Internal Kinematics of Seven Dwarfs: Carina, Draco, Fornax, Leo I, Leo II, Sculptor,

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Internal Kinematics of Seven Dwarfs Carina,
Draco, Fornax, Leo I, Leo II, Sculptor, Sextans
With Thanks To Dan Fabricant Gabor Furesz Andy
Szentgyorgyi Nelson Caldwell Daniel
Eisenstein Richard Cool Kurtis Williams Perry
Berlind John Roll MMT staff and TAC MMT telescope
operators

• Matthew G. Walker University of Michigan
• Collaborators
• Mario Mateo University of Michigan
• Edward Olszewski University of Arizona,
  Steward Observatory
• Bodhisattva Sen University of Michigan, Dept.
  of Statistics
• Xiao Wang University of Michigan, Dept. of
  Statistics
• Jayanta Kumar Pal University of Michigan,
  Dept. of Statistics
• Michael Woodroofe University of Michigan,
  Dept. of Statistics
• Rebecca Bernstein University of Michigan
• Jim Joyce University of Michigan, Dept. of
  Philosophy

First Symposium on Science at the MMTO 14 June,
2006
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Dark Matter from Observations

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Dark Matter From Simulations
Center for Cosmological Physics (U. Chicago)
Klypin et al. 1999
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Dwarf Spheroidal Galaxies
Dra
Car
Leo II
For
Leo I
UMi
Sex
Sgr
CMa
UMa
Boo
Scl
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Dwarf Spheroidal (dSph) Galaxies

• 12 satellites of the Milky Way
• L 105-7 Lsun
• R 0.5 3 kpc
• Stellar speeds of 10 - 20 km/s
• Smallest stellar systems with dark matter
• M/L a few to a few hundred
• M(r)?
• Origin?
• Interaction with MW?
• Sufficiently nearby to study individual stars

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Great Moments in dSph Kinematics
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Great Moments in dSph Kinematics
Carina N17
Fornax N44
N91
Leo I N34
Leo II N31
N94
Sextans N21
Sculptor N32
Armandroff Da Costa 1986 Mateo et al. 1991
Mateo et al. 1993 Hargreaves et al. 1994 Vogt
et al. 1995 Armandroff et al. 1995 Mateo et al.
1998
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Large Telescopes Fiber-Echelle Spectrographs
Great Moments in dSph Kinematics

• MMT Hectochelle
• 240 fibers over 1 degree
• 5150 5300 A (R 30000)
• /- 1-2 km/s velocities for V20.5 stars in 1.5
  hours exposure time
• 600-1000 spectra per night!

• Magellan MIKE
• 256 fibers over 30 arcmin
• 5140-5180 A (R 20000-25000)
• /- 1-2 km/s velocities for V20.5 stars in 2
  hours exposure time
• 600-800 spectra per night!

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Extracted Spectra
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MMT Sample
Leo I N303 M290
Draco N642 M514
Leo II N86 M74
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Magellan Sample
Sculptor N950 M875
Fornax N996 M974
Sextans N702 M408
Carina N1276 M456
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Velocity Distribution
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Velocity Distribution
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Velocity Dispersion Profiles
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Analysis
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Assumptions

• Spherical symmetry
• Equilibrium
• Jeans Equation
• Parameterized forms for f(r) and µ(r)
• Velocity isotropy (ß0)
• Mass follows light

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Non-Equilibrium Models Tidal Disruption

• Tidal disruption simulations
• Velocity gradient along major axis
• Rotation axis perpendicular to proper motion
• Non-decreasing dispersion profile

Read et al. (2005)
Piatek Pryor. (1995)
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Nonparametric Mass Estimation (Wang et al. 2005)

• Assumptions
• Spherical symmetry
• Dynamical equilibrium
• Velocity isotropy
• Parametric model
• Mass follows light
• Jeans Equation
• where
• Estimate f(r) and µ(r) separately
• f(r) as a step function, recover from star count
  data
• M(r) as a cubic spline subject to shape
  restrictions

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Non-parametric M(r) Estimates for 3 dSphs
Sculptor
Fornax
Carina
M(lt1300pc) 2 x 108 Msun
M(lt375pc) 4 x 107 Msun
M(lt460pc) 3 x 107 Msun
M/LV 70
M/LV 20
M/LV 13
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Nonparametric M(r) and vcirc(r)
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Dependence on Sample Size
N100 stars
N400
N700
N1000
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2-D Kinematic Substructure
Velocity dispersion surface
Significance of cold features
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Summary

• Measured radial velocities for 5000 stars (3600
  members) in 7 dSphs
• 1000 stellar velocities (900 members) for 3 dSphs
  with MMT in 4 nights
• Velocity dispersion profiles are generally flat,
  but perhaps rising at large radius.
  Contamination?
• Future work more spectra, larger radius, lets
  push MMT/Hectochelle

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Distinct Kinematic Populations in
Sculptor(Tolstoy et al., 2005)
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Equilibrium Models 2 Two-Component King Model

• Spherical symmetry
• Equilibrium
• Parameterized DF (truncated isothermal sphere)
• Velocity isotropy
• Mass follows light
• Luminous Dark component (dynamically coupled)

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Brief History of dSph kinematic studies
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Equilibrium Models 2 Two-Component King Model
Walker et al. (2006)
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Equilibrium Models 3 Jeans Analysis

• Spherical symmetry
• Equilibrium
• Parameterized moments of DF
• Velocity isotropy
• Mass follows light
• Luminous Dark component (dynamically coupled)
• E.g., Strigari et al. (2006)

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Equilibrium Models 3 Jeans Analysis
Strigari et al. (2006)
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Equilibrium Models 4 Nonparametric Models

• Spherical symmetry
• Equilibrium
• Parameterized moments of DF
• Velocity isotropy
• Mass follows light
• Luminous Dark component (dynamically coupled)
• E.g. Wang et al. (2005)
• Mass nondecreasing with r
• Density decreases with r

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Equilibrium Models 4 Nonparametric Models
v_disp(r)
M(r) and v_circ(r)
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Non-Equilibrium Models Tidal Disruption
Walker et al. (2006)
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Issues
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Issue 1 Foreground Contamination

• Improve decontamination algorithms (using stellar
  positions and foreground model)
• Washington photometry
• Model the DF with foreground component

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Issue 2 Distinct Stellar Populations
Tolstoy et al. (2004)

• Need to determine metallicity information from
  MMFS spectra
• Calibrate RGB photometry

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Issue 3 dSph Substructure

• Complicates equilibrium analysis
• Interesting in its own right
• Origin and evolution of dSphs
• Survival of substructure constrains halo models
• Disruption
• Dynamical friction

Coleman et al. (2004)
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Velocity Dispersion Surface
Walker et al. (2006)
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Recovering f(r) from its Projection

• Let
• projected density gS(s) relates to 3-D density by
• Let
• We estimate GS directly from star counts
• Treat f as step function
• for

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Substructure
Coleman et al. (2004 2005)
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