Einteilung der VL Einführung Hubblesche Gesetz Antigravitation Entwicklung des Universums Temperaturentwicklung Kosmische Hintergrundstrahlung CMB kombiniert mit SN1a Strukturbildung Neutrinos Grand Unified Theories -13 Suche nach DM HEUTE Schafft man gerade, aber nicht viele Folien auf Projektor und 1Grad Bild zuerst an der Tafel. Braucht man als Ref. Für BAO

Vorlesung 8 Roter Faden: Powerspektrum der CMB Baryonic Acoustic Oscillations (BAO) 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.

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 Lineweaver 1997 peak trough

Vom Bild zum Powerspektrum Temperaturverteilung ist Funktion auf Sphäre: ΔT(θ,φ) bzw. ΔT(n) = ΔΘ(n) T T n=(sinθcosφ,sinθsinφ,cosθ) Autokorrelationsfunktion: C(θ)=<ΔΘ(n1)∙ΔΘ(n2)>|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 „Weißes Rauschen“: flaches Powerspektrum

Temperaturschwankungen als Fkt. des Öffnungswinkels 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 Raum-Zeit x t Inflation Entkopplung max. T / T unter 10 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 nλ/2=cstr

Erste akustische Peak unter bei einem CMB zeigt: Un iversum ist flach 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!

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

WMAP analyzer tool Summary: rotverschiebung hängt von tiefe des Potentials ab, Wenn DM dominiert, ist rotverschiebung durch dm bestimmt und baryonen aendern ersten oberton, weil phase umgekehrt Wenn baryonen dominiert, dann ändern baryonen power extrem: wenig baryonen-> große amplituden durch photondruch->viel power, weil bei dieser freq. Grosse amplitude auftritt http://wmap.gsfc.nasa.gov/resources/camb_tool/index.html

Neueste WMAP Daten (2008)

Neueste WMAP Daten (2008) Polarisation Reionisation nach 2.108 a http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.0732v2.pdf Polarisation Reionisation nach 2.108 a Temperatur Polarisation propto fluss, d.h. Geschwindigkeit, daher in Gegenphase zum Ort Temperatur- und Polarisationsanisotropien um 90 Grad in Phase verschoben, weil Polarisation Fluss der Elektronen, also wenn x  cos (t), dann v  sin (t)

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.

CMB Polarisation bei Quadrupole-Anisotropie 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) http://gyudon.as.utexas.edu/~komatsu/presentation/wmap7_ias.pdf

Entwicklung des Universums

Kurz vor Entkoppelung: Streuung der CMB Photonen. 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.html

(winkel-erhaltende Raum-Zeit) Conformal Space-Time (winkel-erhaltende Raum-Zeit) Raum-Zeit x t t From Ned Wright homepage x  = x/S(t) = x(1+z) t    = t / S(t) = t (1+z) conformal=winkelerhaltend z.B. mercator Projektion 

Woher kennt man diese Verteilung? If it is not dark, it does not matter

Vergleich mit den SN 1a Daten = (SM+ DM)  SN1a empfindlich für Beschleunigung a, d.h. a   - m (beachte: DM und DE unterschei- den sich im VZ der Grav. a   - m CMB empfindlich für totale Dichte d.h. tot =  + m =1 tot =  + m =1

Akustische Baryon Oszillationen I: http://cmb. as. arizona 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 II: http://cmb. as. arizona 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 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 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 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 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 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 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) (Einsentein et al. 2005) 150 Mpc. 150 Mpc =2cs tr (1+z)=akustischer Horizont

Akustische Baryonosz. in Korrelationsfkt. der Dichteschwankungen der Materie! 150 Mpc. 105 h-1 ¼ 150 2-point correlation of density contrast The same CMB oscillations at low redshifts !!! SDSS survey (astro-ph/0501171) (Eisentein et al. 2005)

Combined results http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.4142v1.pdf http://nedwww.ipac.caltech.edu/level5/March08/Frieman/Frieman4.html

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 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).

Zum Mitnehmen If it is not dark, it does not matter

Zusatzfolien mit Text der Nobelpreisankündigungen „just for fun“, kein Prüfungsstoff.

Cosmology and the Cosmic Microwave Background 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. From Nobel prize 2006 announcement

Early work 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. From Nobel prize 2006 announcement

First observations of CMB 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. CN=Cyan

Further observations of CMB 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).

Dipol Anisotropy 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. Explanation: two effects compensate the temperature anisotropies: DM dominates the gravitational potential after str<< m so hot spots in the grav. potential wells of DM have a higher temperature, but photons climbing out of the potential well get such a strong red shift that they are COLDER than the average temperature!

The COBE mission 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 success 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.

CMB Anisotropies 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).

Outlook 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.

The colour of the universe 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 = 2.9106/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 ~ 3106/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.

Light Intensity 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 = 2.210-7 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 = 2.210-72.74 = 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 = 81021 W/m2 ~ 1019 Isun (you boil away in much less than a nano-second).