DARK MATTER IN GALAXIESNAME

INSTITUTE

Overview

The concept of Dark Matter

Dark Matter in Spirals, Ellipticals, dSphs

Dark and Luminous Matter. Global properties.

Direct and Indirect Searches of Dark Matter.

What is Dark Matter?In a galaxy, the radial profile of the gravitating matter M(r) and that of the sum of all luminous components ML(r) do not match.

A MASSIVE DARK COMPONENT is introduced to account for the disagreement:

Its profile MH(r) must obey:

The DM phenomenon can be investigated only if we accurately meausure the distribution of: Luminous matter. Gravitating matter.

Dark Matter Profiles from N-body simulationsIn ΛCDM scenario the density profile for virialized DM halos of all masses is empirically described at all times by the universal (NFW) profile (Navarro+96,97).

More massive halos and those formed earlier have larger overdensities d.Object today virialized:mean halo density inside Rvir = 100 ϱc

Concentration c=Rvir/ rs

The concentration scales with mass and redshift (Zhao+03,08; Gao+08, Klypin+10):

At z=0, c decreases with mass.

-> Movie 1

Aquarius simulations, highest mass resolution to date.

Density distribution: still a cuspy profile but similar to the Einasto Law Navarro+10No difference, for mass modelling, with the NFW one.

density and circular velocity for an halo of 1012 MSUN V=const

Central surface brightness vs galaxy magnitude

The Realm of Galaxies

The range of galaxies in magnitude, types and central surface density : 15 mag, 4 types, 16 mag arsec2

Spirals : stellar disk +bulge +HI disk

Ellipticals & dSph: stellar spheroidThe distribution of luminous matter :

Dwarfs

SPIRALS

Stellar Disks

M33 very smooth structure

NGC 300 - exponential disk goes for at least 10 scale-lengths

Bland-Hawthorn et al 2005Ferguson et al 2003

scaleradius

HI

Flattish radial distribution

Deficiency in the centre

CO and H2

Roughly exponential

Negligible mass

Wong & Blitz (2002)

Gas surface densities

GAS DISTRIBUTION

Circular velocities from spectroscopy- Optical emission lines (H, Na)

- Neutral hydrogen (HI)-carbon monoxide (CO)

Tracer angular spectral resolution resolution

HI 7" … 30" 2 … 10 km s-1

CO 1.5" … 8" 2 … 10 km s-1

H, … 0.5" … 1.5" 10 … 30 km s-1

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

50

100

150

200

250

V

R/Rd

UGC2405

ROTATION CURVES (RC) Symmetric circular rotation of a disk characterized by

• Sky coordinates of the galaxy centre

• Systemic velocity Vsys

• Circular velocity V(R)

• Inclination angle

= azimuthal angle

bai arccos

iRVVV sysobs sincos)(),(

V(R

/RD)

R/RD

EXEMPLE OF HIGH QUALITY RC

Early discovery from optical and HI RCs

MASS DISCREPANCY AT OUTER RADII

disk

observed

NO RC FOLLOWS THE DISK VELOCITY PROFILE

Rubin et al 1980

disk

The mass discrepancy emerges as a disagreement between light and mass distributions

GALEX

SDSS

Extended HI kinematics traces dark matter - -

NGC 5055 Light (SDSS) HI velocity field

Bosma, 1981

Bosma, 1981

Bosma 1979Radius (kpc)

Evidence for a Mass Discrepancy in Galaxies

The distribution of gravitating matter, unlike the luminous one, is luminosity dependent.

Tully-Fisher relation exists at local level (radii Ri)

no DM

Yegorova et al 2007

Rotation Curves

Coadded from 3200 individual RCs

Salucci+07

6 RD

mag

TYPICAL INDIVIDUAL RCs OF INCREASING LUMINOSITY

Low lum

high lum

The Concept of the Universal Rotation Curve (URC)

The Cosmic Variance of the value of V(x,L) in galaxies of same luminosity L at the same radius x=R/RD is negligible compared to the variations that V(x,L) shows as x and L varies.

The URC out to 6 RD is derived directly from observationsExtrapolation of URC out to virial radius by using -> Movie 2

Extrapolating the Universal Curve to the Virial Radius

Virial halo masses Mh and VVIR are obtained - directly by weak-lensing analysis - indirectly by correlating dN/dL with theoretical DM halo dN/dM

Shankar et al 2006

Mandelbaum et al 2006

Mh

An Universal Mass Distribution

ΛCDM URC Observed URC

NFW

high

low

Salaucci+,2007

theory

obs

obs

Rotation curve analysisFrom data to mass models

➲ from I-band photometry ➲ from HI observations➲ Dark halos with constant density cores (Burkert)Dark halos with cusps (NFW, Einasto)

The mass model has 3 free parameters:

disk mass, halo central density and core radi radius (halo length-scale).

Vtot2 = VDM

2 + Vdisk2 + Vgas

2

NFW

Burkert

core radiushalo central density

luminosity

disk

halohalo

halodisk disk

MASS MODELLING RESULTS

fract

ion

of D

M

lowest luminosities highest luminosities

All structural DM and LM parameters are related with luminosity.g

Smaller galaxies are denser and have a higher proportion of dark matter.

Dark Halo Scaling Laws

There exist relationships between halo structural quantiies and luminosity. Investigated via mass modelling of individual galaxies - Assumption: Maximun Disk, 30 objects-the slope of the halo rotation curve near the center gives the halo core density - extended RCs provide an estimate of halo core radius rc

Kormendy & Freeman (2004)

o ~ LB- 0.35

rc ~ LB 0.37

~ LB 0.20

o

rc

The central surface density ~ orc =constant 3.0 2.5

2.0

1.5

1.0

The distribution of DM around spirals Using individual galaxies Gentile+ 2004, de Blok+ 2008  Kuzio de Naray+ 2008, Oh+  2008, Spano+ 2008, Trachternach+ 2008, Donato+,2009A detailed investigation: high quality data and model independent analysis

- Non-circular motions are small.- No DM halo elongation- ISO/Burkert halos preferred over NFW

- Tri-axiality and non-circular motions cannot explain the CDM/NFW cusp/core discrepancy

General results from several samples including THINGS, HI survey of uniform and high quality data

DDO 47

NFW Burkert

disk B gas Bdisk

gas

disk gas

SPIRALS: WHAT WE KNOW

AN UNIVERSAL CURVE REPRESENTS THE ALL INDIVIDUAL RCsMORE PROPORTION OF DARK MATTER IN SMALLER SYSTEMSRADIUS IN WHICH THE DM SETS IN FUNCTION OF LUMINOSITYMASS PROFILE AT LARGER RADII COMPATIBLE WITH NFWDARK HALO DENSITY SHOWS A CENTRAL CORE OF SIZE 2 RD

ELLIPTICALS

Surface brightness of ellipticals follows a Sersic (de Vaucouleurs) law

Re : the effective radius

By deprojecting I(R) we obtain the luminosity density j(r):

The Stellar Spheroid

R Rr

drrrjdzrjRI22

)(2)()(

ESO 540 -032

Sersic profile

Modelling Ellipticals

Measure the light profile

Derive the total mass profile from

Dispersion velocities of stars or Planetary Nebulae

X-ray properties of the emitting hot gas

Combining weak and strong lensing data

Disentangle the dark and the stellar components

Line-of-sight, projected Velocity Dispersions, 2-D kinematics

SAURON data of N 2974

SDSS early-type galaxies

The Fundamental Plane: central dispersion velocity, half light radius and central surface brightness are related

From virial theorem

FP “tilt” due to variations with σ0 of: Dark matter fraction? Stellar population?

Hyde & Bernardi 2009

Fitting gives: a=1.8 , b~0.8)then:

Bernardi et al. 2003

RESULTSThe spheroid determines the aperture dispersion velocity Stars dominate inside Re

More complications when:presence of anisotropiesdifferent halo profile (e.g. Burkert)

Two components: NFW halo, Sersic spheroid Assumed isotropy

Dark-Luminous mass decomposition of dispersion velocitiesNot an unique model: example a giant elliptical with reasonable parameters

Mamon & Łokas 05

Dark matter profile unresolved

1011

Weak and strong lensing

SLACS: Gavazzi et al. 2007)

Inside Re, the total (spheroid + dark halo) mass increases proportionally to the radius

Gavazzi et al 2007

UNCERTAIN DM DENSITY PROFILEI

Mass Profiles from X-ray

Temperature

Density

Hydrostatic Equilibrium

M/L profile

NO DM

Nigishita et al 2009

CORED HALOS?

The mass in stars in galaxiesThe luminous matter in the form of stars M* is a fundamental quantity. It often plays a role in inferring the properties of Dark Matter M*/L of a galaxy obtained via Stellar Population Synthesis models

Fitted SED

Dynamical and photometric estimates agree

Shankar & Bernardi 2009

ELLIPTICALS: WHAT WE KNOW

A LINK AMONG THE STRUCTURAL PROPERTIES OF STELLAR SPHEROIDSMALL AMOUNT OF DM INSIDE REMASS PROFILE COMPATIBLE WITH NFW AND BURKERTDARK MATTER DIRECTLY TRACED OUT TO RVIR

dSphs

Low luminosity, gas-free satellites of Milky Way and M31

Large mass-to-light ratios (10 to 100 ), smallest stellar systems containing dark matter

Dwarf spheroidals: basic properties

Luminosities and sizes of Globular Clusters and dSph

Gilmore et al 2009

Kinematics of dSph1983: Aaronson measured velocity dispersion of Draco based on observations of 3 carbon stars - M/L ~ 30 1997: First dispersion velocity profile of Fornax (Mateo) 2000+: Dispersion profiles of all dSphs measured using multi-object spectrographs

2010: full radial coverage in each dSph, with 1000 stars per galaxy

Instruments: AF2/WYFFOS (WHT, La Palma); FLAMES (VLT); GMOS (Gemini); DEIMOS (Keck); MIKE (Magellan)

STELLAR SPHEROID

Dispersion velocity profiles

dSph dispersion profiles generally remain flat to large radii

Wilkinson et al 2009

STELLAR SPHEROID

Mass profiles of dSphs

Jeans equation relates kinematics, light and underlying mass distribution

Make assumptions on the velocity anisotropy and then fit the dispersion profile

Results point to cored distributions

Jeans’ models provide the most objective sample comparison

Gilmore et al 2007

DENSITY PROFILE

n(R)

PLUMMER PROFILE

Degeneracy between DM mass profile and velocity anisotropyCusped and cored mass models fit dispersion profiles equally well

However: dSphs cored model structural parameters agree with those of Spirals and Ellipticals

Halo central density vs core radius

σ(R

) km

/s

Donato et al 2009

Walker et al 2009

NFW+anisotropy = CORED

Global trend of dSph haloes

• Sculptor

AndII

Mateo et al 1998

Gilmore et al 2007

Strigari et al 2008

UNIQUE MASS PROFILE ?

M ~ THE SAME IN ALL DWARF SPHEROIDALS

DSPH: WHAT WE KNOW

PROVE THE EXISTENCE OF DM HALOS OF 1010 MSUN AND ρ0 =10-21 g/cm3

DOMINATED BY DARK MATTER AT ANY RADIUS MASS PROFILE CONSISTENT WITH THE EXTRAPOLATION OF THE URC HINTS FOR THE PRESENCE OF A DENSITY CORE

WEAK LENSING

Weak Lensing around galaxies

Critical surface density

Lensing equation for the observed tangential shear

Donato et al 2009

NFWB

SAME VALUES FOUND FROM THE URC

Mandelbaum et al 2009

0.10.1

MODELLING WEAK LENSING SIGNALS

Lenses: 170 000 isolated galaxies, Sources : 30 M SDSS galaxies

HALO MASS FUNCTION OF LUMINOSITY

tar

tHALOS EXTEND OUT TO VIRIAL RADII ar

tar

NFW

EXTENDED HALOS EXISTDENSITY PROFILE: NFW/BURKERTHALO MASSES: exceed the stellar masses more than the cosmological value correlate with the mass of the stellar components

Walker+ 2010

Mass correlates with luminosityURC mass profile Mh(r) = F(r/Rvir, Mvir) valid for S, dSph, LSB, to check for E

Unique mass profile Mh(r) = G(r)

Unique value of halo central surface density

Salucci+ 2007

Donato et al. 2009, KF, 2004

Walker+ 2010

GALAXY HALOS: WHAT WE KNOW

Mandelbaum,+ 06

DETECTING DARK MATTER

DM

Anti-proton spectrum

CONCLUSIONSThe distribution of DM halos around galaxies shows a striking and complex phenomenology This leads to essential information on:

the very nature of dark matter; the galaxy formation process

Baryon +DM Simulations should reproduce:Shallow DM inner distribution, the observed relationships between the halo mass and 1) central halo density, 2) baryonic mass, 3) half-mass baryonic radius and 4) baryonic central surface density, a constant central halo surface density. Theory, phenomenology, simulations, experiments should all play a role in the search for dark matter and for its role.

In any case the mass discrepancy in galaxies is a complex function of radius, total baryonic mass, Hubble Type

Unlikely to mask a new law of Nature