations”  Tidal streams will generally be dispersed due to small scale tidal heating from dark and luminous subhalos (Also Johnston et al 2002)  In non- spherical halos precession of streams will dominate over the effect of subhalos (Mayer et al 2002) and only very cold (e.g. globular cluster streams) will be useful for identifying dark subhalos (Ibata et al. 2002) Mayer et al. 2002

4. Why revisit the issue? “Missing Satellites” problem not entirely solved: currently popular solutions to this problem imply a population of dark subhalos they should have gravitational influence on streams New SDSS dwarfs: How important are tidal effects from 10 7 msun dwarf spheroidals in modeling tidal streams (and infering halo shape)? It seems unlikely that DM halos are spherical. Are there unique signatures of the tidal effects of dark subhalos that are independent of halo shape?

5. N-body Simulations NFW halo (10 12 M sun ) –Spherical –Oblate (replace r 2 by m 2 =R 2 +z 2 /q 2 ; q=0.6) –Prolate (q=1.3) Miyamoto-Nagai disk (4  10 10 M sun ) Hernquist bulge (8  10 9 M sun ) 250+ dynamic dark matter subhalos drawn from 2 separate cosmological realizations of a MW size halo (Kravtsov et al 2004), set up with same total KE and angular momentum but in equilibrium with galaxy potential. Softened point masses. Spherical NFW satellite: represent DM dominated dE and dSph with 8% of particles in a Hernquist density distribution “painted” as stars total mass 3x10 9 M sun - dynamical friction can be ignored) Rotation curve deviates slightly from KZS (Similar to the preferred model of Klypin, Zhao & Somerville 2002 (KZS)) Background potential

6. Halo shape and orbital type Spherical DM halo: –all satellite orbits rosettes confined to a plane –tidal streams appear as great circles on the sky (Johnston 1998) –presence of substructure should be easily detecable (Johnston et al. 2002, Ibata et al. 2002, Mayer et al. 2002) Out of plane scattering Small scale heating (increased velocity dispersion) (4,-2,-1) In an Oblate, Prolate or Triaxial halo: –Most orbits fill 3-dimensional volumes (e.g “regular orbits”) Tidal streams on regular orbits are broad and not coherent –Resonant orbits are not generally very numerous Confined to a sheet if orbital frequencies satisfy one resonant condition l  x + m  y + n  z = 0 (i.e. only two frequencies are linearly independent) Confined to a closed loop if orbital frequencies satisfy two resonant conditions (only one frequency is linearly independent) (Merritt & Valluri 1999)

7. Surface-of-section of halo orbits map out range of orbits Resonant (sheet or loop) orbits appear as points on SOS Regular “volume filling” orbits appear as continuous invarient curves on SOS Chaotic “volume filling” orbits appear as broken scattered points  On the timescales of the formation of tidal streams (<10 halo dynamical times) the distinction between “chaotic” and “regular” is irrelevant so we just call both “volume filling” or “non resonant”

8. Example of orbits used Resonant orbit Regular orbit

9. Streams in a Prolate Halo Whether the stream is coherent or dispersed depends more on nature of orbit than on presence or absence of subhalos –P2 is “volume filling” therefore more dispersed –P4 is “sheet filling” - resonant. –P2 more dispersed with subhalos –P4 similarly dispersed with and without subhalos –Whether or not subhalos increase dispersion of streams depends on type of orbit !

10. Oblate Halo Suhalos cause: – increased stream clumpiness/ transient projected density enhancements –Features that appear like “bifurcations” (Fellhauer et al 2006) Resonant “Volume filling” but close O2 resonance

11. Increased clumpiness is only in projection No difference seen in phase space density of debris - i.e. clumping is transient Results from formation of a “wake” of tidal stream particles behind a subhalo when the halo passes through the stream. Stream-subhalo encounter is impulsive: wake does not persist Responsible for slightly increased velocity disepersion What causes increased clumping?

12. Spherical Halo Stream with and without subhalos are similarly dispersed Streams do not trace orbital path - subhalos cause significant deviations from orbit in smooth halo Increases difficulty of “tracing” a satellite orbit from observed streams may make it impossible to infer halo shape from stream orbits even with multiple streams.

13. Velocity dispersion of streams expected to increase. Need velocity information for large numbers of stars so use V los which will be the most easy ti measure for large samples. Clumping also is seen in (V los,l) plots Increased velocity dispersion not a robust prediction - in some cases streams appear thinner (and have lower dispersion) Line of sight Velocity Galactic Longitude

14. Phase Space plots  Tidal streams are may be hard to detect in projection but are identifiable in phase space plots (V los vs R) thin contours even in the presence of substructure. Harding et al. 2001 (also Bullock & Johnston 2005)

15. Phase space plots - prolate halo Only use easily observable quantities - radial velocity, distance Subhalos produce “streams” of high velocity stars at large radii Heliocentric LOS velocity Galactocentric distance

16. Oblate halo Heliocentric LOS velocity Galactocentric distance

17. Spherical halo The formation of HVLR streams is –Independent of halo shape –Independent of orbit type (resonant or non-resonant/ coherent or not coherent) –Not sensitive to choice of softening parameter of subhalos –Seen in two independent realizations of the subhalo distribution Heliocentric LOS velocity Galactocentric distance High velocity large radius (HVLR) streams: “smoking gun” of dark subhalos?

18. Possible mechanisms for generating HVLR streams? Distance from galactic center Galactic Longitude (l)

19. Possible mechanisms for generating HVLR streams (Tentative) Resonant pumping - orbital frequencies of one or more subhalos are resonant with orbital frequency of the stream particles at so that the same subhalos interact with the stream particles multiple times with favorable encounter parameters “kicking out particles” (Sideris & Kandrup 2004). (currently no evidence for multiple encounters with the same subhalo). Interaction/heating by the largest subhalos (significant evidence for “wake” - need to quantify mechanism for such a large kick) Interaction of stream particles with two “bound subhalos” (see Sales, Navarro, Abadi, Steinmetz 2007: 1/3 of DM subhalos of a MW sized galaxy have been part of a bound pair). (This type of interaction is seen in almost all the simulations but we need to quantify the effect.)

20. Open issues and future directions What is the effect of the known satellite population on the observable properties of streams? –With/ without additional “dark subhalos” Can the clumpy wakes in streams seen in the simulations be observed and can it be used to identify faint or dark subhalos? How likely is it that HVLR streams will be observationally detected (i.e. put observational errors on all parameters).

21. Summary Shape of halo and nature of the orbit (“resonant” or “volume filling”) has a more significant effect on tidal debris than presence of absence of subhalos Streams in simulations with substructure can deviate significantly from those in simulations without subhalos. Using tidal debris to trace orbit of progenitor could be very tricky with dark subhalos. Subhalos cause significant “transient clumping” in projected distributions due to formation of “wakes” behind subhalos more massive than ~10 7 msun A “smoking gun” of subhalos in all halo shapes are high velocity large radius (HVLR) streams seen in phase space (V los, R) plots. Further investigations are needed to determine the origin of HVLR streams - interactions of streams with binary subhalos currently appears to be a promising mechanism.

22. Thank You!

23. SOS with static subhalos  Stronger resonances: resonant zones are enlarged (more orbits associated)  Orbits remain trapped near resonance RESONANCES