Einteilung der VL - KITdeboer/html/Lehre/Kosmo... · 2012. 12. 13. · Lineweaver 1997 peak trough Sky Maps Power Spectra We “see” the CMB sound as waves on the sky. Use special

Wim de Boer, Karlsruhe

Kosmologie VL, 13.12.2012 1

Einteilung der VL

1. Einführung

2. Hubblesche Gesetz

3. Antigravitation

4. Gravitation

5. Entwicklung des Universums

6. Temperaturentwicklung

7. Kosmische Hintergrundstrahlung

8. CMB kombiniert mit SN1a

9. Strukturbildung

10. Neutrinos

11. Grand Unified Theories

12.-13 Suche nach DM

HEUTE



Vorlesung 8

Roter Faden:

1. Powerspektrum der CMB

2. Baryonic Acoustic Oscillations (BAO)

3. Energieinhalt des Universums



Akustische Peaks von WMAP

Ort-Zeit

Diagramm



Kugelflächenfunktionen

Jede Funktion kann in orthogonale

Kugelflächenfkt. entwickelt werden. Große

Werte von l beschreiben Korrelationen unter

kleinen Winkel.

l



Lineweaver 1997

peak

trough

Sky Maps Power Spectra

We “see” the CMB sound

as waves on the sky.

Use special methods

to measure the strength

of each wavelength.

Shorter wavelengths

are smaller frequencies

are higher pitches



• Temperaturverteilung ist

Funktion auf Sphäre:

ΔT(θ,φ) bzw. ΔT(n) = ΔΘ(n)

T T

n=(sinθcosφ,sinθsinφ,cosθ)

• Autokorrelationsfunktion:

C(θ)=|n1-n2|

=(4π)-1 Σ∞l=0 (2l+1)ClPl(cosθ)

• Pl sind die Legendrepolynome:

Pl(cosθ) = 2-l∙dl/d(cos θ)l(cos²θ-1)l.

• Die Koeffizienten Cl bilden das Powerspektrum von ΔΘ(n).

mit cosθ=n1∙n2

Vom Bild zum Powerspektrum

„Weißes Rauschen“:

flaches Powerspektrum



Temperaturschwankungen als Fkt. des Öffnungswinkels

Θ 180/l Balloon exp.



Das Leistungsspektrum (power spectrum)

Ursachen für Temperatur-

Schwankungen:

Große Skalen:

Gravitationspotentiale

Kleine Skalen:

Akustische Wellen

l=1 nicht gezeigt, da

sehr stark wegen

Dipolterm durch

Bewegung der Galaxie

gegenüber CMB



Temperaturanisotropie der CMB



Position des ersten akustischen Peaks bestimmt

Krümmung des Universums!



Position des ersten Peaks

Berechnung der Winkel, worunter man

die maximale Temperaturschwankungen

der Grundwelle beobachtet:

Maximale Ausdehnung einer akust. Welle

zum Zeitpunkt trec: cs * trec (1+z)

Beobachtung nach t0 =13.8 109 yr.

Öffnungswinkel θ = cs * trec * (1+z) / c*t0 Mit (1+z)= 3000/2.7 =1100 und

trec = 3,8 105 yr und Schallgeschwindigkeit

cs=c/3 für ein relativ. Plasma folgt:

θ = 0.0175 = 10 (plus (kleine) ART Korrekt.)

Beachte: cs2 ≡ dp/d = c2/3, da p= 1/3 c2

Raum-Zeit x

t Inflation

Entkopplung

max. T / T

unter 10

nλ/2=cstr



Erste akustische Peak unter bei einem

Öffnungswinkel von 0.8 Grad oder l=220

bedeutet:

das Universum ist flach

oder die mittlere Dichte entspricht der

kritischen Dichte von 2. 10-29 g/cm3 oder =1

und

Gesamtenergie (kin. + pot. Energie) ist Null!

CMB zeigt: Un iversum ist flach



Präzisere Berechnung des ersten Peaks

Vor Entkopplung Universum teilweise strahlungsdominiert.

Hier ist die Expansion t1/2 statt t2/3 in materiedominiertes Univ.

Muss Abstände nach bewährtem Rezept berechnen:

Erst in mitbewegten Koor. und dann x S(t)

Abstand < trek: S(t) c d = S(t) c dt/S(t) = 2ctrek für S t1/2

Abstand > trek: S(t) c d =S(t)c dt/S(t) = 3ctrek für S t2/3

Winkel θ = 2 * cs * trec * (1+z) / 3*c*t0 = 0.7 Grad

Auch nicht ganz korrekt, denn Univ. strahlungsdom. bis t=50000 a,

nicht 380000 a. Richtige Antwort: Winkel θ = 0.8 Grad oder l=180/0.8=220



http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html

WMAP analyzer tool

http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html



Neueste WMAP Daten (2008)



http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0732v2.pdf

Neueste WMAP Daten (2008)

Polarisation

Temperatur

Temperatur- und Polarisationsanisotropien um 90 Grad in Phase verschoben,

weil Polarisation Fluss der Elektronen, also wenn x cos (t), dann v sin (t)

Reionisation

nach 2.108 a



CMB Polarisation durch Thomson Streuung

(elastische Photon-Electron Streuung)

Prinzip: unpolarisiertes Photon unter 90 Grad gestreut, muss immer

noch E-Feld Richtung haben, so eine Komponente verschwindet!

Daher bei Isotropie keine Pol. , bei Dipol auch nicht, nur bei Quadr.



Polarization entweder radial oder tangential um hot oder cold spots

(proportional zum Fluss der Elektronen, also zeigt wie Plasma sich

bewegte bei z=1100 and auf große Skalen wie Plasma in Galaxien

Cluster sich relativ zum CMB bewegt)

CMB Polarisation bei Quadrupole-Anisotropie

http://gyudon.as.utexas.edu/~komatsu/presentation/wmap7_ias.pdf



Entwicklung des Universums



CMB polarisiert durch Streuung an Elektronen

(Thomson Streuung)

Kurz vor Entkoppelung:

Streuung der CMB Photonen.

Nachher nicht mehr, da mittlere

freie Weglange zu groß.

Lange vor der Entkopplung:

Polarisation durch Mittelung

über viele Stöße verloren.

Nach Reionisation der Baryonen

durch Sternentstehung wieder

Streuung.

Erwarte Polarisation also kurz

nach dem akust. Peak (l = 300)

und auf großen Abständen (l < 10) Instruktiv:http://background.uchicago.edu/~whu/polar/webversion/node1.htm

l



= x/S(t) = x(1+z)

Raum-Zeit x

t

= t / S(t) = t (1+z)

Conformal Space-Time

(winkel-erhaltende Raum-Zeit)

conformal=winkelerhaltend

z.B. mercator Projektion

x

t

t

From Ned Wright homepage



If it is not dark,

it does not matter

Woher kennt man diese Verteilung?



Vergleich mit den SN 1a Daten

SN1a empfindlich für

Beschleunigung a, d.h.

a - m (beachte:

DM und DE unterschei-

den sich im VZ der Grav.

CMB empfindlich für

totale Dichte d.h.

tot = + m =1

= (SM+ DM)



Let's consider what happens to a point-

like initial perturbation. In other words,

we're going to take a little patch of space

and make it a little denser. Of course, the

universe has many such patchs, some

overdense, some underdense. We're just

going to focus on one. Because the

fluctuations are so small, the effects of

many regions just sum linearly.

The relevant components of the universe

are the dark matter, the gas (nuclei and

electrons), the cosmic microwave

background photons, and the cosmic

background neutrinos.

Akustische Baryon Oszillationen I: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html



Akustische Baryon Oszillationen II: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

Now what happens?

The neutrinos don't interact with anything and are too fast

to be bound gravitationally, so they begin to stream away

from the initial perturbation.

The dark matter moves only in response to gravity and has

no intrinsic motion (it's cold dark matter). So it sits still.

The perturbation (now dominated by the photons and

neutrinos) is overdense, so it attracts the surroundings,

causing more dark matter to fall towards the center.

The gas, however, is so hot at this time that it is ionized. In

the resulting plasma, the cosmic microwave background

photons are not able to propagate very far before they

scatter off an electron. Effectively, the gas and photons are

locked into a single fluid. The photons are so hot and

numerous, that this combined fluid has an enormous

pressure relative to its density. The initial overdensity is

therefore also an initial overpressure. This pressure tries

to equalize itself with the surroundings, but this simply

results in an expanding spherical sound wave. This is just

like a drum head pushing a sound wave into the air, but

the speed of sound at this early time is 57% of the speed of

light!

The result is that the perturbation in

the gas and photon is carried outward:



Akustische Baryon Oszillationen III: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

As time goes on, the spherical shell of gas

and photons continues to expand. The

neutrinos spread out. The dark matter

collects in the overall density perturbation,

which is now considerably bigger because

the photons and neutrinos have left the

center. Hence, the peak in the dark matter

remains centrally concentrated but with an

increasing width. This is generating the

familiar turnover in the cold dark matter

power spectrum.

Where is the extra dark matter at large

radius coming from? The gravitational

forces are attracting the background

material in that region, causing it to contract

a bit and become overdense relative to the

background further away



Akustische Baryon Oszillationen IV: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

The expanding universe is cooling.

Around 400,000 years, the

temperature is low enough that the

electrons and nuclei begin to combine

into neutral atoms. The photons do

not scatter efficiently off of neutral

atoms, so the photons begin to slip

past the gas particles. This is known

as Silk damping (ApJ, 151, 459, 1968).

The sound speed begins to drop

because of the reduced coupling

between the photons and gas and

because the cooler photons are no

longer very heavy compared to the

gas. Hence, the pressure wave slows

down.



Akustische Baryon Oszillationen V: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

This continues until the photons have

completely leaked out of the gas

perturbation. The photon perturbation

begins to smooth itself out at the speed

of light (just like the neutrinos did).

The photons travel (mostly)

unimpeded until the present-day,

where we can record them as the

microwave background (see below).

At this point, the sound speed in the

gas has dropped to much less than the

speed of light, so the pressure wave

stalls.



Akustische Baryon Oszillationen VI: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

We are left with a dark matter

perturbation around the original

center and a gas perturbation in a shell

about 150 Mpc (500 million light-

years) in radius.

As time goes on, however, these two

species gravitationally attract each

other. The perturbations begin to mix

together. More precisely, both

perturbations are growing quickly in

response to the combined gravitational

forces of both the dark matter and the

gas. At late times, the initial

differences are small compared to the

later growth.



Akustische Baryon Oszillationen VII: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

Eventually, the two look quite

similar. The spherical shell of the

gas perturbation has imprinted

itself in the dark matter. This is

known as the acoustic peak.

The acoustic peak decreases in

contrast as the gas come into lock-

step with the dark matter simply

because the dark matter, which has

no peak initially, outweighs the gas

5 to 1.



Akustische Baryon Oszillationen VIII: http://cmb.as.arizona.edu/~eisenste/acousticpeak/acoustic_physics.html

At late times, galaxies form in the

regions that are overdense in gas and

dark matter. For the most part, this is

driven by where the initial

overdensities were, since we see that the

dark matter has clustered heavily

around these initial locations. However,

there is a 1% enhancement in the

regions 150 Mpc away from these

initial overdensities. Hence, there

should be an small excess of galaxies

150 Mpc away from other galaxies, as

opposed to 120 or 180 Mpc. We can see

this as a single acoustic peak in the

correlation function of galaxies.

Alternatively, if one is working with the

power spectrum statistic, then one sees

the effect as a series of acoustic

oscillations.

Before we have been plotting the mass profile

(density times radius squared). The density

profile is much steeper, so that the peak at 150

Mpc is much less than 1% of the density near

the center.



One little telltale bump !!

A small excess in correlation at 150 Mpc.!

SDSS survey

(astro-ph/0501171)

150 Mpc.

(Einsentein et al. 2005)

1 2( ) ( ) ( )r r r

150 Mpc =2cs tr (1+z)=akustischer Horizont



The same CMB oscillations at

low redshifts !!!

SDSS survey

(astro-ph/0501171)

150 Mpc.

(Eisentein et al. 2005)

105 h-1 ¼ 150

Akustische Baryonosz. in Korrelationsfkt. der

Dichteschwankungen der Materie!



http://nedwww.ipac.caltech.edu/level5/March08/Frieman/Frieman4.html

Combined results

http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.4142v1.pdf



Zum Mitnehmen

Die CMB gibt ein Bild des frühen Universums 380.000 yr nach dem Urknall und zeigt

die Dichteschwankungen T/T, woraus später die Galaxien entstehen.

Die CMB zeigt dass

1. das Univ. am Anfang heiß war, weil akustische Peaks, entstanden

durch akustische stehende Wellen in einem heißen Plasma, entdeckt wurden

2. die Temperatur der Strahlung im Universum 2.7 K ist wie erwartet bei einem

EXPANDIERENDEN Univ. mit Entkopplung der heißen Strahlung und Materie

bei einer Temp. von 3000 K oder z=1100 (T 1+z !)

3. das Univ. FLACH ist, weil die Photonen sich seit der letzten Streuung

zum Zeitpunkt der Entkopplung (LSS = last scattering surface) auf gerade

Linien bewegt haben (in comoving coor.)

4) BAO wichtig, weil Sie unabhängig von der akustischen Horizont in der CMB ein

zweiter wohl definierter Maßstab (akustischer Horizont der Materie) bestimmt,

dessen Vergrößerung heute gemessen werden kann. Dies bestätigt die

Energieverteilung des Univ. unabh. von der Frage ob SN1a Standardkerzen sind.

5) Polarisation der CMB bestätigt Natur der Dichtefluktuationen zum Zeitpunkt der

Entkopplung und bestimmt Zeitpunkt der Sternbildung (Ionisation->Polarisation)

Die schnelle Sternbildung kann nur mit Potentialtöpfen der DM zum Zeitpunkt der

Entkopplung erklärt werden. (die neutrale Kerne fallen da hinein).



If it is not dark,

it does not matter

Zum Mitnehmen



Zusatzfolien mit Text der Nobelpreisankündigungen

„just for fun“, kein Prüfungsstoff.



The Universe is approximately about 13.7 billion years old, according to the

standard cosmological Big Bang model. At this time, it was a state of high

uniformity, was extremely hot and dense was filled with elementary particles

and was expanding very rapidly. About 380,000 years after the Big Bang, the

energy of the photons had decreased and was not sufficient to ionise hydrogen

atoms. Thereafter the photons “decoupled” from the other particles and could

move through the Universe essentially unimpeded. The Universe has expanded

and cooled ever since, leaving behind a remnant of its hot past, the Cosmic

Microwave Background radiation (CMB). We observe this today as a 2.7 K

thermal blackbody radiation filling the entire Universe. Observations of the

CMB give a unique and detailed information about the early Universe, thereby

promoting cosmology to a precision science. Indeed, as will be discussed in

more detail below, the CMB is probably the best recorded blackbody spectrum

that exists. Removing a dipole anisotropy, most probably due our motion

through the Universe, the CMB is isotropic to about one part in 100,000. The

2006 Nobel Prize in physics highlights detailed observations of the CMB

performed with the COBE (COsmic Background Explorer) satellite.

Cosmology and the Cosmic Microwave Background

From Nobel prize 2006 announcement



The discovery of the cosmic microwave background radiation has an

unusual and interesting history. The basic theories as well as the necessary

experimental techniques were available long before the experimental

discovery in 1964. The theory of an expanding Universe was first given by

Friedmann (1922) and Lemaître (1927). An excellent account is given by

Nobel laureate Steven Weinberg (1993).

Around 1960, a few years before the discovery, two scenarios for the

Universe were discussed. Was it expanding according to the Big Bang

model, or was it in a steady state? Both models had their supporters and

among the scientists advocating the latter were Hannes Alfvén (Nobel prize

in physics 1970), Fred Hoyle and Dennis Sciama. If the Big Bang model

was the correct one, an imprint of the radiation dominated early Universe

must still exist, and several groups were looking for it. This radiation must

be thermal, i.e. of blackbody form, and isotropic.

Early work

From Nobel prize 2006 announcement



The discovery of the cosmic microwave background by Penzias and Wilson in 1964

(Penzias and Wilson 1965, Penzias 1979, Wilson 1979, Dicke et al. 1965) came as a

complete surprise to them while they were trying to understand the source of

unexpected noise in their radio-receiver (they shared the 1978 Nobel prize in

physics for the discovery). The radiation produced unexpected noise in their radio

receivers. Some 16 years earlier Alpher, Gamow and Herman (Alpher and Herman

1949, Gamow 1946), had predicted that there should be a relic radiation field

penetrating the Universe. It had been shown already in 1934 by Tolman (Tolman

1934) that the cooling blackbody radiation in an expanding Universe retains its

blackbody form. It seems that neither Alpher, Gamow nor Herman succeeded in

convincing experimentalists to use the characteristic blackbody form of the

radiation to find it. In 1964, however, Doroshkevich and Novikov (Doroshkevich

and Novikov 1964) published an article where they explicitly suggested a search for

the radiation focusing on its blackbody characteristics. One can note that some

measurements as early as 1940 had found that a radiation field was necessary to

explain energy level transitions in interstellar molecules (McKellar 1941).

Following the 1964 discovery of the CMB, many, but not all, of the steady state

proponents gave up, accepting the hot Big Bang model. The early theoretical work

is discussed by Alpher, Herman and Gamow 1967, Penzias 1979, Wilkinson and

Peebles 1983, Weinberg 1993, and Herman 1997.

First observations of CMB

CN=Cyan



Following the 1964 discovery, several independent measurements of the

radiation were made by Wilkinson and others, using mostly balloon-borne,

rocket-borne or ground based instruments. The intensity of the radiation has

its maximum for a wavelength of about 2 mm where the absorption in the

atmosphere is strong. Although most results gave support to the blackbody

form, few measurements were available on the high frequency (low

wavelength) side of the peak. Some measurements gave results that showed

significant deviations from the blackbody form (Matsumoto et al. 1988).

The CMB was expected to be largely isotropic. However, in order to explain

the large scale structures in the form of galaxies and clusters of galaxies

observed today, small anisotropies should exist. Gravitation can make small

density fluctuations that are present in the early Universe grow and make

galaxy formation possible. A very important and detailed general relativistic

calculation by Sachs and Wolfe showed how three-dimensional density

fluctuations can give rise to two-dimensional large angle (> 1°) temperature

anisotropies in the cosmic microwave background radiation (Sachs and

Wolfe 1967).

Further observations of CMB



Because the earth moves relative to the CMB, a dipole temperature

anisotropy of the level of ΔT/T = 10-3 is expected. This was observed in the

1970’s (Conklin 1969, Henry 1971, Corey and Wilkinson 1976 and Smoot,

Gorenstein and Muller 1977). During the 1970-tis the anisotropies were

expected to be of the order of 10-2 – 10-4, but were not observed

experimentally. When dark matter was taken into account in the 1980-ties,

the predicted level of the fluctuations was lowered to about 10-5, thereby

posing a great experimental challenge.

Dipol Anisotropy

Explanation: two effects compensate the temperature anisotropies:

DM dominates the gravitational potential after str



Because of e.g. atmospheric absorption, it was long realized that

measurements of the high frequency part of the CMB spectrum

(wavelengths shorter than about 1 mm) should be performed from

space. A satellite instrument also gives full sky coverage and a long

observation time. The latter point is important for reducing systematic

errors in the radiation measurements. A detailed account of

measurements of the CMB is given in a review by Weiss (1980).

The COBE story begins in 1974 when NASA made an announcement of opportunity

for small experiments in astronomy. Following lengthy discussions with NASA

Headquarters the COBE project was born and finally, on 18 November 1989, the

COBE satellite was successfully launched into orbit. More than 1,000 scientists,

engineers and administrators were involved in the mission. COBE carried three

instruments covering the wavelength range 1 μm to 1 cm to measure the anisotropy

and spectrum of the CMB as well as the diffuse infrared background radiation:

DIRBE (Diffuse InfraRed Background Experiment), DMR (Differential Microwave

Radiometer) and FIRAS (Far InfraRed Absolute Spectrophotometer). COBE’s

mission was to measure the CMB over the entire sky, which was possible with the

chosen satellite orbit. All previous measurements from ground were done with limited

sky coverage. John Mather was the COBE Principal Investigator and the project

leader from the start. He was also responsible for the FIRAS instrument. George

Smoot was the DMR principal investigator and Mike Hauser was the DIRBE principal

investigator.

The COBE mission



For DMR the objective was to search for anisotropies at three

wavelengths, 3 mm, 6 mm, and 10 mm in the CMB with an

angular resolution of about 7°. The anisotropies postulated to

explain the large scale structures in the Universe should be

present between regions covering large angles. For FIRAS

the objective was to measure the spectral distribution of the

CMB in the range 0.1 – 10 mm and compare it with the

blackbody form expected in the Big Bang model, which is

different from, e.g., the forms expected from starlight or

bremsstrahlung. For DIRBE, the objective was to measure

the infrared background radiation. The mission, spacecraft

and instruments are described in detail by Boggess et al.

1992. Figures 1 and 2 show the COBE orbit and the satellite,

respectively.

The COBE mission



COBE was a success. All instruments worked very

well and the results, in particular those from DMR

and FIRAS, contributed significantly to make

cosmology a precision science. Predictions of the Big

Bang model were confirmed: temperature

fluctuations of the order of 10-5 were found and the

background radiation with a temperature of 2.725 K

followed very precisely a blackbody spectrum.

DIRBE made important observations of the infrared

background. The announcement of the discovery of

the anisotropies was met with great enthusiasm

worldwide.

The COBE success



The DMR instrument (Smoot et al. 1990) measured temperature

fluctuations of the order of 10-5 for three CMB frequencies, 90, 53 and

31.5 GHz (wavelengths 3.3, 5.7 and 9.5 mm), chosen near the CMB

intensity maximum and where the galactic background was low. The

angular resolution was about 7°. After a careful elimination of

instrumental background, the data showed a background contribution

from the Milky Way, the known dipole amplitude ΔT/T = 10-3 probably

caused by the Earth’s motion in the CMB, and a significant long sought

after quadrupole amplitude, predicted in 1965 by Sachs and Wolfe. The

first results were published in 1992.The data showed scale invariance for

large angles, in agreement with predictions from inflation models.

Figure 5 shows the measured temperature fluctuations in galactic coordinates, a figure

that has appeared in slightly different forms in many journals. The RMS cosmic

quadrupole amplitude was estimated at 13 ± 4 μK (ΔT/T = 5×10-6) with a systematic

error of at most 3 μK (Smoot et al. 1992). The DMR anisotropies were compared and

found to agree with models of structure formation by Wright et al. 1992. The full 4 year

DMR observations were published in 1996 (see Bennett et al. 1996). COBE’s results

were soon confirmed by a number of balloon-borne experiments, and, more recently, by

the 1° resolution WMAP (Wilkinson Microwave Anisotropy Probe) satellite, launched

in 2001 (Bennett et al. 2003).

CMB Anisotropies



The 1964 discovery of the cosmic microwave background had a large impact

on cosmology. The COBE results of 1992, giving strong support to the Big

Bang model, gave a much more detailed view, and cosmology turned into a

precision science. New ambitious experiments were started and the rate of

publishing papers increased by an order of magnitude.

Our understanding of the evolution of the Universe rests on a number of observations,

including (before COBE) the darkness of the night sky, the dominance of hydrogen and

helium over heavier elements, the Hubble expansion and the existence of the CMB.

COBE’s observation of the blackbody form of the CMB and the associated small

temperature fluctuations gave very strong support to the Big Bang model in proving

the cosmological origin of the CMB and finding the primordial seeds of the large

structures observed today.

However, while the basic notion of an expanding Universe is well established,

fundamental questions remain, especially about very early times, where a nearly

exponential expansion, inflation, is proposed. This elegantly explains many

cosmological questions. However, there are other competing theories. Inflation may

have generated gravitational waves that in some cases could be detected indirectly by

measuring the CMB polarization. Figure 8 shows the different stages in the evolution

of the Universe according to the standard cosmological model. The first stages after the

Big Bang are still speculations.

Outlook



The young Universe was fantastically bright. Why? Because everywhere it

was hot, and hot things glow brightly. Before we learned why this was:

collisions between charged particles create photons of light. As long as the

particles and photons can thoroughly interact then a thermal spectrum is

produced: a broad range with a peak.

The thermal spectrum’s shape depends only on temperature: Hotter objects

appear bluer: the peak shifts to shorter wavelengths, with: pk = 0.0029/TK

m = 2.9106/T nm. At 10,000K we have peak = 290 nm (blue), while at

3000K we have peak = 1000 nm (deep orange/red).

Let’s now follow through the color of the Universe during its first million

years. As the Universe cools, the thermal spectrum shifts from blue to red,

spending ~80,000 years in each rainbow color.

At 50 kyr, the sky is blue! At 120 kyr it’s green; at 400 kyr it’s orange; and

by 1 Myr it’s crimson. This is a wonderful quality of the young Universe: it

paints its sky with a human palette.

Quantitatively: since peak ~ 3106/T nm, and T ~ 3/S K, then peak ~ 106 /

S nm. Notice that today, S = 1 and so peak = 106 nm = 1 mm, which is, of

course, the peak of the CMB microwave spectrum.

The colour of the universe



Hotter objects appear brighter. There are two reasons for this:

More violent particle collisions make more energetic photons. Converting pk ~

0.003/T m to the equivalent energy units, it turns out that in a thermal spectrum,

the average photon energy is ~ kT. So, for systems in thermal equilibrium, the

mean energy per particle or per photon is ~kT. Faster particles collide more

frequently, so make more photons. In fact the number density of photons, nph

T3. Combining these, we find that the intensity of thermal radiation increases

dramatically with temperature Itot = 2.210-7 T4 Watt /m2 inside a gas at

temperature T.

At high temperatures, thermal radiation has awesome power – the multitude of particle

collisions is incredibly efficient at creating photons. To help feel this, consider the light

falling on you from a noontime sun – 1400 Watt/m2 – enough to feel sunburned quite

quickly. Let’s write this as Isun.

Float in outer space, exposed only to the CMB, and you experience a radiation

field of I3K = 2.210-72.74 = 10 W/m2 = 10-8 Isun – not much! Here on Earth at

300K we have I300K ~ 1.8 kW/m2 (fortunately, our body temperature is 309K so

you radiate 2.0 kW/m2, and don’t quickly boil!). A blast furnace at 1500 C

(~1800K) has I1800K = 2.3 MW/m2 = 1600 Isun (you boil away in ~1 minute).

At the time of the CMB (380 kyr), the radiation intensity was I3000K = 17 MW/m2

= 12,000 Isun – you evaporate in 10 seconds.

In the Sun’s atmosphere, we have I5800K = 250 MW/m2 = 210,000 Isun. That’s a

major city’s power usage, falling on each square meter.

Radiation in the Sun’s 14 million K core has: I = 81021 W/m2 ~ 1019 Isun (you

boil away in much less than a nano-second).

Light Intensity

Documents

Einteilung der VL - KITdeboer/html/Lehre/Kosmo... · 2012. 12. 13. · Lineweaver 1997 peak trough Sky Maps Power Spectra We “see” the CMB sound as waves on the sky. Use special