DARK MATTER IN GALAXIESNAME
INSTITUTE
Overview
The concept of Dark MatterDark Matter in Spirals, Ellipticals, dSphsDark Matter at outer radii. Global propertiesDirect 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 simulations
In ΛCDM scenario the density profile for virialized DM halos of all masses
of all masses is empirically described at all times by the universal NFW
formula (Navarro+96,97).
More massive and halos formed
earlier have larger overdensities d.
Concentration c=R200/ rs is an
alternative density measure.
The concentration scales with mass and redshift (Zhao+03,08; Gao+08, Klypin+10):
At low z, c decreases with mass.
-> Movie 1
Aquarius simulations, highest resolutions to date.
Results: Cuspy Einasto profiles (Navarro+10).
No difference for mass modelling with NFW ones
with a dependent slightly on mass.
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 :
SPIRALS
Stellar Disks
M33 - outer disk truncated, 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 centre
CO and H2
Roughly exponential
Negligible mass
Wong & Blitz (2002)
Gas surface densities
Circular velocities from spectroscopy
- Optical emission lines (H, NN a)
- 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
HN, … 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
N = azimuthal angle
b
ai arccos
iRVVV sysobs sincos)(),(
Example of a recent high quality RC: Radial coordinate in units of RD
V(2)
V(R/RD)
R/RD
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
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
The distribution of gravitating matter is luminosity dependent.
Tully-Fisher relation exists at local level (radii Ri)
no DM slope
Yegorova et al 2007
Rotation Curves
Coadded from 3200 individual RCs
PSS
6 RD
mag.
TYPICAL INDIVIDUAL RC
low
high
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 observationsHow to extrapolate the URC out to virial radius?Needed
-> Movie 2
Extrapolating the URC to the Virial radius
Virial halo masses and VVIR are obtained - directly by weak-lensing - indirectly by correlating dN/dL with theoretical DM halo dN/dM
Shankar et al 2006
An Universal Mass Distribution
ΛCDM theoretical URC from NFW Observed URC profile and MMW theory
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
Dark halos with cusps (NFW, Einasto)
Model has three free parameters:
disk mass, halo central density
and core radius (halo length-scale).
Vtot
2 = VDM
2 + Vdisk
2 + Vgas
2
core radius
halo central density
luminosity
disk
halo
halo
halo
diskdisk
MASS MODELLING RESULTS
fract
ion o
f 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 radiusrc rc
Kormendy & Freeman (2003)
No ~ LB- 0.35
rc ~ LB 0.37
N ~ LB 0.20
No
rc
N
The central surface density N ~ Norc =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+,2009
A detailed investigation: high quality data and model independent analysis
NGC3621
- Non-circular motions are small.- No DM halo elongation- ISO halos often preferred over NFW
Tri-axiality and non-circular motions cannot explainthe CDM/NFW cusp/core discrepancy
General results from several samples including THINGS, HI survey of uniform and high quality data
DDO 47
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 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
drrrjdzrjRI
22
)(2)()(
ESO 540 -032
Sersic profile
Modelling Ellipticals
Measure the light profile
Derive the total mass profile from
Dispersion velocities of stars Planetary Nebulae
X-ray properties of the emitting hot gas
Combining weak and strong lensing data
Disentangle the dark and the stellar components
19.10.10
Line-of-sight, projected Velocity Dispersions, 2-D kinematics
SAURON data of N 2974
The Fundamental Plane: central dispersion velocity, half light radius and central surface brightness are related
SDSS early-type galaxies
Fitting r ~ Na Ib gives: (a<2, b~0.8)
→ M/L not constant ~ L0.14
From virial theorem
The FP “tilt” is due to variations in: Dark matter fraction? Stellar population? Likely.
Bernardi et al. 2003
Shankar & Bernardi 2009
Hyde & Bernardi 2009
Stars dominate inside Re
Dark matter profile unresolved
Mamon & Łokas 05
Assumed IsotropyThree components: DM, stars, Black Holes
Dark-Luminous mass decomposition of dispersion velocities
Weak and strong lensing
SLACS: Gavazzi et al. 2007)
Inside R_e, the total (spheroid + dark halo) mass increases in proportion to the radius
Gavazzi et al 2007
Mass Profiles from X-ray
Temperature
Density
Hydrostatic Equilibrium
M/L profile
NO DM
Nigishita et al 2009
ELLIPTICALS: WHAT WE KNOW
A LINK AMONG THE STRUCTURAL PROPERTIES OF STELLAR SPHEROIDSMALL AMOUNT OF DM INSIDE RE
MASS PROFILE COMPATIBLE WITH NFW AND BURKERTDARK MATTER DIRECTLY TRACED OUT TO RVIR
19.10.10
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)
Dispersion velocity profiles
dSph dispersion profiles generally remain flat to large radii
Wilkinson et al 2009
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
Degeneracy between DM mass profile and velocity anisotropyCusped and cored mass models fit dispersion profiles equally well
However: dSphs cored distribution structural parameters agree with those of Spirals and Ellipticals
Halo central density vs core radius
Walker et al 2009
Donato et al 2009
Global trend of dSph haloes
• SculptorAndII
Mateo et al 1998
Gilmore et al 2007
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
The stellar mass of galaxiesThe luminous matter in the form of stars M* is a crucial quantity.Indispensable to infer the amount of Dark Matter M*/L of a galaxy obtained via Stellar Population Synthesis models
Fitted SED
Dynamical and photometric estimates agree
WEAK LENSING
Weak Lensing around galaxies
Critical surface density
Lensing equation for the observed tangential shear
Donato et al 2009
HALO MASSES ARE A FUNCTION OF LUMINOSITY
Mandelbaum et al 2009
Walker+ 2010
Mass correlates with luminosityURC mass profile Mh(r) = F(r/Rvir, Mvir) valid
for S, dSph, LSB, checking for E
Unique mass profile Mh(r) = G(r)
Unique value of halo central surface density
Salucci+ 2007
Donato et al. 2009
Walker+ 2010
GALAXY HALOS: WHAT WE KNOW
Mandelbaum,+ 06
DETECTING DARK MATTER
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 eventually 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 play a balanced role in the search for dark matter and its role.