Measuring Dark Matter Properties with Astrometry

Louie StrigariTASC 2006

10/20/2006

In collaboration with: James Bullock, Manoj Kaplinghat, Stelios Kazantzidis, Steve Majewski

€

QCDM ≈ 7 ×1014 mcdm100GeV

⎛

⎝ ⎜

⎞

⎠ ⎟3 / 2

Msun pc−3(km /s)−3

€

QCDM ≈ 7 ×1014 mcdm100GeV

⎛

⎝ ⎜

⎞

⎠ ⎟3 / 2

Msun pc−3(km /s)−3

€

Q ≈ 5 ×10−4 m

keV

⎛

⎝ ⎜

⎞

⎠ ⎟4

Msun pc−3(km /s)−3

€

Q ≈ 5 ×10−4 m

keV

⎛

⎝ ⎜

⎞

⎠ ⎟4

Msun pc−3(km /s)−3

CDM

WDM

Dark Matter and Galaxy Central Densities

€

Q ≈10−6 10−3

Δm /mDM

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

3

zdecay1000

⎛

⎝ ⎜

⎞

⎠ ⎟

3

Msun pc−3(km /s)−3

€

Q ≈10−6 10−3

Δm /mDM

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

3

zdecay1000

⎛

⎝ ⎜

⎞

⎠ ⎟

3

Msun pc−3(km /s)−3

Louie Strigari UC Irvine

cusp

core

Simon et al 05

SuperWIMPS & Meta-CDM

Dwarf Spheroidal Galaxies

Exhibit no rotation

DM dominated

Information on DM halo from line of sight velocities

Walker et al. 2006

Fornax

To observer

€

σ LOS2 =

2

I(R)1−β

R2

r2

⎡

⎣ ⎢

⎤

⎦ ⎥∫ ρ stars(r)σ r,dm

2 (r)r

R2 − r2dr

Strigari et al. 2006

Degeneracy with cores and cusps in all systems

Nothing prevents dark halos from being very extended

Line of sight profiles

Fornax

Projections

Degeneracy remains unbroken even with 10,000 stars

Space Interferometry Mission (SIM): extragalactic astrometry with micro-arcsec resolution

Errors of order km/s on a few hundred stars at a typical dSph distance

UC IrvineLouie Strigari

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

http://planetquest.jpl.nasa.gov/SIM/sim_index.cfm

Hipparcos Positional Error Circle(0.64 mas)

How Precise is SIM?

HST Positional Error Circle (~1.5 mas)

Reflex Motion of Sun from 100pc (axes 100 µas)

Parallactic Displacement of Galactic Center

Apparent Gravitational Displacement of a Distant Star due to Jupiter 1 degree away

SIM Positional Error Circle

(4µas)

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σR2 =

2

I(R)1−β + β

R2

r2

⎡

⎣ ⎢

⎤

⎦ ⎥∫ ρ stars(r)σ r,dm

2 (r)r

R2 − r2dr

€

σ LOS2 =

2

I(R)1−β

R2

r2

⎡

⎣ ⎢

⎤

⎦ ⎥∫ ρ stars(r)σ r,dm

2 (r)r

R2 − r2dr

€

σφ2 =

2

I(R)1−β[ ]∫ ρ stars(r)σ r,dm

2 (r)r

R2 − r2dr

R

φ

= velocity anisotropy of the stars

Constructing moments for proper motions

Dark matter

4th momen

t

2nd momen

t

Error estimates

€

ε2 =2(n − 2)

n2σ theory

2

n = number of stars in sample

Reconstructing the central slope I. (NFW)

Proper motionsLine of Sight

=

+ +

Reconstructing the central slope II. (Cores)

+ +

=

Proper motionsLine of Sight