The CMB and the SZ Effect

Current Topics 2008Dr. Katy Lancaster

Course Content

•Introduction-The Cosmic Microwave Background-The Sunyaev Zel’dovich Effect•Science from the SZ effect-The Hubble constant-Gas fractions-Number counts•Practicalities-Telescopes-Issues

Lecture 1

•A brief history

•Production of the CMB

•Production of primary anisotropies

•The Sunyaev Zel’dovich effect

Brief history lesson

•1950s, two conflicting cosmological theories

•Steady State theory •Universe always has been and always will be in a static, homogenous state.

•Expanding Universe•Hubble’s observations, 1929•Gamov - realised that the Universe was once extremely dense and hot, thus must have since expanded and cooled

Penzias and Wilson•1965, were making

sensitive observations of microwave emission from the galaxy

•Detect ‘annoying level of static’ in all directions

•At the same time, Dicke at Princeton predicted the existence of ‘relic’ radiation from the Big Bang

•Nobel Prize, 1978

COBE•NASA satellite launched late 80s

•‘Cosmic Microwave Background radiation’ was found to have a perfect blackbody spectrum

•Implies Universe was once isothermal. Only Big Bang models predict this.

•For this (and other reasons), the COBE scientists won the Nobel prize in 2007

Primordial Universe

•Early Universe: Devoid of structure. •T > 4000K, entirely ionised - ‘sea’ of electrons, protons, helium nuclei and photons

•Too hot for atoms to form•Photons repeatedly Thomson scatter from electrons, unable to propagate freely

•Almost perfect thermal equilibrium due to the ‘coupling’ of matter and radiation

•Predicted and required by Big Bang models

•Universe is ‘opaque’

Thermalisation•As COBE discovered, the CMB has a perfect blackbody spectrum.

•Two contributory processes during the first year after the Big Bang, each creates/destroys photons:

•At very early times, thermal Bremstrahlung radiation / absorption: e+pe+p+. This ceased as the Universe cooled. Produces thermal spectrum

•Later, double Compton scattering: e+ e+2.

•Only effective while collision rate > expansion rate

•Since then there has been no process capable of destroying the spectrum (although there may be tiny distortions)

Recombination•Early Universe filled with free electrons, photon mean-free path small (Universe in thermal equilbrium, ‘opaque’)

•Impossible for any information about this time to be communicated to us via radiation

•Temperature of Universe falls to ~4000K, very few photons with energy > Hydrogen binding energy, 13.6eV

•Electrons and protons combine: e+p H+

•Vast majority of free electrons disappear. Universe now neutral, photons can free-stream

•In fact recombination happens over a time or redshift ‘slice’ (1500 > z > 1200 ) rather than instantaneously.

Surface of last scattering•The CMB photons were emitted at the same time,

and thus underwent their final scattering event at the same time

•All CMB photons move at the speed of light, have travelled the same distance since this time

•We can think of the CMB as being emitted from a fictitious spherical surface, of which we are at the centre

•Like observing the surface of the sun, although it is the outer reaches (or rather, the very early Universe) that we can not observe, rather than the inner workings

•Strictly speaking, recombination is not instantaneous, so we sometimes talk about the ‘thickness’ of the surface

Surface of last scattering

The CMB today•The CMB photons have been significantly redshifted by the Hubble expansion.

• Photon wavelengths have increased by R(t)=1/(1+z)

•CMB temperature falls as 1/R(t): a specific prediction of the Big Bang model

•Temperature of the CMB today T0= T/(1+z) = 2.73K

•Can test the relation at other redshifts by observing stellar line emission from CN molecules

•Actually first measured in circa 1940 but not identified as the CMB until much later!

Observing the CMB

•Uniform high energy glow - the sky is not dark at radio frequencies

The Dipole

•Doppler shift introduces ‘hot’ and ‘cold’ regions•The Local group is moving at 400km/s relative to the CMB!•Also see annual modulation due to Earth’s orbit

Primary Fluctuations

•The CMB appears isotropic (same temperature everywhere) unless we look very carefully

•Initial isotropy actually slightly distorted during / before recombination

•We observe temperature variations, referred to as ‘primordial anisotropies’ or ‘fluctuations’ (see pic)

•We measure the temperature difference in two directions separated by some angle .

•Take many measurements and find the mean value for a particular angular scale

•All CMB anisotropies are characterised in this way

•WMAP, monopole, dipole and galactic emission removed•K in the presence of 3K background

Primary Fluctuations

•The CMB appears isotropic (same temperature everywhere) unless we look very carefully

•Initial isotropy actually slightly distorted during / before recombination

•We observe temperature variations, referred to as ‘primordial anisotropies’ or ‘fluctuations’ (see pic)

•We measure the temperature difference in two directions separated by some angle .

•Take many measurements and find the mean value for a particular angular scale

•All CMB anisotropies are characterised in this way

•Measure size of temperature difference for a range of

•Plot against : ‘Power Spectrum’

Sources of anisotropy

•Sachs Wolfe Effect

•Acoustic Oscillations

•Doppler Shift

•Silk Damping

•Secondary processes

Sachs Wolfe Effect

•Quantum fluctuations in the dark matter distribution led to density inhomogeneities

•These developed under gravity•A CMB photon released from a region with a non-zero gravitational potential will experience an additional redshift

•It has to ‘climb out’ of the potential well

•This creates ‘power’ on the scales > 1

Acoustic Oscillations

•Over-dense regions in dark matter amplified during inflation, collapse under gravity

•Baryons falls into the resulting potential wells

•Radiation pressure increases as the material collapses

•Eventually the pressure overcomes gravity and causes an expansion….

•…..expansion continues until gravity wins again

Acoustic Oscillations•This was taking place at recombination

•Oscillations were happening on all scales. Largest scale: sound horizon. Other scales were not ‘causally connected’.

•Modes which had reached their extrema by recombination produced enhanced features in the CMB

•Compressions - hot spots. (Recombined slightly later, thus suffered less cosmological redshifting)

•Rarefactions - cold spots. (Recombined slightly earlier)

Acoustic Oscillations•Oscillating modes form harmonic sequence:

Largest regions had diameter of the sound horizon, next largest were half this size etc

•Oscillation frequencies corresponded to this: largest region oscillates at half the speed of the next largest etc

•First peak: region which had time to compress exactly once before recombination

•Second peak: region which had time to compress and rarefy, ie one full oscillation before recombining

•Third peak, fourth peak….

Doppler shifts•Also related to the acoustic oscillations

•At times inbetween the extrema of expansion for each oscillation region, the motion of the fluid reached its maximum velocity

•This resulted in a Doppler shift of the photons released when the plasma recombined

•This contriubutes power inbetween the locations of the acoustic peaks: the power spectrum does not go to zero

Silk Damping

•On the smallest scales, the effect of photons ‘escaping’ from the oscillating region becomes important

•The loss of these photons ‘damps’ the power on the smallest angular scales

What can we learn?

•The power spectrum is a complicated function which depends on the values of the various cosmological parameters: H0, ΩM, Ωb, Ω, Ωk, zre, t0….and many more.

•We observe the CMB and then try fitting the powere spectrum to the data. We tweak the parameters to find the best fit.

•And hey presto, we have our very own measurement of the cosmological model

What can we learn?

Galaxy formation•The anisotropies in the CMB are widely regarded as imprints of the ‘seeds’ of structure formation

•That is, those oscillating regions from the early Universe grew and developed under gravity into the stars and galaxies we see today

•If we take the CMB and compare it to observations of large scale structure, we can constrain structure formation scenarios

Secondary Anisotropies•Majority of CMB photons have

travelled through the unimpeded since last scattering

-Hence observed power spectrum•Some have interacted with ionised matter on their path towards us

•This imprints structures on the observable CMB - ‘Secondary Anisotropies’

-Also contribute to the power spectrum

Sources of anisotropy

•Integrated Sachs-Wolfe effect

•Gravitational lensing

•Rees-Sciama effect

•Ostriker-Vishniac effect

•Cosmic strings

•Sunyaev Zel’dovich effect - by far the largest

•Many more postulated…..

•Rich Clusters - congregations of hundreds or even thousands of galaxies

•See cluster galaxies and lensing arcs in the optical

•But only around 5% of a cluster’s mass is in galaxies

•Most of the mass is in Dark Matter

•But a sizable fraction is found in baryonic gas......

Galaxy Clusters

X-rays - see hot gasvia Bremstrahlung emission

10-30% of total mass

Chandra Image of the Coma cluster

Cluster Gas•Clusters of galaxies have masses ~ 3x1014M

•Deep potential wells, gas temperatures ~7keV

•Ionised and energetic

•Constitutes ~30% of the cluster mass

•Gas characteristics may reflect those of the Universe as a whole - interesting to study

Compton Scattering•Compton scattering: Photon

loses energy on interacting with matter

•Inverse Comptin scattering: Photon gains energy on interacting with matter

•In the SZ effect: low energy CMB photon scatters from high energy cluster electron

Photon energy is boosted

SZ Effect basics•CMB photons incident on a galaxy cluster

•Scattering probability is small

•Those which do collide receive energy boost due to inverse Compton scattering

•Spectrum shifted to higher frequency

•Decrement - null - increment

Optical Depth•For a cluster atmosphere with electron density ne(r), the optical depth for scattering along a particular line of sight is:

•Where Tis the Thomson cross section

•The cluster gas is optically thine<<1, ie the probability of scattering is small

Comptonisation•The degree to which the CMB is affected by inverse Compton scattering is described by the Comptonisation parameter:

•Or for the isothermal approximation (often employed in the past):

Brightness Temperature

•Often used in Radio / CMB astronomy

•Defined as: ‘The temperature of a blackbody that would be observed with the same intensity as the observed source, at a particular frequency’

•From the Planck law:

•For the low frequency Rayleigh-Jeans region:

Temperature Decrement

•The change in the brightness temperature of the CMB due to the thermal SZ effect is given by:

•Where the frequency dependence is given by:

•For the Rayleigh Jeans region:

Intensity Change•In units of specific intensity:

•With frequency dependence given by:

Kinematic SZ Effect•Additional spectral distortion caused

by cluster velocity component along line of sight, z

•Collective motion of cluster gas modifies CMB spectrum via Doppler shift

•Observe decrement:

•Frequency dependence:

SZ Intensity Spectra

•g(x), h(x) •Thermal: decrement, null, increment

•Kinematic: Near maximum at the thermal null

Thermal vs Kinematic•Specific intensity

changes:

•Spectral dependence similar at low freq.

•i.e for a typical cluster:

The KSZ effect is < 10% of the thermal effect at low freq.

Decrement - Null - Increment

•ACBAR produced these nice images of a galaxy cluster at 150, 220 and 275 GHz

•Multi-frequency observations useful for eliminating primordial CMB contamination (as well as detecting the kinematic effect)

Summary 1•CMB - blackbody spectrum, primordial features

•Fit ‘power spectrum’ to deduce values of the cosmological parameters

•CMB photons incident on a galaxy cluster may be inverse Compton scattered by hot gas

•This ‘Sunyaev Zel’dovich Effect’ manifests itself as a decrement - null - increment depending on observing frequency

•Cluster peculiar velocity also modifies the radiation via the smaller ‘Kinematic’ effect