Astronomy 422 Lecture 20: Cosmic Microwave Background
Key concepts: The CMB Recombination Radiation and matter eras Next time: Astro 422 Peer Review - Make sure to read all 6 proposals and send in rankings and written reports by Monday afternoon
Term papers Monday, May 9, 5pm: The full paper is due. April 28 May 5: Term paper presentations. Each presentation will be 15 minutes, plus 5 minutes for questions. Attending these presentations is required. Audience participation counts (everybody has to ask a question). Paper format: The paper should be between 10-15 pages in length, font size 12pt (single-spaced). Include an abstract, figures and citations, and a reference list. Some good info on format of a report can be found at http://www.studygs.net/labreports.htm Also an example report is posted on the class web page (good even if it was missing an abstract; make sure you remember to include one).
Astro 422 Presentations: Thursday April 28: 9:30 9:50 _Isaiah Santistevan 9:50 10:10 _Cameron Trapp 10:10 10:30 Tuesday May 3: 9:30 9:50 9:50 10:10 10:10 10:30 Thursday May 5: 9:30 9:50 _Montie Avery 9:50 10:10 _Andrea Tallbrother 10:10 10:30 10:30 10:50 Send me your preference. First come, first served.
Papers graded on three main criteria: 1. Structure and readability did you divide text into proper sections? do you have good titles/subtitles for the sections? (use your outline!) Does your paper tell a story? 2. Content is the material in a logical order? have you repeated material (don't do that! restructuring is needed if this is the case) did you include figures to explain? With a good figure caption? 3. Use of references do you have a reference list? are you referring to these references in the text?
Recap: 1 1 2 3 2 3
k=0: : E>0 Critical: E=0 Bound: E<0
Recollapsing Universe: expansion will someday halt and reverse Critical Universe: will not collapse, but approach steady state Coasting Universe: will expand forever with little slowdown Accelerating Universe: expansion will accelerate with time
Redshift The redshift factor 1+z is a parameter to describe the expansion of the universe. The light of a redshift 6.4 quasar left the source when the universe was 1/7.4 times as large as it is now. How old was it then? If k=0 we derived Thus t= 650 Myr.
Who Discovered the Microwave Background?
Cosmic Microwave Background First seen by McKellar in 1940 using optical observations of interstellar molecules. Rotationally excited CN is observed with T ~ 2.3 K A microwave background was predicted in the hot big bang model of Gamow, including classic 1948 paper by Alpher, Bethe, and Gamow explaining high He abundance Alpher & Herman in 1948 predict T 0 ~ 1K or 5K
Cosmic Microwave Background Discovered in 1964 by Penzias and Wilson Interpreted in companion paper by Dicke, Roll and Wilkinson as the CMB COBE 1991: perfect blackbody spectrum Primary anisotropies measured. T CMB = 2.725 K
Cosmic Microwave Background Relic radiation from early Universe, when it was hot and dense, in thermal equilibrium. Expansion => universe cooled and became optically thin. CMB could propagate with negligible interaction with matter. Radiation decoupled. Thermal equilibrium => blackbody spectrum.
The CMB Relic radiation from early Universe, when it was hot and dense, in thermal equilibrium. T 0 = 2.725 K Blackbody spectrum. Energy density from integrating across all wavelengths, and correcting for solid angle (ch 9).
Current energy density of the CMB = 0.261 MeV m -3 But energy per photon small, so number density of CMB photons high: Compare to those of baryons (p,n): ~800 times bigger Thus baryons are outnumbered by photons, but energy density larger.
Energy per CMB photon is 6x10-4 ev COBE (1989 launch) resulted in three important results: 1. At any position on the sky, the spectrum is very close to that of an ideal blackbody.
2. The CMB has a dipole distortion (slightly blueshifted in one part of the sky, and redshifted in another). Doppler shift of COBE satellite relative to frame of reference where CMB is isotropic. Since λ max 1/T, a shift in λ max implies a shift in T.
Generally is the direction of motion. If v<<c: Thus, we can measure Sun's motion with respect to the CMB (Hubble flow): 370 km/s toward RA=11.2h, Dec=-7.
Taking into account the motion of COBE around Earth the orbital motion of Earth around the Sun the motion of the Sun in the Milky Way and the motion of the Milky Way within the Local Group => the LG has a peculiar motion: 627 km/s toward RA=11.1h, Dec=-27. We (mostly) understand this as gravitational effect on us by large masses (e.g. "Great Attractor", other superclusters).
3. Subtracting the dipole, there are small anisotropies (and the galactic plane) remaining: Temperature fluctuations of the order of 10-5 K.
3. Subtracting the galactic background: Temperature fluctuations of the order of 10-5 K.
Planck
The horizon problem (without inflation)
That the CMB has a nearly perfect BB spectrum, and is nearly isotropic provide strong support for the Big Bang model of the universe. As universe expands, u R -4 (R -3 from space expansion, R -1 from wavelength increase with R and E=hc/λ).
Recombination and decoupling What are the CMB fluctuations? They reflect small density fluctuations at the time of decoupling. Before decoupling, matter and radiation interacted constantly. Process: Baryonic matter goes from ionized plasma to a gas of neutral atoms. Closely related process: By which universe goes from being opaque to transparent.
Three closely related, but not identical moments: 1. The epoch of recombination. When baryonic components go from ionized to neutral state. 1. Numerically defined as when number density of ions equals number density of neutral atoms. 2. The epoch of decoupling. When the time rate at which photons scatter from electrons becomes smaller that the Hubble parameter (ie expansion rate of the universe). Universe becomes transparent. 3. The epoch of last scattering. When a typical CMB photon underwent its last scattering off an electron. Defines the surface of last scattering.
When does recombination take place? Early universe was hot, ionized. High opacity due to electron scattering. As universe expands, gas cools and becomes atomic We can estimate temperature from the Saha equation:
Considering only hydrogen, we can solve for T when half of e and p combine to neutral. Find T ~ 3000 K. Since RT=R 0 T 0 =T 0., R recomb ~10-3 R 0. Since R=1/(1+z), recombination happened at z~1000. Actual WMAP value, z=1089±1.
Radiation and Matter eras For CMB Using m=e/c 2, can express a mass density associated with radiation. For matter, Currently,
Early universe was radiation dominated. Later it became matter dominated. Now evidently dark matter/energy dominated (more in next lecture).
Let's get back to the temperature fluctuations: Dipole distortion is due to the fact that Universe is not perfectly homogeneous today. Gravitationally accelerated toward lumps of matter, causing a Doppler shift. Distortions on smaller scales due to the fact that universe was not perfectly homogeneous at the time of the last scattering. Angular size reflects physical size of density fluctuations.
What causes the fluctuations? Assume a CMB photon in the minima of a potential well, in a dense region. Climbing out, it looses energy and becomes redshifted (cooler). Thus, denser regions are cooler. This is referred to as the Sachs-Wolfe effect. Regions of higher mass-energy density had higher radiation pressure => photons stream into lower pressure regions => pressure went up in those regions => oscillations driven by photon pressure.
Nature of a sound wave depends on the material in which it travels e.g. travels faster in water than in air By studying the fluctuations caused by sound waves we will learn about the material Average density of matter (and dark energy) Hubble constant
Largest CMB oscillations at time of decoupling correspond to distance that light could have traveled by that time (the "sonic horizon distance"). C&O show that At decoupling: t dec = 370,000 yrs => For a flat universe, k=0, the relation between proper distance to remote objects and angular diameter is: We also have
With (for matter era) With How does this compare to actual angular size of anisotropies?
Angular scale
So angular size of CMB fluctuations consistent with a flat universe. Now, radiation energy density is negligible, so
The CMB anisotropies depend critically on Cosmological parameters: H 0,Ω R, Ω M, Ω Λ, Ω b,... Different parameters predict different CMB power spectra.
2003 WMAP, 2004 Models Planck 2013
Secondary anisotropies The Sunyaev-Zel'dovich effect, predicted in the 1970s. CMB photons T = (1 + z) 2.725K galaxy cluster with hot ICM z ~ 0-3 scattered photons (hotter) last scattering surface z ~ 1100 CMB photons have a ~1% chance of inverse Compton scattering off of the ICM electrons; photon number is conserved
This wavelength shift translates into a temperature shift Thus, can be seen as a higher order effect in the CMB The shift is independent of redshift Since clusters of galaxies collapse from large volumes (1000 Mpc^3), the ratio of baryons to dark matter should be representative of the universe as a whole. Observations of SZ determine the baryon fraction in the universe.
Next time: Chapter 29.3