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Dark Matter and Baryons on
Small Spatial Scales
Rosemary Wyse
Johns Hopkins University
Gerry Gilmore, Mark Wilkinson, Vasily Belokurov, John Norris
Wyn Evans, Dan Zucker, Andreas Koch, Eva Grebel
ΛCDM cosmology extremely successful on large scales.
Galaxies are the scales on which one must see the
nature of dark matter & galaxy formation astrophysics
Ostriker & Steinhardt 03
Galaxy mass function
depends on DM type
Inner DM mass density depends
on the type(s) of DM
GHALO (Stadel et al 09)
MW Dark Halo in ΛCDM
In ΛCDM the first scales to form
are small, and galaxies like the
Milky Way evolve through merging
and assimilation of smaller systems.
Highest resolution N-body
simulations (gravity only)
show persistent small-scale
substructure, with many more darkmatter subhaloes surviving to the
present-day than we see as
satellite galaxies around the
Milky Way or Andromeda Galaxy
 `feedback’ to match mass
function of CDM to galaxy
luminosity function, on all scales
Dark-matter halos in ΛCDM have
`cusped’ density profiles
ρ α r -1.2
in inner regions
Diemand et al 2008
Main halo
Sub-halos
Lower limits
here
Galaxy-scale Challenges for CDM
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On galaxy scales there is an opportunity to learn
some (astro)physics:
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Large galaxies of old stars, small galaxies of young (plus old) stars
‘downsizing’
Massive pure-thin-disk galaxies exist: None should since mergers
heat and puff-up disks, create bulges
The MWG has a thick disk, and these stars are old, as in the bulge.
This seems common but implies little merging since early times, to
build them up
Sgr dSph in the MWG proves late minor merging happens, but is
clearly not dominant process in evolution of MWG except the outer
~
halo, RGC > 25 kpc
The ‘feedback’ requirement: otherwise gas cools and stars form too
efficiently, plus angular momentum transported away from gas in
mergers: stellar disks are too massive and compact
The substructure problem – how to hide them?
The smallest galaxies as probes of Dark Matter:
 Spatial distribution of stars contains clues as to dark
matter scale length
 Minimum scale length of dark matter, suggests not CDM
 Motions of stars constrain the (dark) matter density
profile
 Most straightforward analysis  all have similar dark matter
halos, with cores not cusps, suggests not standard CDM
 Beware claimed masses for the `ultra-faint’ systems, too
uncertain
 Full distribution function modelling for luminous dwarfs
 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
Dwarf Spheroidals
 Low luminosity, low surface-brightness satellite galaxies,
‘classically’ L ~ 106L, V ~ 24 mag/•
 (~10 L/pc2)
 plus ultra-faint galaxies discovered in SDSS
 Extremely gas-poor
 No net rotation, supported by stellar ‘pressure’, velocity
dispersion, measured by line-of-sight velocities of members
 Apparently dark-matter dominated
 velocity dispersion ~ 10km/s, 10 < M/L < 1000
~
~
 Metal-poor, mean stellar metallicity < 1/30 solar value
~
 Extended, low-rate star-formation histories typical, all from
early epochs, perhaps before reionization
 Most common galaxy in nearby Universe
 Crucial tests for models of structure formation and star
formation
Field of Streams
(and dots)
Belokurov et al (inc RW, 2006)
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Boo I
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Segue 1
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
Self-gravitating
Star clusters
Dark matter, galaxies
~ 103L
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 (Belokurov et al 09,10)
Minimum scale-length not just in Local Group:
nearby (<10Mpc; M81 group, Sculptor group..)
low-luminosity dwarfs do not lie on scale-length
scaling of larger disks: scale-lengths are larger
Sharina et al 08
– consistent with same minimum
Open: gas rich
Filled: gas poor
Exponential fits to surface photometry from HST
Minimum Dark Matter Length Scale
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There is a well-established size bi-modality:
♦ all equilibrium systems with size < 35pc are purely
stellar −16 < Mv < −1, M/L~< 4; e.g. globular clusters,
nuclear star clusters..
♦ all systems with size greater than ~120pc have darkmatter halo : minimum scale of dark matter?
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Expect dark matter scale length to be at least equal to stellar
scale length (gas dissipates prior to star formation)
Extreme baryon loss in dSph – expand to new equilibrium (?)
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Stars could not have formed at the extremely low surface
densities observed today
 No confirmed (equilibrium) galaxies with half-light radius
less than ~ 120pc
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Exceptions are faint and closer than ~50kpc to Galactic
center – regime of Sgr tidal tails/streams, may be
associated (e.g. Segue 1, Niederste-Ostholt et al inc.
RW 2009) – and on deep images often appear tidally
disturbed systems
Membership uncertainties due to difficulty of modelling
field contamination plus small number statistics,
together with expected low intrinsic velocity dispersion
hampers mass determinations
Focus on more luminous dwarf spheroidals for
masses, mass profiles
From kinematics to dynamics:
Jeans equation, then full distribution function modelling
Only possible for large sample sizes  more luminous dSph
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Jeans equation relates spatial distribution of stars and their
velocity dispersion tensor to underlying mass profile
Mass-anisotropy degeneracy
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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)
Jeans’ equation results allow objective comparisons among
galaxies: isotropy is simplest assumption, derive mass profile
Mass density profiles:
Jeans’ equation with
assumed isotropic
velocity dispersion:
Gilmore et al, inc RW 2007
All consistent with
cores (independent
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 different ‘feedback’
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 our results
Red symbols: Ultra-faint dSph, data only in central
region, extrapolation in radius by factor of at least 100
 reflects approximately constant velocity dispersions
Beware underestimated errors….and non-members
Wil 1 not a bound system (Geha); Segue 1 status unclear:
cluster or galaxy?
Segue 1: Most dark-matter dominated,
faintest galaxy or star cluster?
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Segue 1 is at location of debris from the Sgr dSph
-- line-of-sight, distance and velocity (NiedersteOstholt et al inc RW, 2009), and radial-velocity
members very extended on sky
Cannot exclude contamination and spuriously
high velocity dispersion – plausibly star cluster of
Sgr dSph
Available metallicity distribution based on four
stars: two radial-velocity members at ~ 0.01 solar
(Norris, RW et al. 2010), equal to that of the field
halo, and of Sgr debris, two others very metalpoor, at 0.0003 solar ([Fe/H] ~ -3.5)
Chemical abundances:
Norris, RW et al 2010
Mean iron abundance of member stars
against total luminosity of host system:
clear trend, hard to maintain if
significant loss of stars through tidal
stripping of host
Segue 1 (filled red star) based on
4 stars, 2 at 0.0003 solar iron value
([Fe/H] = -3.5), 2 at 0.01 solar iron:
all members??
Dispersion in metallicity increases as
luminosity decreases – consistent with
inhomogeneous stochastic enrichment
but need more data!!
Full velocity distribution functions:
breaking the anisotropy-mass profile degeneracy
Abandon Jeans
x
Same dispersion
profile
Different radial
velocity distribution
Very large samples with precision kinematics now exist.
Good data in inner parts for density profiles on small scales,
outer regions for total masses.
Members:
Fornax: 2737
Sculptor: 1368
Sextans: 441
Carina: 1150
Plus new VLT
Yield:
Car, Sext ~50%
For, Scl ~80%
Non-members:
Wyse et al 2006
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Magellan (Walker data) +VLT (Gilmore, RW et al)
Focus on Fornax: largest dataset, turndown
in dispersion, well-behaved kurtosis
Comparing models with kinematic data
Wilkinson
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Surface brightness profile determined from stars
with good velocity data
Two-integral velocity distribution function models
Generalized Hernquist/NFW halo (Zhao 1996)
Parameters: 3 velocity distribution parameters
(anisotropy); 5 halo parameters (density profile)
Markov-Chain-Monte-Carlo used to scan
parameter space
Multiple starting points for MCMC used - chains run in
parallel and combined once “converged”
Error convolution included - using only data with
Tests with spherical models
Core
Log ρ (M/kpc3)
Log ρ (M/kpc3)
Cusp
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
Core
Log ρ (2e5 M/kpc3)
Log ρ (2e5 M/kpc3)
Cusp
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
Left: Accepted radially anisotropic models, right: tangentially anisotropic
Fornax dSph
We build 2-integral, spherical anisotropic
distribution function general models, and
match data by Markov Chain Monte Carlo
- half of the chains start with γ > 0.5, but
converge to γ < 0.5  favour cores
Sanity check only
Fornax - PRELIMINARY profiles
Mass
ρα r
-1.2
Log M/M
Log ρ (M/kpc3)
Density
Stars
Log r (kpc)
Log r (kpc)
• 3 MCMC chains combined: total of ~5000 models
• M/L ~ 10, stars important, but yet to be subtracted
• Clear constraints on profile – flatter than cusp
• Very large dataset for Carina just obtained (VLT)
The smallest galaxies as probes of Dark Matter:
 Spatial distribution of stars contains clues as to dark
matter scale length
 Minimum scale length of dark matter, suggests not CDM
 Motions of stars constrain the (dark) matter density
profile
 Most straightforward analysis  all have similar dark matter
halos, with cores not cusps, suggests not standard CDM
 Beware claimed masses for the `ultra-faint’ systems, too
uncertain
 Full distribution function modelling for luminous dwarfs
 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
Summary:
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A minimum physical scale for galaxies:
half-light radius >100pc
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Reflects characteristic minimum scale for dark matter?
Cored mass profiles preferred, with similar mean mass
densities ~ few 0.1M/pc3, ~10GeV/cc
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An apparent characteristic (minimum) mass dark halo in all
7
luminous dSph, mass ~10 M within half-light radius
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Approx constant density plus scale, not new info
masses for the lowest luminosity systems more uncertain
Wide range of stellar populations (age distributions,
chemical evolution) despite similar dark matter haloes –
constrains ‘feedback’ and effects on DM
Adds to challenges for CDM: need to consider a variety
of DM candidates e.g. STERILE NEUTRINOS
Formation of a (bulge-dominated) disk
galaxy in CDM: mergers dominate
Abadi et al
2003
Face-on
Edge-on
Stars are colour-coded by age: red = old, blue = young
Norris, RW et al 2010
‘Things’ survey -- low-mass gas-rich
spirals consistent
Log Core density 10-3M/pc-3
Inner density slope
Oh et al 2008
de Blok et al 2008
dSph
But see Kuzio de Naray et al 2010 for alternative : 9 gas-rich lowsurface brightness galaxies, argue core fits do not show proper
scalings or agree with Lyman-α forest bounds
Plausible orbits of Sgr
Radial velocities of
Blue Horizontal
Branch stars from
SDSS show streams,
match Segue 1 (dot)
Wide-area data from AAT/AAΩ
(Gilmore, Wyse, Norris)
plus stellar contours
Easy to inflate velocity
dispersion with Sgr stream
contaminants
Little evolution in dark matter profile in models of dwarf spheroidals
Read et al 2006
A, B denote star-formation prescriptions;
B includes feedback from supernovae
`weak’ wind has average speed 222km/s
Dark solid line is dark-matter only simulation
108 M
Small-scale ~1Mpc N-body/SPH simulations
High resolution (103 M), 199 < z < 10
Governato et al 2010
Leo I, classical dSph
Three fainter discoveries from SDSS (Belokurov et al, inc RW 06a) –
all require confirmation with deeper imaging, then spectroscopy
dSph (?) d=45kpc
dSph d=150kpc
glob (?) d=25kpc
The next step
• 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
2-Integral Distribution function
Gerhard (1991)
Constructing the line of sight
velocity distributions
 Fit surface brightness profile
 Use method by P. Saha to invert integral
equation for DF:
 Project to obtain LOS velocity distribution on a
grid of
and
 Spline to required radii for observed stars, and
convolve with individual velocity errors
Fitting to kinematic data
 Surface brightness profile determined from observations
 Markov-Chain-Monte-Carlo scheme used to scan
parameter space
 Parameters: 3 velocity distribution parameters (
 5 halo parameters (
)
 Multiple starting points for MCMC used - chains run in
parallel and combined once “converged”
 Error convolution included - using only data with
);
Belokurov et al 2010
(distant, 180kpc)
(near, 16kpc)
Star cluster
Contours of stellar density from red giants and main sequence
stars, with red ellipses being 1,2 x half-light radii. Black dots
are blue horizontal branch star candidates (very likely members)
ß(r)
Velocity anisotropy profiles: isotropic input
 Data 
Radius (kpc)
Reassuring, but need to test with models that do not
satisfy our modelling assumptions.....e.g. triaxial
Walker et al (2009): similar results to us from Jeans analysis on his
data for classic dSph (constant mass within half-light radius),
obtain trends when add ultra-faints – but concerns about data
interpretation (membership?) and robustness for these.
Blue curve: fixed NFW halo, scale radius 795pc, Vmax = 15km/s
Red curve: fixed cored halo, scale radius 150pc, Vmax = 13km/s
dSph Star-formation histories are measured (CMDs)
Hernandez, Gilmore & Valls-Gabaud 2000
Leo I
UMi dSph
Atypical
SFH
Intermediate-age population dominates in typical dSph satellite
galaxies – with very low average SFR over long periods
(~5M/105yr), until recently
 Different baryonic histories, same dark matter halos (Gilmore et al,
inc RW 07): not strong feedback from baryons to dark halo
(cf Read et al 06, Fellhauer et al 08)
Dwarf spheroidals all only upper limits
on atomic hydrogen content
Log mass HI/M
Grcevich & Putman 09
Log Distance to parent galaxy (kpc)
Linear power spectrum at z ~ 300, showing influence of
WIMP microphysics:
Physical scales of interest correspond to smallest galaxies
Anticipated DM effects on scales of pc up  first systems
Green, Hofmann & Schwarz 2005
Adding velocity dispersion anisotropy:
Koch et al, inc RW 2007
Leo II
Fixed β
Radially varying β
Cores slightly favoured, but not conclusive
Fornax - surface brightness profile
Fornax - dispersion profile
NB: Dispersion data not used to constrain models