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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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:
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, gr < 0.4 colourcoded by mag (distance), blue (~10kpc), green, red (~30kpc)
~ 107L
~ 103L
Selfgravitating
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)
Widearea spectroscopy









Red: Segue 1
Black: Boo I
Geha et al
Segue 1 is very extended!
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
Massanisotropy degeneracy
Mass density profiles:
Jeans’ equation with
assumed isotropic
velocity dispersion:
All consistent with
cores(independent
analysis agrees, Wu 07, plus gasrich 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
Gilmore RW et al 07; Mateo et al 93; Walker et al 07, 09; Strigari et al 08
Very darkmatter dominated. Constant mass within optical
extent for more luminous satellite galaxies.
Extension to lowest luminosities:
Strigari et al 2008
(Walker et al, Wolf et al)
Getting the most from Flames on VLT: BootesI 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
Members:
Fornax: 2737
Sculptor: 1368
Sextans: 441
Carina: 1150
Plus new VLT
Yield:
Car, Sext ~50%
For, Scl ~80%
Nonmembers:
Wyse et al 2006
Surface brightness profile input, determined from data
Twointegral 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)
MarkovChainMonteCarlo, scan 13parameter 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
Wilkinson
Log ρ (M/kpc3)
Log r (kpc)
Accuracies:
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
multicolour multiepoch spectrophotometry to V = 20
dense quasar link to inertial reference frame
Capabilities:
10 as 10% at 10 kpc (units=picorads)
[~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 6D phase space for over 300 million stars,
and 5D phasespace for over 109 stars
where
Gerhard (1991)
NB: Dispersion data not used to constrain models
NB: Dispersion data not used to constrain models
Draco: Okamoto 2010, PhDCarina: 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
Cusp
Core
Log ρ (M/kpc3)
Log ρ (M/kpc3)
Log r (kpc)
Log r (kpc)
confidence limits
Tests with (anisotropic) triaxial models
Cusp
Core
Log ρ (2e5 M/kpc3)
Log ρ (2e5 M/kpc3)
Log r (kpc)
Log r (kpc)
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
Analyse velocities
starbystar, no
binning
Abandon Jeans
Different radial
velocity distribution
Same dispersion
profile
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
Subhalos
Lower limits
here