Dark Matter in Dwarf Galaxies

Rosemary WyseRosemary Wyse

Johns Hopkins UniversityJohns Hopkins University

Gerry Gilmore, Mark Wilkinson, Vasily Belokurov, Sergei Koposov, Matt Walker, John Norris

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

Spatial distribution of stars limits dark matter scale lengthSpatial distribution of stars limits dark matter scale length Implies minimum scale length of dark matter, suggests not CDMImplies minimum scale length of dark matter, suggests not CDM

Motions of stars constrain (dark) matter density profileMotions of stars constrain (dark) matter density profile Most straightforward analysis Most straightforward analysis all have similar dark matter halos, all have similar dark matter halos,

with cores not cusps, suggests not standard CDMwith cores not cusps, suggests not standard CDM Densities imply form at redshifts ~ 10, reionization?Densities imply form at redshifts ~ 10, reionization? All contain old starsAll contain old stars

Velocity dispersions & masses for the ‘ultra-faint’ systems Velocity dispersions & masses for the ‘ultra-faint’ systems uncertainuncertain

Full distribution function modelling for luminous dwarfs: large Full distribution function modelling for luminous dwarfs: large samplessamples

Astrophysical constraints: Astrophysical constraints: Chemical abundances of dwarf galaxies show trends, not Chemical abundances of dwarf galaxies show trends, not

consistent with severe tidal stripping as in CDM modelsconsistent with severe tidal stripping as in CDM models Fossil record constrains `feedback’ – each dwarf galaxy has own Fossil record constrains `feedback’ – each dwarf galaxy has own

star formation history, but similar dark halostar formation history, but similar dark halo Elemental abundances: invariant massive-star IMFElemental abundances: invariant massive-star IMF

Targets for indirect detectionTargets for indirect detection

The Smallest Galaxies as Probes of Dark Matter and Early Star Formation:

Field of StreamsField of Streams (and dots)(and dots)

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

Belokurov et al (inc RW, 2006)Belokurov et al (inc RW, 2006)

Outer stellar halo is lumpy: but only ~15% by mass Outer stellar halo is lumpy: but only ~15% by mass (total mass ~ 10(total mass ~ 1099MM) and dominated by Sgr dSph ) and dominated by Sgr dSph streamstream

Segue 1

Boo I

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)

Dark matter, galaxiesSelf-gravitatingStar clusters

Update from Gilmore et al 07

~ 107L

~ 103L

~ 109L

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?

Norris, RW et al 2010 Wide-area spectroscopyRed: Segue 1 Black: Boo I

Geha et al

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From kinematics to dynamics: From kinematics to dynamics: Jeans equation, then full distribution function Jeans equation, then full distribution function

modellingmodelling

Jeans equation relates spatial distribution of stars and their Jeans equation relates spatial distribution of stars and their velocity dispersion tensor to underlying mass profilevelocity 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 beware unphysical models!models!

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

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

Mass-anisotropy degeneracy

Mass density profiles:Jeans’ equation with assumed isotropic velocity dispersion:All consistent with cores (independentanalysis agrees, Wu 07, plus gas-rich systems, Oh et al 08)

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

CDM predicts slope of −1.2 at 1% of virial radius, asymptotes to −1 (Diemand et al. 04) as indicated in plot

Gilmore et al, inc RW 2007

Enclosed massEnclosed mass

Very dark-matter dominated. Constant mass within optical extent for more luminous satellite galaxies.

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

Blue symbols: ‘classical’ dSph, velocity dispersion profiles to last modelled point, reproduces earlier resultsRed symbols: Ultra-faint dSph, data only in central region, extrapolation in radius by factor of up to 10reflects approximately constant velocity dispersions (Walker et al, Wolf et al)

Strigari et al 2008

Extension to lowest luminosities:

Beware underestimated errors….and non-members

Wil 1 not a bound system (? Geha)

Koposov et al 2011

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), submittedRetain full covariance:map spectra modelsonto data, find ‘best’match log(g),[Fe/H],T_eff, with a Bayesian classifier.

Black: data r=19; red=model

Literature value

37 members, based on Velocity, [Fe/H], log g

Members:Fornax: 2737Sculptor: 1368Sextans: 441Carina: 1150Plus new VLT

Yield:Car, Sext ~50%For, Scl ~80%

Non-members:Wyse et al 2006

Very large samples with precision kinematics now exist, motivating full velocity distribution function modeling, going beyond moments

Walker et al, Gilmore et al

Comparing models with kinematic Comparing models with kinematic datadata Surface brightness profile input, determined from Surface brightness profile input, determined from

data data Two-integral velocity distribution function modelsTwo-integral velocity distribution function models Invert integral equation for stellar density profile as a function of Invert integral equation for stellar density profile as a function of

the potential to find all DFs consistent with observed datathe potential to find all DFs consistent with observed data Project to obtain LOS velocity distribution on a grid of R and v Project to obtain LOS velocity distribution on a grid of R and v los los

Generalized Hernquist/NFW halo (Zhao 1996) Generalized Hernquist/NFW halo (Zhao 1996) Parameters: 3 velocity distribution parameters (anisotropy, Parameters: 3 velocity distribution parameters (anisotropy,

scale), 5 halo parameters & 5 stellar parameters (density scale), 5 halo parameters & 5 stellar parameters (density profiles)profiles)

Markov-Chain-Monte-Carlo, scan 13-parameter space Markov-Chain-Monte-Carlo, scan 13-parameter space Multiple starting points for MCMC used - chains run in parallel Multiple starting points for MCMC used - chains run in parallel

and combined once “convergedand combined once “converged”” Error convolution included - using only data with Error convolution included - using only data with Many tests carried out e.g. effects on models of ignored Many tests carried out e.g. effects on models of ignored

triaxiality, tides, uncertainty in surface brightness profile etc triaxiality, tides, uncertainty in surface brightness profile etc

Wilkinson

Fornax: real data - Fornax: real data - PRELIMINARY PRELIMINARY density density profileprofile

Log r (kpc)

Log ρ

(M

/kpc3

)

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 capabilitiesGaia capabilities

Main Performances and CapabilitiesMain Performances and Capabilities

Accuracies:Accuracies: 220 0 as at V = 15as at V = 15 0.2 mas at V = 20 0.2 mas at V = 20 radial velocities to <10 km/s complete to V ~ 17.5radial velocities to <10 km/s complete to V ~ 17.5 sky survey at ~0.2 arcsec spatial resolution to V = 20sky survey at ~0.2 arcsec spatial resolution to V = 20 multi-colour multi-epoch spectrophotometry to V = 20multi-colour multi-epoch spectrophotometry to V = 20 dense quasar link to inertial reference framedense quasar link to inertial reference frame

Capabilities:Capabilities: 10 10 as as 10% at 10 kpc (units=pico-rads) 10% at 10 kpc (units=pico-rads) [~1cm on the Moon][~1cm on the Moon] 10 10 as/yr at 20 kpc as/yr at 20 kpc 1 km/s at V=15 1 km/s at V=15 every star Gaia will see, Gaia will see moveevery star Gaia will see, Gaia will see move GAIA will quantify 6-D phase space for over 300 million GAIA will quantify 6-D phase space for over 300 million

stars,stars,and 5-D phase-space for over 10and 5-D phase-space for over 1099 stars stars

Construct line of sight velocity Construct line of sight velocity distributionsdistributions

MCMC comparison to dataMCMC comparison to data Fit surface brightness profileFit surface brightness profile Use method by P. Saha to invert integral Use method by P. Saha to invert integral

equation for all DFs consistent with equation for all DFs consistent with observed observed ρρ

wherewhere

Project to obtain LOS velocity distribution on a Project to obtain LOS velocity distribution on a grid of and grid of and

convolve with individual velocity errors, and convolve with individual velocity errors, and compare to data (MCMC)compare to data (MCMC)

Going beyond velocity Going beyond velocity momentsmoments

• 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

• More general halo profile:

2-Integral Distribution function2-Integral Distribution function

Gerhard (1991)

Fornax - dispersion profileFornax - dispersion profile

NB: Dispersion data not used to constrain models

Fornax - dispersion profileFornax - dispersion profile

NB: Dispersion data not used to constrain models

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

Draco: Okamoto 2010, PhD Carina: Monelli et al 2003

1Gyr

5Gyr

12Gyr

Tests with spherical modelsCusp Core

• 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

Log r (kpc) Log r (kpc)

Log ρ

(M

/kpc3

)

Log ρ

(M

/kpc3

)

Tests with (anisotropic) triaxial models

• 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

Cusp Core

Log ρ

(2e5 M

/kpc3

)

Log ρ

(2e5 M

/kpc3

)

Log r (kpc) Log r (kpc)

Ostriker & Steinhardt 03Ostriker & Steinhardt 03

Galaxy mass Galaxy mass function depends on function depends on DM typeDM type

Inner DM mass density dependsInner DM mass density dependson the type(s) of DMon the type(s) of DM

ΛΛCDM cosmology extremely successful on large scales. CDM cosmology extremely successful on large scales. Galaxies are the scales on which one must see theGalaxies are the scales on which one must see thenature of dark matter:nature of dark matter:

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

degeneracydegeneracy

Same dispersionprofile

Different radial velocity distribution

Abandon JeansAnalyse velocities star-by-star, no binning

Dark-matter halos in Dark-matter halos in ΛΛCDM CDM have ‘cusped’ density profileshave ‘cusped’ density profiles

ρρ αα r r -1.2 -1.2

in inner regionsin 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