Transcript 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.

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)
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 3/8 area (Belokurov et al 09,10)
Red: Segue 1
Black: Boo I
Geha et al
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Norris, RW et al 2010
Wide-area spectroscopy
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
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Very far out, parameters and velocity confirmed by follow-up:
 Segue 1 is very extended!
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Both systems show a large spread in iron
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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
Latter only possible for large sample sizes  more luminous dSph, now
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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) beware unphysical models!
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 expect 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 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
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Koposov, et al (inc RW), submitted
Retain full covariance:
Black: data r=19; red=model
map spectra models
onto data, find ‘best’
match log(g),[Fe/H],
T_eff, with a
Bayesian classifier.
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
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
Comparing models with kinematic data
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Wilkinson
Surface brightness profile input, determined from data
Two-integral velocity distribution function models
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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
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Generalized Hernquist/NFW halo (Zhao 1996)
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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
Log ρ (M/kpc3)
Fornax: real data - PRELIMINARY density profile
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
Gaia capabilities
Main Performances and Capabilities
Accuracies:
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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
Capabilities:
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
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Construct line of sight velocity distributions
MCMC comparison to data
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Fit surface brightness profile
Use method by P. Saha to invert integral
equation for all DFs consistent with observed ρ
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where
Project to obtain LOS velocity distribution on a grid of
and
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convolve with individual velocity errors, and compare to
data (MCMC)
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
2-Integral Distribution function
Gerhard (1991)
Fornax - dispersion profile
NB: Dispersion data not used to constrain models
Fornax - dispersion profile
NB: Dispersion data not used to constrain models
Draco: Okamoto 2010, PhD
Carina: Monelli et al 2003
1Gyr
5Gyr
12Gyr
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
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
ΛCDM cosmology extremely successful on large scales.
Galaxies are the scales on which one must see the
nature of dark matter:
Ostriker & Steinhardt 03
Galaxy mass function
depends on DM type
Inner DM mass density depends
on the type(s) of DM
Full velocity distribution functions:
breaking the anisotropy-mass profile degeneracy
Analyse velocities
star-by-star, no
binning
Abandon Jeans
Same dispersion
profile
Different radial
velocity distribution
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
Test best in systems
with least contribution
to mass from baryons :
dwarf spheroidal
galaxies