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Dark Matter in Dwarf Galaxies . Rosemary Wyse Johns Hopkins University. Gerry Gilmore, Mark Wilkinson, Vasily Belokurov, Sergei Koposov, Matt Walker, John Norris Wyn Evans, Dan Zucker, Andreas Koch, Anna Frebel, David Yong . The Smallest Galaxies as Probes of Dark Matter

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dark matter in dwarf galaxies

Dark Matter in Dwarf Galaxies

Rosemary Wyse

Johns Hopkins University

Gerry Gilmore, Mark Wilkinson, Vasily Belokurov,

Sergei Koposov, Matt Walker, John Norris

Wyn Evans, Dan Zucker, Andreas Koch, Anna Frebel, David Yong


The Smallest Galaxies as Probes of Dark Matter

and Early Star Formation:

  • Spatial distribution of stars limits dark matter scale length
    • Implies minimum scale length of dark matter, suggests not CDM
  • Motions of stars constrain (dark) matter density profile
    • Most straightforward analysis  all have similar dark matter halos, with cores not cusps, suggests not standard CDM
      • Densities imply form at redshifts ~ 10, reionization?
      • All contain old stars
    • Velocity dispersions & masses for the ‘ultra-faint’ systems uncertain
    • Full distribution function modelling for luminous dwarfs: large samples
  • Astrophysical constraints:
    • Chemical abundances of dwarf galaxies show trends, not consistent with severe tidal stripping as in CDM models
    • Fossil record constrains `feedback’ – each dwarf galaxy has own star formation history, but similar dark halo
    • Elemental abundances: invariant massive-star IMF
  • Targets for indirect detection

field of streams and dots
Field of Streams(and dots)

Belokurov et al (inc RW, 2006)

Segue 1

Boo I

Outer stellar halo is lumpy: but only ~15% by mass (total mass ~ 109M) and dominated by Sgr dSph stream

SDSS data, 19< r< 22, g-r < 0.4 colour-coded by mag (distance), blue (~10kpc), green, red (~30kpc)


~ 109L

~ 107L

~ 103L


Star clusters

Dark matter, galaxies

Update from Gilmore et al 07

Add ~20 new satellites, galaxies and star clusters - but note low yield from Southern SEGUE/SDSS imaging : only Segue 2 and Pisces II as candidate galaxies 3/8 area (Belokurov et al 09,10)


Norris, RW et al 2010

Wide-area spectroscopy










Red: Segue 1

Black: Boo I

Geha et al

  • Members well beyond the nominal half-light radius in both
  • Stars more iron-poor than -3 dex exist in both
    • Extremely rare in field halo, membership very likely
    • Very far out, parameters and velocity confirmed by follow-up:

Segue 1 is very extended!

  • Both systems show a large spread in iron
    • Implies dark halo for self-enrichment (cf Simon et al 2010)
    • Caveat: Segue 1 in complex part of Galaxy: higher metallicity stars?
from kinematics to dynamics jeans equation then full distribution function modelling
From kinematics to dynamics: Jeans equation, then full distribution function modelling

Jeans equation relates spatial distribution of stars and their velocity dispersion tensor to underlying mass profile

Either (i) determine mass profile from projected dispersion profile, with assumed isotropy, and smooth functional fit to the light profile

Or (ii) assume a parameterised mass model M(r) and velocity dispersion anisotropy β(r) and fit dispersion profile to find best forms of these (for fixed light profile) beware unphysical models!

Jeans’ equation results allow objective comparisons among galaxies: isotropy is simplest assumption, derive mass profile

Latter only possible for large sample sizes  more luminous dSph, now

Mass-anisotropy degeneracy


Gilmore et al, inc RW 2007

Mass density profiles:

Jeans’ equation with

assumed isotropic

velocity dispersion:

All consistent with


analysis agrees, Wu 07, plus gas-rich systems,

Oh et al 08)

CDM predicts slope of −1.2 at 1% of virial radius, asymptotes to

−1 (Diemand et al. 04) as indicated in plot

  • These Jeans’ models are to provide the most objective comparison among galaxies, which all have different baryonic histories and hence expect different ‘feedback’
enclosed mass
Enclosed mass

Gilmore RW et al 07; Mateo et al 93; Walker et al 07, 09; Strigari et al 08

Very dark-matter dominated. Constant mass within optical

extent for more luminous satellite galaxies.


Extension to lowest luminosities:

Strigari et al 2008

  • Blue symbols: ‘classical’ dSph, velocity dispersion
  • profiles to last modelled point, reproduces earlier results
  • Red symbols: Ultra-faint dSph, data only in central
  • region, extrapolation in radius by factor of up to 10
  • reflects approximately constant velocity dispersions

(Walker et al, Wolf et al)


Beware underestimated errors….and non-members

Koposov et al 2011

Wil 1 not a bound system (? Geha)


Getting the most from Flames on VLT: Bootes-I sample,

12 x 45min integrations ~1 half light radius FOV, 130 fibres

. Koposov, et al (inc RW), submitted

Retain full covariance:

map spectra models

onto data, find ‘best’

match log(g),[Fe/H],

T_eff, with a

Bayesian classifier.

Black: data r=19; red=model

37 members, based on

Velocity, [Fe/H], log g

Literature value


Very large samples with precision kinematics now exist, motivating

full velocity distribution function modeling, going beyond moments

Walker et al, Gilmore et al


Fornax: 2737

Sculptor: 1368

Sextans: 441

Carina: 1150

Plus new VLT


Car, Sext ~50%

For, Scl ~80%


Wyse et al 2006

comparing models with kinematic data
Comparing models with kinematic data

Surface brightness profile input, determined from data

Two-integral velocity distribution function models

Invert integral equation for stellar density profile as a function of the potential to find all DFs consistent with observed data

Project to obtain LOS velocity distribution on a grid of R and v los

Generalized Hernquist/NFW halo (Zhao 1996)

Parameters: 3 velocity distribution parameters (anisotropy, scale), 5 halo parameters & 5 stellar parameters (density profiles)

Markov-Chain-Monte-Carlo, scan 13-parameter space

Multiple starting points for MCMC used - chains run in parallel and combined once “converged”

Error convolution included - using only data with

Many tests carried out e.g. effects on models of ignored triaxiality, tides, uncertainty in surface brightness profile etc


fornax real data preliminary density profile
Fornax: real data - PRELIMINARY density profile

Log ρ (M/kpc3)

Log r (kpc)

  • 3 MCMC chains combined: total of ~5000 models
  • At radii where most of data lie, clear constraints on profile
    • Inner regions uncertain, few stars observed
  • Mass profiles are now/soon being derived from kinematics
main performances and capabilities
Main Performances and Capabilities


20 as at V = 15 0.2 mas at V = 20

radial velocities to <10 km/s complete to V ~ 17.5

sky survey at ~0.2 arcsec spatial resolution to V = 20

multi-colour multi-epoch spectrophotometry to V = 20

dense quasar link to inertial reference frame


10 as  10% at 10 kpc (units=pico-rads)

[~1cm on the Moon]

10 as/yr at 20 kpc  1 km/s at V=15

 every star Gaia will see, Gaia will see move

 GAIA will quantify 6-D phase space for over 300 million stars,

and 5-D phase-space for over 109 stars

construct line of sight velocity distributions mcmc comparison to data
Construct line of sight velocity distributionsMCMC comparison to data
  • Fit surface brightness profile
  • Use method by P. Saha to invert integral equation for all DFs consistent with observed ρ


  • Project to obtain LOS velocity distribution on a grid of and
  • convolve with individual velocity errors, and compare to data (MCMC)
going beyond velocity moments
Going beyond velocity moments
  • More general halo profile:
  • 2-integral distribution functions F(E,L) constructed using scheme of Gerhard; Saha
  • Models projected along line of sight and convolved with velocity errors
  • Data analysed star-by-star: no binning
fornax dispersion profile
Fornax - dispersion profile

NB: Dispersion data not used to constrain models

fornax dispersion profile1
Fornax - dispersion profile

NB: Dispersion data not used to constrain models


Draco: Okamoto 2010, PhDCarina: Monelli et al 2003




Luminous dSph contain stars with a very wide age, varying from systems to system, but all have old stars: ancient, stable.

Extended, very low star formation rates  Minimal feedback


Tests with spherical models



Log ρ (M/kpc3)

Log ρ (M/kpc3)

Log r (kpc)

Log r (kpc)

  • Artificial data sets of similar size, radial coverage and velocity errors to observed data set in Fornax
  • Excellent recovery of input profiles (solid black), even in inner regions; green dashed is most likely, black dashed enclose 90%

confidence limits


Tests with (anisotropic) triaxial models



Log ρ (2e5 M/kpc3)

Log ρ (2e5 M/kpc3)

Log r (kpc)

Log r (kpc)

  • Axis ratios 0.6 and 0.8, similar to projected 0.7 of Fornax dSph; ~2000 velocities, to match data
  • Models have discriminatory power even when modelling assumptions not satisfied

ΛCDM cosmology extremely successful on large scales.

Galaxies are the scales on which one must see thenature of dark matter:

Ostriker & Steinhardt 03

Inner DM mass density depends

on the type(s) of DM

Galaxy mass function depends on DM type

full velocity distribution functions breaking the anisotropy mass profile degeneracy
Full velocity distribution functions:breaking the anisotropy-mass profile degeneracy

Analyse velocities

star-by-star, no


Abandon Jeans

Different radial

velocity distribution

Same dispersion


dark matter halos in cdm have cusped density profiles
Dark-matter halos in ΛCDM have ‘cusped’ density profiles

ραr -1.2

in inner regions

Diemand et al 2008

Test best in systems with least contribution to mass from baryons :

dwarf spheroidal galaxies

Main halo


Lower limits