Cosmology andClusters of Galaxies

Cosmology: - what is cosmology? - principles

- Big Bang: theory and tests - structure in the Universe

Clusters: - largest bound objects- X-ray observation- a many-purpose tool - the SZ effect

Patrick Koch

Summer student lecture, july 17, 2007

What is cosmology?

- scientific study of the large scale properties of the Universe as a whole- tries to understand origin, evolution and ultimate fate of the Universe- Big Bang- scientific discipline: theory prediction of phenomena observations- century of high-precision cosmology- large scales and small scales and the links in between- interdisciplinary: combining all kind of physics (plasma, gravity, particle, solid states, chemistry, biology)-tremendous future investements (satellites...)- ....

The Principles (1)

The location principle:

- It is unlikely that we occupy a special place in the Universe- Universality: the laws of physics are the same everywhere

The cosmological principle:

- Homogeneity: on the largest scale the Universe has the same physical properties everywhere- Isotropy: on the largest scale the Universe looks the same in any direction

The Principles (2)

The anthropic principle:

the Universe is fine-tuned to our existence:

- strength of gravity- smoothness of Big Bang- strength of strong nuclear force- finally the earth

Why??? - chance - luck

-‘theory of everything‘- ...?

Big Bang: theoretical pillars (1)

... expresses the idea that everything started from something very small:

why do we need a Big Bang?

- expansion of the Universe- abundance of light elements- cosmic microwave background}observational

tests!

framework given by:

General Relativity (Einstein equations)+

cosmological principle+

microphysics (particle physics/thermodynamics)

Exp

erim

ent

The

ory

Big Bang: theoretical pillars (2)

... something about General Relativity:

Achievements: - correct gravitational bending of light by sun - Mercury perihel

- gravitational wave prediction- prediction of black holes as coordinate singularities- Big Bang for a homogeneous expanding Universe

- generalization of Newton‘s law, special relativity (covariant formalism)- Space (curvature) linked to matter and energy (all kinds) → equation of state (pressure – energy relation)- missing: the small one (quantum gravity)

Basic matter classification: - radiation: photons, neutrinos (positive pressure)

- baryonic matter (=‚ordinary matter‘): composed of protons, neutrons, electrons (no pressure)

- dark matter: no direct detection yet, but existent (no pressure)- dark energy: the mysterious one (vaccum property?) (negative pressure)

Big Bang: Intermezzo

...some common misconceptions:

- Big Band did not occur at a single point in space as an explosion (space not yet born!)- there is no center of expansion (both for finite and infinite Universes)- Universe is all space and time we know, thus no information about the embedding- what gave rise to the Big Bang is beyond the Big Bang model (speculations in Pre-Big-Bang models)

Big Bang tests (1): Universe expansion

Hubble, 1929

galaxies outside of Milky Way systematicallymoving away from us: v ~ d (Hubble Law),light from galaxies shifted towards red end

Redshift z = (ν‘-ν)/ν

Hubble law confirms homogeneous expandingUniverse

ν‘:emitted freq.ν: observed freq.

on the very large scale in time and space:Einstein equations+matter distributiongive global dynamics

Expansion: Intermezzo

common misconception: redshift (z) = Doppler shift? NO!

- it is not galaxies moving through space, but space is expanding, carrying the galaxies along- the galaxies themselves are not expanding (gravitationally bound, isolated system)- cosmological redshift (z) is NOT a Doppler shift (Doppler shift would put us in the center of expansion, location principle violated)- redshift to velocity/distance conversion requires specific model

Big Bang tests (2): light elements

Big Bang theory:

- early Universe was very hot, 1s after Big Bang: 10 billion degrees, filled with neutrons, protons, electrons, positrons, photons, neutrinos- in 3 minutes (Universe expands and cools): T and density right for nuclear fusion: Big Bang nucleosynthesis: (=light element formation in early Universe) n → p + e- , n combine with p to deuterium, deuterium mostly combines to He, some Li about 24% of ordinary matter is He, produced in Big Bang, also observed! abundance depends on ordinary matter in the early Universe

next step: constrain ordinary matter → WMAP

about 8% of critical density

Light elements: Intermezzo

Big Bang produces no heavy elements

-elements heavier than Li are all synthesized in stars (bottleneck in BBN: triple collision of He-4-nuclei, takes 1000 yr for He – C conversion)- late stage of stellar evolution: massive stars burn He to carbon, oxygen, silicon, sulfur, iron- elements heavier than iron: outer envelopes of super-giant stars and in supernovae explosion

tool: linear perturbation of Einstein equations

initial conditions primary fluctuations + time evolution +secondary fluctuations + foreground = today‘s CMB

(primary fluctuations: intrinsic temperature change due to compression, Doppler shift, Sachs-Wolf effect)

size, matter content, age, geometry of the Universe

Big Bang tests (3): CMBBBN

surfaces of last scattering= snapshots of the Universe

different opacities:

- z ~ 1032: graviton opacity- z ~ 1010: neutrino opacity- z ~ 103: photon opacity: CMB

immense progress: - 30 x better resolution - 45 x higher sensitivity integration: 2 yr WMAP=4500 yr COBE

ΔT ~ 10-4

Big Bang tests (3): ...CMB

CMB: Intermezzo

... the story of a Nobel Prize:

The well known thing: 1963: Penzias and Wilson: radio emission from Cassiopeia A SN remnant,

uniform noise source → NP in 19781965: Dicke et al.: explain cosmological significance of measurement

The unknown things in theory:1934: Tolman: TD in expanding Universe (no relic predicted)1946: Gamov: Hot Big Bang model1948: Alpher and Herman: Nucleosynthesis in early Universe, predict T ~ 10 K1949: Alpher and Herman: T ~ 5 K1964: Doroshkevich and Novikov suggest CMB detectability as test if Gamov’s model1964: Dicke: search for radiation

The unknown things in observations:1940: Andrew McKellar: interstellar absorption lines from rotationally excited CN molecules, consistent with thermal equilibrium of T ~ 2.3 K (remark in footnote of PhD thesis!)1941: Walter Adams: similar data1955: Emile Le Roux: all sky survey at 33cm wavelength: finds isotropic emission from T ~ 3K.1957: Shmaonov: signal at 3.2cm corresponding to T ~ 4K, independent of direction

Big Bang tests (3): CMB – angular power spectrum

Decomposing patterns of structures in spherical harmonics

l

l

lm lmlmYaT

T),(),(

(“Fourier transform” of anisotropy on the sphere)

m lmlml aal

C *

12

1

Rotational invariance (average over m)

Cl is the variance of structures on scale l, on angular scales

ll

deg180~~

Angular power spectrum

1

deg1180~

l

T/T map

ΔT ~ 10-4

Big Bang tests (3): CMB - fundamental physics

Acoustic oscillations:Interaction photon/baryon fluid with gravity

DM density

geometry, age

Baryon density

detailed physicsworked out in cosmological perturbation theory

In summary: Universe = 95% unknown!

Structure in the Universe- observed structures: from stars to galaxies to cluster to supercluster- Big Bang does NOT explain the existence of structure: structure formation scenario must be built in Big Bang framework

Idea:- Structure grown from gravitational pull of small fluctuations (where do the fluctuations come from?)- hierarchical formation

SDSS: galaxy survey

Clusters of galaxies• largest bound objects in the universe: hot plasma virialized, hydrostatic equilibrium M ~ 1015 MS, T ~ 107-108 K, n ~ 10-2 - 10-4cm -3, r ~1-2 Mpc high luminosity Lbol 1041-1046 ergs/s observations: X-rays, radio, optical

Clusters of galaxies:present at least sincez ~ 1.5

Merger tree

major mergers

back in redshift z

Non-linear processes: different morphologies!

Linear perturbation theory

Clusters of galaxies:coma

optical diffuse radio (Effelsberg)

X-ray (Rosat) X-ray (XMM) X-ray (Chandra)

Merger example: a lot of microphysics! core: turbulences?

Clusters of galaxies

same scale: very different characteristics/emission extension!

stars, galaxieshigh energy emission: ~ keVmechanism: thermal bremsstrahlungsource: intracluster medium

How can it be so hot? → deep grav. potential

What is the gravitational potential?the ‚invisible‘ DM

Clusters of galaxies: DM (1)... or how do we know about DM?

• 1930: Fritz Zwicky discovered that the galaxies in the Coma cluster were moving too fast to remain bound in the cluster according to the Virial Theorem:

• Stable galaxies should obey this law: 2K = -U

• where K=½mV2 is the Kinetic Energy

• U = -aGMm/r is the Potential Energy (a is usually 0.5 - 2,

and depends on the mass distribution)

• Putting these together, we have M=V2r/aG.

• Measure M= Σi mi, r and V2 from observations of the galaxies;

then use M and r to calculate Vvirial

• Compare Vmeasured to Vvirial

• Vmeasured > Vvirial which implies M was too small

• Mass/Luminosity comparison: 10/

/

SS

tottot

LM

LM 90 % DM

Evi

denc

e fo

r D

M

Clusters of galaxies: DM (2)

... or how to measure the weight of clusters?

ICM in (most) clusters close to gravitational equilibrium: outward gas pressure ≈ inward gravitational pull

Pressure reachesmaximum in clustercore

Outward pressure forcebalances inward gravity at every location withinthe cluster

Crude diagram ofcluster atmosphere

Cluster gas pressure profile:

- Separable problem:measure gas density profilemeasure gas temperature profile

- Need X-ray observations!

Hydrostatic Equilibrium

Poisson’s Equation

Spherical Symmetry

X-r

ay

obs.

total mass!(including DM)

luminous matter:temp., density

Clusters of galaxies: DM (3)

Measure T in Each Annulus

Points: Observations

Line: Best Fit

[millions of light years]

spectrum temperture

brightness density

x ~ n2

X-r

ay

obs.

heavy elements:Hints for stellar nucleosynthesis,Supernovae, galaxy-galaxy interactionRem

ark

Clusters of galaxies: DM (4)... or how to use clusters as cosmological probes

• Recall Primordial nucleosynthesis:– Light elements Deuterium, Helium and Lithium were produced when the

universe was minutes old– Observations of the abundances of D, He and Li tightly constrain the mean

baryon density WB of the universe:

• Consider the universal baryon fraction fU?

– ratio of mean baryon density ΩB to mean matter density ΩM

• Can we use clusters as testbed for universal baryon fraction?– Galaxy clusters are the largest collapsed structures in the Universe. Next best thing to taking a census of the entire observable universe!

• We can measure the fraction of galaxy cluster mass which is baryonic

– Cluster baryon fraction fB

• three baryon reservoirs: gas fgas, galaxies fgal and possibly even dark baryons fdb

fU BM

B 0.076 0.005

fB fgas fgal fdb fB fgas fgal

because fgas fB M B

fgas

Clusters of galaxies: DM (5)

• Measuring the mean matter density parameter WM

– Measure cluster baryon fraction fB and calculate WM

• Gas constitutes ~20% of the total mass in the most massive clusters

• This provides lower limit on cluster baryon fraction, and hard, upper limit on cosmological density parameter ΩM

Moh

r, M

ath

iese

n &

Evr

ard

Ap

J 19

99

M 0.36 0.01

M 0.25

• Combined with measurements of the galaxy contribution to the cluster mass we get a best estimate of the density parameter

fU BM

if fU fB then M B

fB

,

Clusters of Galaxies and the Sunyaev-Zeldovich effect (SZE)

cleT

cl e

gB dlncm

TkxgxI

2)()(

Effect depending on frequency and cluster!

Spectral (x) functionScattering process Cluster properties / state

What is it?

•Inverse Compton scattering (CMB photons – hot cluster e-

•Spectral distortion of CMB

•Up-scattering of photons (Rayleigh-Jeans to Wien)

•Secondary anisotropy

radio signal,very weak ~ 100 mJy

Clusters of Galaxies and the SZE(2): power of SZE

OVRO/BIMA SZE vs. X-ray (insets)

• X-ray emission brightness falls off sharply with distance

• SZE brightness independent of distance (hν/kTcmb ~ const.)– only depends on profile (potential well growth with frequency shift) with z and slight z dependence in Tcmb.

– can locate very distant clusters, if they exist…

1010'' 1010'' 66''

X-rayX-ray X-ray

(Carlstrom et al.)

(1) Cluster Survey via the Sunyaev-Zel’dovich Effect (SZE)

Evolution of number counts of galaxy clusters, N(z)

Dark Energy Equation-of-State, cosmological parameters

scaling relations: SZ(y0) – M(r500), SZ(y0) – Tx, SZ(y0) – Lx,

Sν/fν – y0 (SZ only)

information of large-scale structure formation, entropy floor

(non-gravitational processes)

Probing high-z universe (z>1)

(2) Targeted cluster SZ observations: suitable target at right z

complementary to other SZ observations at lower frequency:

e.g. additional data point for spectrum of thermal SZ fit,

evolution of CMB temperature with selected clusters in z-range

Clusters of Galaxies and the SZE(3): science

multifrequency thermal SZ spectral fit: cluster microphysics

additional AMiBA data point @ 90 GHz:

- further constraint on cross-over frequency → relativistic e- population, cluster l.o.s velocity

- further constraint on maximum SZ decrement → relativistic, non-thermal e-

BIMA/OVRO30 GHz

SuZIE140,210,270 GHz

AMiBA90 GHz

Clusters of Galaxies and the SZE(4): cluster microphysics

→ AMiBA science goals: next lecture by Keiichi Umetsu

Clusters of galaxies: what else?

• X-ray: the ‚classical‘ way

• zoomed-in substructures: a lot of microphysics! (mergers, relativistic particles, magnetic fields, turbulences, ....)

• X-ray with SZ observations: e.g. Hubble constant

• clusters (huge mass!) as gravitational lenses for background objects (cosmological parameters, including DE)

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WMAP

LIGO

Hubble

Chandra

GLAST

Scie

nce a

nd

Tech

nolo

gy P

recu

rsors

Appendix: The Beyond Einstein Program