Joe Wolf (UC Irvine) - University of California, Irvinewolfj/WolfRioIAUAugust2009.pdf · A...
Transcript of Joe Wolf (UC Irvine) - University of California, Irvinewolfj/WolfRioIAUAugust2009.pdf · A...
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A comparison between Milky Way and Andromeda satellites
Joe Wolf (UC Irvine)
Dark Matter in Early-Type Galaxies Rio de Janeiro, Brazil August 3rd, 2009
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Greg Martinez James Bullock Manoj Kaplinghat Frank Avedo
KIPAC: Louie Strigari OCIW: Josh Simon
Yale: Marla Geha Ricardo Munoz
Haverford: Beth Willman
Team Irvine:
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1. A new mass estimator: accurate without knowledge of anisotropy/beta
2. Applications of new mass determinations for MW dSphs
3. Comparison between MW and M31 dSphs
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Many gas-poor dwarf galaxies have a significant, usually dominant hot component. They are dispersion supported, not rotation supported.
Consider a spherical, dispersion supported system whose stars are collisionless and are in equilibrium. Let us consider the Jeans Equation:
We want mass
Unknown:
Anisotropy
Radial
dispersion
(depends
on beta)
Assume known:
3D deprojected
stellar densityFree function
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Jeans
Equation
Velocity
Anisotropy
(3 parameters)
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Jeans
Equation
Velocity
Anisotropy
(3 parameters)
Mass Density
(6 parameters)
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Jeans
Equation
Velocity
Anisotropy
(3 parameters)
Mass Density
(6 parameters)
Using a Gaussian PDF for the observed stellar velocities, we marginalize
over all free parameters (including photometric uncertainties) using a
Markov Chain Monte Carlo (MCMC).
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Given the following kinematics…
Reff
Walker et al. 2007, ApJ
Rlimit
(Ignore)
LO
S D
ispers
ion (
km
/s)
Projected (On Sky) Radius
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Given the following kinematics, will you derive
a better constraint on mass enclosed within:
a) 0.5 * r1/2 b) r1/2 c) 1.5 * r1/2
Where r1/2 is the derived 3D deprojected half-light radius of the system.
(The sphere within the sphere containing half the light).
Reff
Walker et al. 2007, ApJ
Rlimit
(Ignore)
LO
S D
ispers
ion (
km
/s)
Projected (On Sky) Radius
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Joe Wolf et al., in prep
Confidence Intervals:Cyan: 68%Purple: 95%
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It turns out that the mass is best constrained within r1/2, and despite the given data, is less constrained for r < r1/2 than r > r1/2.
Joe Wolf et al., in prep
Confidence Intervals:Cyan: 68%Purple: 95%
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Radial Anisotropy
Tangential
Isotropic
Joe Wolf et
al., in prep
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Center of system:
Observed dispersion is radial
Edge of system: Observed dispersion is tangential
Radial Anisotropy
Tangential
Isotropic
Joe Wolf et
al., in prep
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Center of system:
Observed dispersion is radial
Edge of system: Observed dispersion is tangential
Newly derived analytic equations predict that the effect of anisotropy is minimal near r1/2 for observed stellar densities:
Radial Anisotropy
Tangential
Isotropic
Joe Wolf et
al., in prep
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Derived equation under several simplifications:
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r1/2 ≈
4/3 * Reff
Derived equation under several simplifications:
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Isn’t this just the scalar virial theorem (SVT)?
Nope! The SVT only gives you limits on the total mass of a system.
This formula yields the mass within r1/2, the 3D deprojectedhalf-light radius, and is accurate independent of our ignorance of anisotropy.
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Joe Wolf et al., in prep
Boom!Equation tested on systems spanning almost eight decades in half-light mass after lifting simplifications.
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“Classical” MW dwarf spheroidals
Joe Wolf et al., in prep
Dotted lines:
10% variation in
factor of 3 in MAppx
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Error dominated by kinematics
Joe Wolf et
al., in prep
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Error dominated by kinematics
Error dominated by anisotropy
Joe Wolf et
al., in prep
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Joe Wolf et
al., in prep
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Joe Wolf et
al., in prep
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Joe Wolf et
al., in prep
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Joe Wolf et
al., in prep
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Strigari, Bullock, Kaplinghat, Simon, Geha, Willman, Walker 2008, Nature
A common mass scale? M(<300)~107 MsunMhalo~109 Msun
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Strigari, Bullock, Kaplinghat, Simon, Geha, Willman, Walker 2008, Nature
A common mass scale? M(<300)~107 MsunMhalo~109 Msun
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Joe Wolf et al., in prep
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Joe Wolf et al., in prep
A common mass scale? Plotted: Mhalo = 3 x 109 Msun
Bullock+ 01
c-M relation
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Bullock+ 01
c-M relation
Notice: No trend with luminosity, as might be expected! Joe Wolf et al., in prep
A common mass scale? Plotted: Mhalo = 3 x 109 Msun
Minimum mass threshold for galaxy formation?
Bullock+ 01
c-M relation
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UC Irvine: James Bullock, Manoj Kaplinghat, Erik Tollerud, Joe Wolf, Basilio Yniguez
UC Santa Cruz: Raja Guhathakurta (SPLASH PI)
STScI: Jason Kalirai
Yale: Marla Geha
U. Washington: Karrie Gilbert
Caltech: Evan Kirby
And others involved in SPLASH
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Observ
ed h
alf-lig
ht ra
diu
s
McConnachie
& Irwin 2006,
MNRAS
Dim Luminosity Bright
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Spectroscopic data from Keck/DEIMOS.
DM halo mass offset by ~10.M(<300 pc) offset by ~2.
Joe Wolf et al., in prep
3x109 Mo
3x108 Mo
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If M31’s DM halo collapsed later Less dense substructure & later forming star formation.
Interesting:
Brown et al. 2008 find that portion of investigated M31 stellar halo is younger (on average) than MW’s.
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Joe Wolf et al., in prep
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Much information about feedback & galaxy formation can be summarized with this plot. Also note similar trend to number abundance matching.
Joe Wolf et al., in prep
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Much information about feedback & galaxy formation can be summarized with this plot. Also note similar trend to number abundance matching.
L*: Efficient at
galaxy
formation
Inefficient at
galaxy formation
Globulars:
Offset from L*
by factor of
three
(Hmm…)
Joe Wolf et al., in prep
Ultrafaint dSphs:
Most DM
dominated
systems known!
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Joe Wolf et al., in prep
Last plot:
Mass floor
This plot:
Luminosity ceiling
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- M31 dSphs: Offset mass scale. What the *&%#?!
- Knowing M1/2 accurately without knowledge of anisotropy gives new constraints for galaxy formation theories to match
- Future simulations must be able to reproduce these results
- GCs vs L*: M/L ratios are offset…hmm?
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Dispersion data from Kalirai et al 2009, in prep
x = Andromeda dSph
And # σ
km/s
I 76 9.1 ±1.0
II 95 7.3 ±0.8
III 43 4.7 ±1.0
X 22 3.9 ±1.2
XIV 38 5.4 ±1.1
Keck/DEIMOS