Dark Matter/Dark EnergyDo we need it?

How Much?Where?

What is It?

Hans-Walter RixJanuary 28, 2004

Observing the Big Bang and its Aftermath

• Historic Overview• Evidence for Dark Matter

– On galactic scales– Galaxy clusters– Abundance of massive clusters– “Large scale structure”

• Measuring the expansion history – Ho measurements

– Supernovae– (CMB)

• The Complementarity of the Approaches• Nature of the dark matter/dark energy

Dark Matter: How it all started

• Zwicky: 1933• Applies virial theorem to individual galaxies in Coma• Applies virial theorem to the ensemble of galaxies

Mtot >> N x Mgalaxies

Zwicky 1933, Helvetica Physica Acta, 6, 110

• Concluded: must be dim stars in the outer parts of M31

• 1959: Woltjer and Kahn: • M31 is approaching (returning after initial expansion on

elongated orbit).

• What mass is needed for torbit < tuniverse? M>1.8x1012 Msun !!

1st rotation curve of M31 (1939)

Dark Matter Evidence from “Rotation Curves”

• E.g. NGC3198: Begeman 1989– HI (neutral hydrogen)more extended than stars, measure 21cm line flat rotation curve -- found in all spiral (=gas rich) galaxies!

Vc=const

M~r or ~r-2

Dark Matter Evidence from X-rays

• How much mass does it take to keep hot gas in hydrostatic equilibrium?

total mass grows M~r also around big ellipticals

X-ray image from ROSAT of M87

Dark Matter From Satellites

Portrait of the “Local Group” (Grebel 2001)

Prada et al 2003

“Stacked satellite velocities” of 500 spiral galaxies

D.M. halos extend to >200kpc

Dark Matter Evidence Nearby:

the Draco dwarf galaxySky image of Draco

Dsun 70 kpc

Stellar density contours of Draco from SDSS

Odenkirchen et al 2001

Draco is a bound system in equilibrium

Radial Profile and Kinematics of Draco

Stellar density profile of Draco

• Estimate *(r) from stellar distribution

Modelling options

1) Stars only tot(r) = *(r)

2) Stars + DM: tot(r) = *(r) + DM(r)

Giant stars with velocities measured

• Giant stars as kinematic tracers

- need velocity precision of 3 km/s

Mass Modelling of Draco

Jeans equation model

Anis

otr

opy

Expected (M/L)* ~ 2

Draco is dark matter dominated

Velocity dispersion profile

Enclosed mass

Try models with different DM profiles M (<10‘) well constrained

Rotation Curves of Spiral Galaxies

Rotation Curves of Spiral Galaxies

•Rotation curves show that DM is needed •Total (stars,gas,DM) rotation curve is v~const. for 2-8 Rexp

•A so-called non-singular isothermal (s=const.) DM distribution often fits well:

•But, is this dark matter profile•Physically motivated?•Physically plausible?

•Expectation from cosmological

simulations: NFW profile~r-1 at small radii and

~r-3 at large radii

2

0( ) / 1 / cr r r

Degeneracies in Fitting Rotation Curves

Van Albada et al 1985, ApJ, 295, 305

Navarro 1997

Rotation curves do not contain enough information to:

Determine the ratio of star to DM mass

Distinguish the radial profile of DM

Dark matter at small radii is poorly understood!

Dark Matter in Galaxy HalosPrada et al 2003

Satellites to the Milky Way

tracers of the mass in the halo

• identify satellite candidates• make a conservative rejection of

unbound systems• calculate resulting velocity dispersion

of satellites• compare to cosmological halo

formation models good match

SDSS sample: isolated MW-like galaxies

0.5 satellites per galaxy x 1000 galaxies

Synthetic galaxy with 500 satellites

unbound systems

MW-like galaxies are at the center of dark matter halos that extend to >200 kpc

DM density profile in the outer parts ~r-3

Galaxy-Galaxy Lensing

Pro

ject

ed

Mass

Overd

en

sity

Projected Radius

As clusters, individual galaxies distort background images, too.

Yet, these distortions are much smaller

Co-add signal from many equivalent (?) galaxies

Galaxy-galaxy lensing signals show that galaxy halos extend far (>200 kpc)

Strong galaxy-galaxy lensing

Dark Matter in Galaxy Clusters

• Orbital motions of the galaxies• X-ray gas• Gravitational lensing

Dark Matter in Galaxy Clusters

T = 106 K X-ray emission

In galaxy clusters the masses can be measured three ways• Galaxy clusters contain hot gas ( bound by dark matter?)• Galaxy velocity dispersion• Gravitational lensing

X-Ray Gas in Hydrostatic Exquilibrium

2

( )dP GM r

dr r

ln ln( ) ( )

ln lnH

kT d g d TM r

m g d r d r

Mstars~Mgas~3x1013MSun

Mtot,cluster(Rvirial)~1015MSun

Mass Census in Clusters(White et al 1993)

• Stars + Hot Gas baryonic mass• Dynamics, etc.. total mass• Within the “Abell radius” there was not enough

time to concentrate baryons Mbary/Mtotal

should be cosmic average

• Observed Mbary/Mtotal~1/8 e.g. in Coma cluster

• From nucleosynthesis: bary~0.035 (H0=70)

total ~ 0.3

What to Expect for Dark Matter Halos?

(e.g. Navarro, Frenk and White 1997)

• Start with “cosmological simulations”• Isolate, and re-simulate at higher resolutions

sub-regions that will lead to a halo.

=1,=0

z=2

z=1

z=0

Density profile of low-mass halo

Density profile of high-mass halo

Universal Dark Matter Halo Profiles(e.g. Navarro, Frenk and White 1997)

• For all simulations with collisionless, cold, dark matter, regardless of – Initial fluctuation spectrum– Mass of collapsed object– “Cosmology”, i.e.

one finds the functional form

Log

(vc)

D.M. halos do not have flat rotation curve!

Log(Masshalo)

c

In simul: and mass are correlated

D.M. Halos are 1-D Sequence?!

Standard Candles

Approach:• Select objects whose intrinsic luminosity can be

estimated, either from physical first principles, from empirical calibrations of nearby examples or can be inferred from another distance-independent observable.

• Instrinsic luminosity + apparent flux distance (modulus)

Examples:• Cepheids: luminosity estimate from their pulsation

period• Spiral Galaxies: luminosity estimate from their disk

rotation curve• Type-Ia Supernovae (SNIa): luminosity estimate from

their light-curve shape

Cepheid Distances• E.g. HST Key-Project to measure Hubble constant,

H0 (Freedman, Kennicutt,Mould, et al.)

• Compare Cepheid brightness in M81 to LMC

and local Milky Way Cepheids DM81=3.63+-0.34• This way we can measure distances to

Galaxies with where Supernovae exploded.

Note: for nearby (<50Mpc) galaxies distance and redshift are correlated with considerable scatter

Measuring H0 is not easy

lightcurves

Supernova Type Ia Distances

• SN Ia: white dwarf stars near the Chandrasekhar mass limit (1.4 Msun), where Carbon and Oxygen burn explosively.

• Most luminous variety of Supernova. Can be seen to z>1!

Perlmutter etal 2002

SN Ia as Pseudo-Standard CandlesPhillips, Hamuy, Ries, Kirshner and others ~1996– Intrinsically bright SN Ia decline slower

SN Ia: H0=67+-5 km/s/Mpc(Current estimate (all methods): H0=70+-5)Note:

- still needs Cepheid calibration- Galaxy velocities differ from the local

mean by ~300 km/s systematic uncertainty in H0

with correction

Distant Supernovae• The distance modulus M-

m to a certain redshift z depends on the expansion history, not just the current expansion rate.

• Type-Ia Supernovae can be seen to great distances: z>1 probes of the expansion history.

• 1998: expansion of the Universe is accelerating (!?)

• Riess etal 1998, AJ, 116, 1009• Perlmutter et al. 1999, ApJ, 517, 565

High-z SNIa (2004)

Literature Compilation

Nesseris et al 2004 (astro/ph-0401556)

H0 d

L=1,=0

=0,=0 =0.2,=0.

8

Remember?

Estimating M from the Abundance of the Most Massive Colapsed Objects at Different

Redshifts

X-ray luminosity

Est

imate

d v

iria

l m

ass

+X-ray luminosity function = f(z)

m~0.3 through comparison with cosmological simulations

Other Lines of Evidence For Dark Matter

• Gravitational lensing (MSB’s lecture) dark matter clumping on largest

scales

• The Cosmic Microwave Background and the curvature of space (Rachel, Friday) M~0.27

• The growth of small fluctuations to strong fluctuations (next lecture)

Matter/Energy Content 1st Synopsis

• Establish need for DM in various environments

• Mean DM density from– Baryonic/total mass in

clusters– Abunance of clusters

(=growth rate of most massive objects)

– Overall expansion history• Angular diameter distance

(CMB)• Luminosity distance (SN Ia)

Alternatives to Dark Matter

• MOND: Modified Newtonian Dynamics (Milgrom 1980s-)Ansatz:

for accelerations a less than a0, gravity behaves as a(a/a0) = GM/r2

as a(r) ~ 1/r of a < a0:

flat rotation curves

Note:

• a < a0 untested in the lab

• single value of a0 works for all rotation curves

But:• No relativistic version of

MOND• MOND has trouble

explaining DM in cluster and far out in halos

Nature of the Dark Matter• Non-baryonic, to reconcile M ~0.27 with primordial

nucleosynthesis b~0.018 and large-scale structure growth

• Cold: must not escape from potential wells

• (Cold) Dark Matter Candidates:– Black holes– Low-mass objects (“MACHO”s, free-floating planets)– Elementary particles

Massive Black Holes as Dark Matter Candidates– (one) plausible mass range: ~106 Msun

(Lacey and Ostriker, 1985)– But, such massive black holes cannot be the dark matter in dwarf

galaxies (Rix and Lake, 1993).– E.g. c.a. 80 BH’s in Draco, they would disrupt the galaxies!

• MACHO’s: Massive Compact Halo Objects– Potential mass range: 0.08 MSun (stellar limit) to MEarth

Observational test: gravitational microlensing• (MACHO and OGLE) experiments.

Idea:• if all the dark matter in the Milky Way’s halo was MACHOS

• there is a 10-6 chance that a star (e.g. in the Magellanic Cloud) has a MACHO exactly along the line of sight

• focussing brightening of the stars’ image• as stars move dime dependent light curve.

Implementation: monitor 106 stars

Microlensing Searches

Large Magellanic Cloud

Micro-Lensing Cartoon

Lensing Lightcurve

Are MACHOs the Dark Matter?

MA

CH

O M

ass

Halo Mass Fraction in MACHOs

•MACHO’s make up (at most) 15% of the Milky Ways halo mass

•Inferred mass range: 0.4MSun Why would they be invisible?

MACHOs are an enigma, but certainly not the solution to the dark matter problem

Alternative: lensing by ordinary stars in the LMC or MW

WIMPS as Dark Matter Candidates

• “cold” Dark Matter: must become non-relativistic already at T >> 104K clumping

• supersymmetric theories (SUSY) can naturally create particle (pairs with their SUSY partner)- lightest SUSY particle stable: neutralino, gravitino, higgsino, etc.

• axions: hypothesized, very light particle; may arise in quantum chromodynamics

WIMPS are a plausible, but not firm, consequence of several theories in particle physics

Towards detecting WIMPS

• WIMPS: may have exceedingly rare elastic scattering events with crystals and one may measure the recoil.

• However: many other particles/processes interact with crystals high false detection rate.

• Reduce background deep tunnels (e.g. Gran Sasso)

• Search for seasonal signature

A first detection? … Or notThe DAMA experiment in the Gran Sasso claimed to have found a seasonal variation

? 50 GeV particles

Other experiments seem to rule out DAMA

PROBLEM: cross-section could be 1000 times smaller than current limits

Summary

and can now be well determined– only through a variety of approaches– Mass census, cluster abundance, luminosity

distance/angular diameter distance

– Need H0 from local measurements

– Too early to discriminate from alternative models

• Hypothesis of universal D.M. explains things on man scales

• Nature of D.M. has been limited, but is not known