University of Durham Institute for Computational Cosmology Carlos S. Frenk Institute for...

University of Durham

Institute for Computational CosmologyInstitute for Computational CosmologyInstitute for Computational Cosmology

Carlos S. Frenk Institute for Computational Cosmology,

Durham

Galaxy clusters



Galaxy clusters - TiajinCarlos Frenk

Institute of Computational Cosmology University of Durham

• Introduction to the large-scale structure of the Universe

• The formation of dark matter halos

• The structure of dark matter halos



What is the Universe made of?



What is the universe made of?

critical density = density that makes univ. flat: = 1 for a flat univ.

(of which stars, Cole etal ‘02) s = 0.0023 ± 0.0003 • Baryons b = 0.044 ± 0.004

density critical density

• Radiation (CMB, T=2.726±0.005 oK) r = 4.7 x 10-5

• Dark matter (cold dark matter) dm =0.20 ± 0.04

• Dark energy (cosm. const. =0.75 ±

0.04 bdm(assuming Hubble parameter h=0.7)

• Neutrinos = 3 x 10-5 if m 6 x 10-2 (<mev)

mass+rel

+vac



m=0.24±0.04 >>

b=0.044±0.004

all matter baryons

Dark matter must be non-baryonic

The nature of the dark matter



Non-baryonic dark matter candidates

hot neutrino a few eV

warm ? a few keV

cold axion

neutralino10-5eV->100 GeV

Type candidate mass



What is the Universe made of?

Dark energy



Evidence for from high-z supernovae

SN type Ia (standard candles) at z~0.5 are fainter than

expected even if the Universe were empty

The cosmic expansion must have been

accelerating since the light was emitted

a/a0=1/(1+z)



€

a.

+ kc 2 =8π

3Gρa2

€

H 2 1− Ωm − Ωγ − ΩΛ( ) = −kc 2

a2

Friedmann equations

For a homogeneous & isotropic Universe

a = expansion factor, k= curvature

mass+rel

+vacπ

GH 23

8=Ω

G

cvac π

8

2=

a

aH

.

=



Evidence for from high-z supernovae

Distant SN are fainter than expected if expansion were decelerating



€

a.

+ kc 2 =8π

3Gρa2

€

H 2 1− Ωm − Ωγ − ΩΛ( ) = −kc 2

a2

)(3 22 cpda

dac

+−=

)13(3

4..

+−= waGa π

Friedmann equations

For a homogeneous & isotropic Universe

a = expansion factor, k= curvature

2nd law of thermodynamics:

2cwp =

p= pressure

Equation of state:

mass+rel

+vacπ

GH 23

8=Ω

G

cvac π

8

2=

a

aH

.

=



Friedmann equations

€

p = wρc 2where totmass+rel

+VAC a-3 a-4 const?

€

..

a = −4π

3Gρa(3w + 1)

€

c 2adρ

da= −3( p + ρc 2)

If VAC = VAC (z,x) and 3

1−<w quintessence

If vacconst ,dda

0 p c 2 w 1

Accelerated expansion

€

⇒ 3w + 1< 0 ⇒ ˙ ̇ a > 0 ⇒ Expansion accelerates

In general,



2cwp =

)13(3

4..

+−= waGa π

Friedmann equations

013 >+w

where

At early times the universe is always decelerating

totmass+rel

+ a-3 a-4 const?

For matter or radiation:

There must be a transition between decelerating and accelerating expansion



Supernovae Ia and dark energy

Reiss etal ‘04Redshift z

(m

-M)

(ma

g)

Transition from decelerated to accelerated expansion at z~0.5

16 new Sn Ia -- 6 @ z>1.25



The large-structure of the Universe



Results from the “2-degree field” galaxy survey

250 nights at 4m AAT 1997-2002

Anglo-Australian team

221,000 redshifts to bj<19.45

Median z=0.11



100

0 m

illion lig

ht yea

rs

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.



The origin of the large-structure of the Universe



The beginning of the Universe

In 1980, a revolutionary idea was proposed: our universe started off in an unstable state (vacuum energy) and as a result expanded very fast in a short period of time cosmic inflation

Inflation

Initially, Universe is trapped in false vacuum

Scalar field

Universe decays to true vacuum keeping v~ const

Universe oscillates converting energy into particles



†

Inflation for beginners

At early times k=0. So, Vacconst.

€

˙ a

a= const Universe expands exponentially

Inflation ends when Vac decay and Universe reheats

a.

kc 2 8π3

Ga22



Conventionalinflation

Chaoticinflation

Cosmic Inflation

t=10-35 s

Inflation theory predicts:

1. Flat geometry (=1)

(eternal expansion)

2. Small ripples in mass distribution



Quantum fluctuations are blown up to macroscopic scales during inflation

Generation of primordial fluctuations

Because of quantum fluctuations, different parts of the Universe finish inflating at slightly different times



Spectrum of inhomogeneities

x



Standard inflation predicts:

1. FLAT GEOMETRY:

2. 2~ k

3

k

2

k2

kn

n = 1

Gaussian amplitudes

123=

+

Hm

Cosmic Inflation







Evolution of an adiabatic perturbation in CDM universe

M=1015 Mo=1, h=0.5

Dak matter baryons

radiationFlu

ctu

atio

n a

mpl

itud

e

Log a(t)/a0

Horizon entry



The origin of cosmic structureQUANTUM FLUCTUATIONS:

k2

kn

n = 1

Gaussian amplitudes

Inflation (t~10-35 s)

P(k)=Akn T2(k,t)

Damping (nature of dark matter)+

n=1

Mezaros damping

Free streaming

P(k)

Transfer functionRh(teq)

• Hot DM (eg ~30 ev neutrino)

- Top-down formation

• Cold DM (eg ~neutralino)

- Bottom-up (hierachical)



The microwave background radiation

z =1000

The microwave background radiation

Plasma

z =

T=2.73 K

380 000 years after the big Bang

inflation



Temperature anisotropies in the CMBIntrinsic anisotropies at last scattering:• Gravitational redshift: Sachs-Wolfe effect• Doppler effect• Adiabatic perturbationsLine of sight effects:

• Time varying potentials: ISW effect• Compton scattering: SZ effect



The origin of cosmic structure

n=1

Mezaros damping

Free streaming

Large scales

P(k)

Rh(teq)

Small scales





QUANTUM FLUCTUATIONS:

k2

kn

n = 1

Gaussian amplitudes


P(k)=Akn T2(k,t)

Damping (nature of dark matter)+

Transfer function





CMB



QuickTime™ and aGIF decompressor

are needed to see this picture.

The acoustic peaks in the CMB

Wayne hu

http://background.uchicago.edu/~whu/

If M<Mjeans the photon-baryon fluid oscillates

of CMB acoustic peak sound horizon at trec



The cosmic microwave background radiation (CMB) provides a window to the universe at t~3x105 yrs

In 1992 COBE discovered temperature fluctuations (T/T~10-5) consistent with inflation predictions

The CMB

1992



The CMB

1992

2003



WMAP temperature anisotropies in the CMB

Bennett etal ‘03



The Emergence of the Cosmic Initial Conditions

curvature

total density

baryons



The Emergence of the Cosmic Initial Conditions

• > 105 independent ~ 5 measurements of T are fit by an a priori model with 6 (physical) parameters

• Best CDM model has: t

o= 13.7±0.2 Gyr

h=0.71±0.03 8=0.84±0.04

t=1.02±0.02

m=0.27±0.04

b=0.044±0.004

e=0.17±0.07 (Bennett etal 03)

• Parameters in excellent agreement with other data T-P x-corr Adiabatic fluctns

curvature

total density

baryons



123=

+

H1. FLAT GEOMETRY:

2. QUANTUM FLUCTUATIONS: k2

kn

n = 1

Gaussian amplitudes


adiabatic

Dark matter

CMB (t~3x105 yrs)Structure

(t~13x109yrs)

The origin of cosmic structure



Evolution of spherical perturbations



n=1

damping

Free streaming

Calculating the evolution of cosmic structure

N-body simulation

“Cosmology machine”

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University of Durham Institute for Computational Cosmology Carlos S. Frenk Institute for...

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