Dark Matter Awareness Week December, 1-8, 2010

Dark Matter in Galaxies

SOC: P. Salucci, E. Aprile, P. Biermann, A. Bosma, A. Burkert, L. Danese, E. de Blok, C. Frenk, K. Freeman, R. Gavazzi, G. Gilmore, U. Klein, G. Mamon, C. Maraston, V. Rubin, P. Salati

OC: C. Frigerio Martins, G. Gentile, A. Lapi, S. Leach, C. Tonini

Overview

The concept of Dark Matter

Dark Matter in Spirals

Dark Matter in Ellipticals

Dark Matter in dSph

Direct and Indirect Method to detect Dark Matter

What is Dark Matter?

The mass profile of the gravitating matter M(r) and that of the sum of all luminous components ML(r) do not match.

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

Its profile MH(r) must obey to:

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

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

The distribution of the luminous matter

Spiral : stellar disk +bulge +HI disk

Ellipticals & dSph: stellar spheroid

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

flattish radial distribution

saturates at ~ 8 - 10 Msun pc-2 (NHI = 1021 cm-2)

deficiency in centre

CO or H2 surface density

roughly exponential

Wong & Blitz (2002)

HI surface density

ROTATION CURVE Symmetric circular rotation of a disk characterized by

sky coordinates (η0 ,ξ0 ) of the centre

• systemic velocity Vsys

• circular velocity V(R)

• position angle χ of the major axis

• inclination angle i

.

=bai arccos

iRVVV sysobs sincos)(),( θηξ +=i = inclination angle (0º = face-on)

θ = azimuthal angle

Vobs (R)= V(R) from spectroscopy:

- optical emission lines (Hα)

- 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

Hα, … 0.5" … 1.5" 10 … 30 km s-1

Optical & HI rotation curves

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

50

100

150

200

250

V

R/Rd

UGC2405

The mass distribution is luminosity dependent. Gravitating matter is related with luminosity.

Tully Fisher exists at local level (radii Ri)

Very inner regions: light traces the mass

No DM there

DISK ONLY

Dark matter in galaxies

Bosma, 1978, 1981 First evidence!

GALEX

SDSS

Extended HI traces dark matterNGC 5055 on same scale:- HI velocity field - SDSS optical image - H-alpha velocity field- deep optical image - GALEX UV image

The Rotation Curves

coadded

PSS

6 RD

mag.

An Universal Mass Distribution?ΛCDM Universal Rotation Curve from NFW profile and MMW theory

The Concept of the Universal Rotation Curve

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

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, Moore) MASS MODEL HAS 2-3 FREE PARAMETERS: disk mass, halo

central density and core radius.

Vtot2 = VDM

2 + Vdisk2 + Vgas

2

Vdisk2

Vgas2

VDM2

EMPIRICAL distribution: Burkert profile

“cuspy” and “cored” density profiles of DM halos

”cusp”

”core”

Modelling the Universal Rotation Curve

Stars

Dark matter

DM

fr

actio

n

core radiushalo central density

luminosity

@Ropt

Stellar vs. Virial Halo Mass

Method: Shankar et al 2006.

The Universal Velocity Curve

URCL

NFW

URCH

Dark Halo Scaling Laws relationships between halo structural quantities (ρo, rc, σ) and luminosity

Kormendy & Freeman (2003) method- Assumed Maximun Disk-The slope of the halo rotation curve near the center gives the halo coredensity ρo

- extended RC provide an estimate of halo core radius rc

ρo ~ LB- 0.35

rc ~ LB 0.37

σ ~ LB 0.20ρo

rc

σ

the surface density Σ ~ ρo rc to be ~ constant

Kormendy & Freeman 2003

3.0 2.5

2.0

1.5

1.0

INDIVIDUAL OBJECTS

For every galaxy produce models with Υ* fixed to predicted value and with Υ* free

M/L* = 0.56

M/L* = 0.60

M/L* = 0.47

M/L* = 0.56

NGC3621: example of mass modeling

• THINGS: HI survey providing data of uniform and high quality

• multi-λ repository: powerful combination with UV and IR data

• high-quality rotation curves:• no declining curves• non-circular motions small• no DM halo elongation• ISO halos preferred over

NFW for low-mass galaxies

• tri-axiality and non-circular motions or “feedback” cannot explain the CDM cusp/core discrepancy

www.mpia.de/THINGS

DDO 47:

s1 negligible

s3 < 3 km s-1

ELLIPTICALS

Intensity distribution of bulges follows de Vaucouleurs (1948) law

or, its generalized form, a Sersic law

where Re is the effective radius, implying that one-half of the total light is emitted interior to Re.

Intensity distribution of a spheroid needs to be deprojected (Binney & Tremaine 1987; Binney & Merrifield 1998):

( )[ ]167.7 41

)( −−⋅= eRRe eIRI

The bulge

( )[ ]11

)( −−⋅=n

en RRbe eIRI

∫∫+ ∞+ ∞

∞− −==

R RrdrrrjdzrjRI

22

)(2)()(observer

Gary Mamon (IAP , Paris), for Dark Matter Awareness Week

Line-of-sight Velocity Dispersions

The Fundamental Plane in 4 bands

Bernardi et al. 2003

SDSS early-type galaxies

Fitting r ~ σa Ib yields (a<2, b~0.8) → M/L not constant

M/L ~ L0.14

The virial theorem (2KE=-W):

The FP “tilt” due to variations in: 1. dark matter fraction? 2. stellar population?

!! Stellar Mass FP!! M/L = (M/M*) (M*/L)Hyde & Bernardi 2009Now a<2 means M/M* not constant

>>> differences in fitting techniques >>> account for evolution + selection effects!

~ M*

Older galaxies have smaller M/M*

Shankar & Bernardi 2009

Mdyn(Re)=M*/2

Gary Mamon (IAP , Paris), for Dark Matter Awareness Week

Stars dominate inside few Re

Mamon & Łokas 05b

Mass decomposition

4 components:DMstarsBlack Holesgas

Gary Mamon (IAP , Paris), for Dark Matter Awareness Week

NGC 3379

dark matter content @ 4 Re still very uncertain!

The stellar mass of galaxies

The luminous matter in a galaxy in form of stars M* is a crucial quantity.Indispensable to infer the amount of Dark Matter Two contributions: - stars that are still alive- dead stellar remnants i.e. white dwarfs, neutron stars, black-holes

Luminosity of a galaxy is modeled via Stellar Population Synthesis models that determine its age and metallicity → M*/L, hence M*

Two methods: t and Z/H are obtained using line indices or colours. The correspondent M*/L (t, Z/H) gives M* the whole photometric SED is fitted and M* is obtained via normalization

Models for the evolution of the stellar mass

The M*/L ratio as a function of age

Maraston, Daddi + 06

SED fit:

M* crucially depends on how well we determine the galaxy star formation history

Mass Profiles from X Rays

Temperature

Density

Hydrostatic Equilibrium

M/L profile

Global dark matter fractionsVirial M/L can be rephrased as star formation efficiency εSF ≡ M* / (fb Mvir),

U-shaped curve observed:• “directly” with weak-lensing,• indirectly by correlating dN/dL with theoretical DM halo dN/dM

early-typelate-type

(fr. van den Bosch et al.)

(Mandelbaum et al. 2006)

εSF maximum near L*:• lower mass galaxies can’t hold gas• higher mass galaxies can’t cool gas

(Dekel & Silk 1986; Cattaneo et al. 2006)

Dark matter trends with galaxy luminosity

~ Reff : DM fraction(Tortora et al. 2009)

Increasing DM content with luminosity/mass: → decreasing star formation efficiency (feedback and/or inefficient cooling)

Detailed DM profiles with radius probe:→ alternative gravity / dark matter→ galaxy formation physics

~5 Reff : M/L gradient(Napolitano et al. 2005)

~ Rvirf weak lensing M/L(Mandelbaum et al. 2006)

WEAK LENSING

Weak Lensing around galaxies

Basic quantities are:

-) Lensing potential

-) The convergence k,that satisfies Poisson equation

and is directly related to the surface mass density

via the critical surface density

Tangential alignment of faint background sources (green ticks) in annuli around massive galaxies.

Gavazzi et al. 2007

Isothermal profile from ~Re/2 out to ~50Re

Bulge/halo «Conspiracy»: combine themselves to form an Isothermal r-2 profile although none of them is isothermal

Mandelbaum et al. 2006

Hoekstra et al. 2005

CFHT data (z~0.4)Scaling with luminosity M ~ Lα .

SDSS data (z~0.1). HOD framework: central/satellite distinction!!

Halo central density vs core radius

ρ0 =10-23 (r0 /kpc)-1 g/cm3 (WDM? De Vega et al 2010)

dSph

BURC

WL

The quantity ρ0r0 = Σ0 is constant among galaxies

census of HI masses: HI Parkes All Sky Survey (HIPASS)

Zwaan et al. (2005)

4315 HI detections

-1200 km s-1 < Vrad < 12700 km s-1

no ‘dark galaxies’

best fit: Schechter function

cosmological density of HI in local universe:

ΩHI = (3.5 ± 0.4 ± 0.4) ·10-4 h75

Zwaan et al. (2005)

−⋅

=Θ *

HI

HI*HI

HI*HI

HIHIHI M

MMMexp

MMM)(M dd

α