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Kinematics of Dwarf Spheroidal Galaxies
Matthew Walker – U. Michigan
Collaborators
Mario Mateo – U. Michigan
Edward Olszewski – U. Arizona, Steward Observatory
Bodhisattva Sen – U. Michigan (Statistics)
Xiao Wang - U. Michigan (Statistics)
Michael Woodroofe – U. Michigan (Statistics)
Rebecca Bernstein – U.C. Santa Cruz
Oleg Gnedin – U. Michigan
Data from Magellan/MMFS and MMT/Hectochelle
The Globular Clusters - Dwarf Galaxies Connection
Ann Arbor, Aug. 27, 2007
Introduction:
Globular Clusters vs. dSphs
• Globulars
–
–
–
–
–
–
Pressure supported
105-6 L_sun
No gas
<v> ~ 10-20 km/s
Single age
Rhalf ~ 10 pc
• dSphs
–
–
–
–
–
–
Pressure supported
105-6 L_sun
No gas
<v> ~ 10-20 km/s
Extended Star formation
Rhalf ~ 100 pc
DSS image of Fornax
Introduction:
Dwarf Spheroidal Galaxies
• Why study dSphs?
– Smallest systems with dark matter
– Dominated by dark matter (baryons negligible!)
– Nearby
• Dark Matter – want to know M(r)
– M/L
– Cusps or cores?
– Halo mass function
Diemand, Kuhlen and Madau (2007)
• Galaxy Evolution – want to understand complex stellar populations
– Star formation histories
– Metallicities/ages
– Stellar kinematics
– Galactic tides
Observations & Data:
Magellan/MMFS and MMT/Hectochelle
Magellan + MMFS
–
–
–
–
256 fibers over 20 arcmin
5140-5180 A (R ~ 20000-25000)
+/- 1-2 km/s velocities for V~20.5
stars in 2 hours exposure time
600 spectra per night!
MMT + Hectochelle
–
–
–
–
240 fibers over 30 arcmin
5150 – 5300 A (R ~ 30000)
+/- 1-2 km/s velocities for V~20.5
stars in 2 hours exposure time
600 spectra per night!
Observations & Data:
Magellan & MMT Samples
~6800 stars, ~5000 members
Kinematics
• 2 tests of Lambda-CDM
– Inner Density profile: cusps vs. cores
– DM halo mass function
• Jeans Equation
Kinematics:
Velocity Dispersion Profiles
Kinematics:
Jeans Equation
If β=0,
If β=0 and constant velocity dispersion,
Kinematics: Mass from Jeans Estimator
ASSUMPTIONS
-Spherical symmetry
-Dynamic equilibrium
-Plummer Model for Stars
-Anisotropy=0
-σV(R)=constant
RESULTS
Central cores, but necessarily so
Kinematics:
NFW Profiles
(Navarro, Frenk & White 1995, 1996, 1997)
ASSUMPTIONS
-Spherical symmetry
-Dynamic equilibrium
-Constant anisotropy
RESULTS
Kinematics:
Non-Parametric Mass Estimation
(Wang et al. 2005)
ASSUMPTIONS
-Spherical symmetry
-Dynamic equilibrium
-Anisotropy=0
-shape restrictions
-M(r) is non-negative
and nondecreasing
-M(r=0)=0
-ρ(r) is non-increasing
Kinematics:
Non-Parametric Estimate, Quadratic vs.
Cubic Spline
P=2 (quadratic spline)
P=3 (cubic spline)
P=2 implies M(r) α r2 as r  0.
P=3 implies M(r) α r3 as r  0.
Thus ρ(r) α r-1 (NFW cusp).
Thus ρ(r) =const. (core).
Kinematics: Robust Measure of M(~2rcore)
see also Strigari et al. (2007); Penarrubia et al. (2007)
Kinematics:
Robust Measure of M(~2r_core)
Kinematics:
Summary of Mass Profiles
• Mass-follows-light models fail.
• Dark Matter dominates even the central mass
density regardless of model.
• Cores vs. cusps? Neither is ruled out by σV(r).
– Isotropy, constant velocity dispersion, Plummer
models  cores
– But, cuspy NFW profiles fit the velocity data.
– We don’t know the anisotropy.
• Halo Mass Function?
– M(600pc) = (2-5) x 107 M_sun regardless of model!
Chemo-dynamics
Chemo-dynamics:
[Fe/H] Distributions and Gradients
Chemo-dynamics:
Stellar Populations
Chemo-dynamics:
spatially, chemically, kinematically distinct populations?
(see also Tolstoy et al. 2004; Battaglia et al. 2006)
Chemo-dynamics:
spatially, chemically, kinematically distinct
populations?
(see also Tolstoy et al. 2004; Battaglia et al. 2006)
Chemo-dynamics: “Tidal
Stirring” as Evolutionary Mechanism
• Distance-morphology relation
– D= 0 -50 kpc  Sgr and streams
– D= 50 -250 kpc  dSph
– D> 250 kpc  dIrr
• Tidal stirring (Mayer et al. 2001, 2005)
– Remove gas
– Convert rotation to pressure support
– Tidal stripping mass lossbar instability decrease in
v_rot/sigma  gas funneled toward center  star formation
– Convert dIrr to dSph in 2-3 perigalactic passages (~5-10) Gyr
– Implies dIrr are the pristine galactic building blocks
Summary
• New spectra of ~ 8000 dSph targets, ~
5000 members
• Flat velocity dispersion profiles
• Neither core/cusp ruled out
• M(600pc) ~ 2-5 x107 M_sun
• Metallicity gradients, metal-rich at center,
metal-poor outward, correlated with
kinematics
4. Galactic Tides
• Tidal disruption simulations:
– Velocity Gradient Along Major Axis (Apparent rotation about
minor axis)
– Major axis aligned with proper motion vector
– Rising velocity dispersion profile
Read et al. (2006)
Piatek & Pryor. (1995)
Galactic Tides:
Kinematic Evidence of Tides?
Rising Velocity Dispersion?
Velocity Gradient?
Magellan/MMT data
Galactic Tides:
Magellan/MMT data
Apparent Rotation?
Galactic Tides:
Magellan/MMT data
Apparent Rotation?
Galactic Tides:
The Case of Leo I
Galactic Tides:
The Case of Leo I
5. Fun with Surfaces


N
q ( x, y) 
i 1
Qi K
N
K
i 1


x  Xi
hx
x  Xi
hx
,
,
y  Yi
hy
y  Yi
hy


Surfaces:
Carina
Surfaces:
Fornax
Surfaces:
Sculptor
Surfaces:
Sextans
5. A Couple of Interesting Things
strigari07
penarrubia07
MoNDian scale length
Substructure
Coleman et al. (2004; 2005)
Nonparametric Mass Estimation
(Wang et al. 2005)
•
•
Assumptions
– Spherical symmetry
– Dynamical equilibrium
– Velocity isotropy
– Parametric model
– Mass follows light
Jeans Equation
where
M (r )  
f (r ) 

r2 (r ) d
G
dr
log[ f (r ) (r )]
f 0 (r , v)dv,
 (r ) 
1
3 f (r )
• 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
2
v
 f 0 (r , v )d v
Recovering f(r) from its Projection
• Let
R  X 12  X 22  X 32 ; S  X 12  X 22
• projected density gS(s) relates to 3-D density
 f (r )r
by
g S ( s)  4 s
s
GS ( s)  P[ S  s] 
G S (rk ) 

s
0
r 2  s2
dr
g ( s')ds'
N1  ...,  N k
N
S
• Let
• We estimate GS directly from star counts:
f (r )  f k
rk 1  r  rk , k  1,..., m
• Treat f as step function:
m
for f j 
1  GS (r j 1 )   a jk f k
k j
1
a jj
[1  GS (r j 1 ) 
m
a
k  j 1
jk
fk ]
Kormendy 1985
There is a size gap between globular clusters and dE gals,
at similar Mv, and similar central velocity dispersion
``ellipticals/bulges, dwarf spheroidal galaxies and globular
clusters are three very different kinds of stellar systems’’
Fundamental Plane Relations
(from Zaritsky et al. 2006)
The Fundamental Manifold
(from Zaritsky et al. 2006)
Jeans Equation (spherical symmetry)
Solution:
Projection:
Kinematics:
Constant-Density Core
(c.f. Strigari et al. 2006)
ASSUMPTIONS
-Spherical symmetry
-Dynamic equilibrium
-Constant Anisotropy
RESULTS
Kinematics:
Robust Measure of M(rcore)
Penarrubia et al. 2007