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Dwarf spheroidal galaxies and the physical
properties of dark matter
Mark Wilkinson
University of Leicester
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Gerry Gilmore (Cambridge) Jan Kleyna (Hawaii)Andreas Koch (UCLA) Wyn Evans (Cambridge)Eva Grebel (Heidelberg)Rosemary Wyse (JHU)Justin Read (Zurich)Vasily Belokurov (Cambridge)Dan Zucker (Cambridge)
Collaborators
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Local Group satellites
Grebel (1999)
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Satellites and dark matter
Moore
Hot Warm Cold
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• Low luminosity, gas-poor satellites of Milky Way and M31
•
• No well-defined tidal radii
• Individual stellar velocities measurable with ≥ 4m telescopes
•
• Core radii
• Inferred mass-to-light ratios in range
Dwarf spheroidal galaxies
Odenkirchen et al. (2001)
L = 3× 104L! − 2× 107L!
σ0 ∼ 7− 12 km s−1
r0 ≈ 130− 500 pc
3− 300 M!/L!
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Velocity dispersion profilesDraco Ursa Minor Sextans
0 2 4
Carina
0 2 4
Leo I
0 2 4
Leo II
0 5 10 15
Omega Centauri
0 5 10 15
Mass follows light
Gilmore et al. (2007)
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Velocity dispersion profiles II
Walker et al. (2007)
dSph dispersion profiles generally remain flat to large radii
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Are dSphs in equillibrium?
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Koch et al. (2007)
• Velocity gradients are signature of tidal disturbance
• No dSph shows evidence of significant velocity gradient in inner regions ⇒ bulk mass estimates are robust
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dSphs: the case for cored haloesJeans equations give simple relation between kinematics, the light distribution and the underlying mass distribution
We can either:
1. Assume a parameterised mass model and velocity anisotropy and fit dispersion profile
or
2. Use Jeans equations to determine mass profile from projected velocity dispersion profile and a fit to the light distribution
M(r) = −r2
G
(1ν
d νσ2r
d r+ 2
βσ2r
r
)
β(r)M(r)
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Fitting dSph dispersion profiles: Leo I• Assume either NFW halo
( ) or more general profile ( )
• Best-fit dispersion obtained for cored profiles with roughly isotropic velocity dispersions
• Significant velocity anisotropy not favoured (but not excluded)
• Enclosed mass in both cored and cusped haloes
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Koch et al. (2007)
∼ 8× 107M!
ρ ∝ r−1
ρ ∝ r−α
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Density profiles from Jeans equations: assumptions
10 20 30 40 500.01
0.1
1
10
100
R (arcmin)
Draco
0 10 20 30 400
5
10
15
20
R (arcmin)
1 5 10 500.01
0.1
1
10
R (arcmin)
Carina
0 10 20 300
5
10
15
R (arcmin)
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• Masses:
• Conclusion: dSph kinematics are consistent with cored haloes
Density profiles from Jeans equations
3− 8× 107 M! =⇒ M/L = 13− 240 M!/L!
r (kpc)
ρ(M
!pc
−3
)
Ursa Minor
Draco
LeoII
LeoI
Carina
Sextans1/r
10−1 10010−3
10−2
10−1
100
Gilmore et al. (2007)
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• Majority of current data consistent with cored dark matter distributions and a mass scale (interior to light) of
• Mean dark matter density
• NFW halo:
Global trend of dSph haloes
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Mateo et al. (1998), Wilkinson et al. (2006), Gilmore et al. (2007)
∼ 3× 107M!
ρ(r < 10 pc) ≈ 60 M! pc−3(2 TeV/c2cm−3)
! 0.1 M! pc−3(5GeV/c2 cm−3)
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Size distribution of stellar systems
Gilmore et al. (2007)
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The next step - resolving the cusp/core issue with the VLT
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• Degeneracy between velocity anisotropy and inner density profile can be broken using ~500 radial velocities in the inner 0.2 kpc
• Program to apply this to Carina dSph currently underway at VLT
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Conclusions
• Dwarf spheroidal galaxies are valuable laboratories for testing the properties of dark matter
• No kinematic evidence that tides have inflated central velocity dispersions of dSphs
• Current kinematic data are consistent with high M/L ratio, cored dark matter distributions - mass scale ( ):
• Mean dark matter density:
• In cusped halo:
• More data being obtained to place more robust constraints on density profiles
∼ 3× 107M!r ! 400 pc
ρ(r < 10 pc) ≈ 60 M! pc−3(2 TeV/c2cm−3)
! 0.1 M! pc−3(5GeV/c2 cm−3)