Astro 13 Galaxies & Cosmology LECTURE 6 Thurs 27 Jan 2011 P. Madau

Transcription

1 Astro 13 Galaxies & Cosmology LECTURE 6 Thurs 27 Jan 2011 P. Madau 25m I Distance Ladder and Key Cosmological Questions 25m II What is the Big Bang & what is the evidence for its existence? 10m III Break 40m IV Continuation of what s the Evidence? NOTE: NEXT CLASS: HW#2 DUE. 3 CLASSES TO GIVE TOPIC OF YOUR TERM PROJECT

2 Cosmic Distance Ladder Objects Remote Galax. Remote Clusters Spiral Galaxies METHOD Supernovae Britest Galx. In Cluster Rotation Velocity Useful Distance Light years Light years 10 8 Light years Cepheid Var. Stars Star Clusters Hyades Star Cluster Planets & Stars Nearby Planets Period-Lum. Relat. Color-Mag Rel. Stat. Parallax Moving Cluster Parallax Radar 5x10 7 Light years 10 6 Light years 1000 Light years 120 Light years 100 Light years light minutes

3 Variable Stars in H-R Diagram Shows location of variable stars, including Cepheid Variable stars.

4 Cepheid Variable Stars Brightness Long Period - Bright Shows relation of period and brightness for Cepheid variables. Short Period - faint Time Note there are two Cepheid relations, with Type I in plane of Milky Way vs Type II in globular clusters.

5 Rotation-Velocity Method For Spiral galaxies, rotation can be measured either through optical emission lines and their Doppler shifts or through width of the 21cm (hyperfine spin-spin splitting of the ground state of neutral hydrogen). Using luminosity in the infrared (to avoid dust problems), one finds the Tully-Fisher Relation: Luminosity (IR) 21cm width 4 For Elliptical galaxies, there is a similar relation - Faber-Jackson using optical luminosity and absorption line velocity width Brightness approaching Approaching gas receding away Average of entire galaxy at 21 cm Width Wavelength ===> Receding gas

6 Brightest Galaxy in Cluster Relative Number of Galaxies Luminosity (Milky Way) Brightest Cluster Galaxies Note the narrow range in luminosity - thus standard candle.

7 Supernovae Explosive death of massive stars, with luminosities reaching an entire galaxy, but all concentrated in a single point. The peak luminosity of the SN may be a good standard candle OR one can calculate the expected luminosity from the hot, expanding surface (assumed to be close to a blackbody): Using the Stefan-Boltzmann relationship for Blackbodies: L = 4πR 2 σt 4 where L = luminosity to be calculated; σ is the Stefan-Boltzmann constant = 5.7x10-8 W/m 2 /K 4 R = size = Velocity x Time where Velocity= velocity (km/s) from spectra and Time (using a clock) T = temperature (K) is from spectral features or color. R expanding ball of gas

8 Supernovae M81(3.6Mpc) Two main types of Supernovae with the Ia appearing to have roughly same PEAK luminosity

9 Key Questions in Cosmology 1) What is the origin of our Physical Universe? Big Bang 2) Why do we believe in the Big Bang? expansion; match of ages; evidence for evolution; cosmic background radiation; light elements nucleosynthesis (H, He, D) 3) Where did matter and radiation come from? How have they evolved? E = mc 2 ; radiation <==> matter ; Hubble expansion & inflation 4) Where did galaxies come from? Gas ---> stars How do they get their diversity? How do they evolve? Not sure 5) What are black holes and Quasars? Outcome of gravitational collapse and gas accretion. 6) What is dark matter? Have some ideas, search at LHC Why do we believe it exists? Several reasons TBD 7) What is dark energy? Have no idea (but needed to explain low matter January and 31, 11flat geometry seen in microwave background)

10 What is the Big Bang? The Universe at Time Zero when its density and temperature were infinite, and expansion began (not really!). Lemaitre (circa 1933): infinitely small pinpoint: SINGULARITY A day without yesterday Primordial atom Big noise Fred Hoyle (a Steady State proponent) intentionally gave it an ugly name --- Big Bang! Note: The Big Bang was historically not the only theory that satisfied the observations and cosmological principles. The Steady State Theory was proposed in 1948 to explain the age problem by adopting the Perfect Cosmological Principle.

11 What Happened Before the Big Bang? Not sure but 3 of perhaps many possibilities: 1) Those who say our Universe is the only one would argue that the question is not valid or does not make sense. 2) Some believe our Universe is but one of an INFINITE number, perhaps spawned by another universe: Our U. 3) Yet others CALCULATE that after years or so, pure nothingness (vacuum energy) may SPONTANEOUSLY spring our Universe into existence!

12 What Evidence Favors the Big Bang? The Big Bang is the most successful and simple explanation of a variety of observations. 1) Hubble Expansion: U was hotter and denser in the past (not true in the SST) 2) Consistency of oldest AGES: 1/Ho is good match to estimates of the ages of known old objects (vs. infinitely old for the Steady State Theory-SST) 3) Evidence for EVOLUTION in the Universe: Many astronomical objects have changed over time --- contrast to no changes expected in the SST 4) Discovery of the Cosmic Background Radiation: Easy to explain with Big Bang vs contrived with SST 5) Hydrogen, Helium, and Deuterium Abundance: Theory matches observations

13 1. Hubble Expansion Recall that the apparent recession of galaxies is explained by an expanding universe & NOT actual motions of galaxies within space. This expansion suggests a Beginning for the U. of infinite density and results in redshifts seen for distant galaxies. Some have proposed that light gets tired or loses energy while traveling and thus there is no expansion -- it is an illusion; (but best measurements of surface brightness vs redshift as well as the CMB show that the TIRED LIGHT model is wrong) Einstein s theory which seems to fit other observations naturally provides an isotropic/homogeneous U that expands (or contracts). Note that the Steady State Theory has continuous creation of matter to keep the average density of the U the same for all time during the expansion ===> no hot, dense phase as in the Big Bang model.

14 2. Consistency of the Oldest Ages 2a) Radioactive Decay: Uranium decays to Lead: Nr = Nb e -DT where: Nr = Number of Remaining undecayed atoms of Uranium Nb = Number of Beginning atoms of Uranium D = Decay Constant that measures rate of decay T = elapsed time and T 1/2 = half-life = 0.693/ D For Uranium to Lead: T 1/2 =4.5 Byr. Observed ratios of uranium to lead imply the oldest rocks on earth are 3.9 Byr while the meteorites from space and moon rocks that are part of the early solar system ==> 4.5 Byr 2b) Models of Chemical Creation Rate: Estimated age of Uranium itself (not the rock) from the rate of creation in the centers of explosive stars in the Milky Way galaxy imply an age of Byr.

15 (Consistency of Old Ages cont.) 2c) Models of the ages of the oldest stars: The H-R diagram (luminosity vs color) of globular clusters suggest their stars are Byr. Because the luminosity of stars L Mass 4 means that the Lifetime Fuel/L Mass/Mass 4 1/ Mass 3 ==> more massive, (hotter and bluer ) stars live much shorter lives (Sun lives ~ 10 Byr). Here are the relatively young ages of open clusters in the Milky Way, less than about 7 Byr.

16 Consistency of Old Ages (cont.) Sun was originally estimated to have ages of more than years, before the realization that only a tiny fraction, of the mass of H that fuses into He is turned into energy and that only ~ 10% of the total mass is burned before the stars leave the main sequence. Oldest stars are associated with Globular Clusters: 10 s pc

17 Consistency of Old Ages (cont.) Based on detailed fits to the turn-off point of the main sequence, estimates of the ages of the stars in the oldest globular clusters are currently: Byr Also, based on the cooling of white dwarf (degenerate C-O metal spheres ) stars and redness of the old stars seen in galaxies at high redshifts, we infer ages of over 10 Byr

18 Consistency of the Oldest Ages (cont) 2d) Hubble Age (1/Ho) and various Cosmological Models suggest ages of Byr. With no matter, and thus no deceleration, the age of the U would be 1/Ho. With a Critical Density of matter in a flat Einstein-deSitter U., the deceleration with time gives ages = 2/3Ho. 2q o =density/critical density Critical Density: expansion just stops after infinite time With less matter in an OPEN U, closer to no deceleration. With repulsive force of Dark Energy, U accelerates later in time but age is still less than 1/Ho. 2/3Ho < AGE < 1/Ho so if Ho=70, ages ~ Byr CLOSED U

19 3. Evolution in the Universe Big Bang model predicts that the U has been and continues to be evolving, that is changing with time. Astronomers find much support for this since the 1950 s: 3a) Counts of Distant Radio Sources, Quasars (QSO 1 ), & Galaxies Generally find more of these in the early history of the U than today. 1 Quasi-stellar Objects (optical version of radio) 3b) Amount of Gas Seen via absorption lines in distant QSOs show more gas in the past. 3c) Color, Luminosities, and Shapes of Distant Galaxies in Clusters Galaxies in distant clusters appear to be brighter, bluer, and more distorted than galaxies in clusters today.

20 Counts of Distant Objects Main Point: Universe is evolving, with more or brighter (or Both) sources in the past. Expected counts in a non-evolving Euclidian U (Log N- Log S Relation): if we assume the density of sources (#/volume) - D and luminosity- L, the number within a sphere of radius -R is N = D 4πR 3 /3 with the faintest sources having fluxes (brightnesses) S = L/4 πr 2 I.e. R = L 4!S so the numbers of sources brighter than flux S: N(> S) = D 4! 3 L 3 / 2 (4!) 3 / 2 S 3/ 2 " S #3/ 2 Note: going 100x fainter, expect to see 1000x more sources

21 Counts of Distant Objects (cont) Note: 1) the equation is true for any L, thus any distribution of L 2) OLBER S PARADOX revisited: Total Flux S(total) S(total) > N (>S) x S S -1/2 which approaches INFINITY as S approaches 0, ie. R approaches infinity. The > sign comes from assuming ALL sources are at the faintest flux 3) Non-relativistic (General Relativity) geometries result in smaller numbers, thus the Euclidian assumption provides a solid UPPER LIMIT. Radio sources (from the 1950 s era) and QSOs (from 1970 s) Show steeper counts than Euclidian for Brighter sources.

22 Counts of Distant Objects (cont) Radio sources (from the 1950 s era) and QSOs (from 1970 s) show steeper counts than Euclidean for Brighter sources. Counts/area of sky (N) ==> Radio Sources Quasars-QSOs S (flux) ==> dimmer Euclidean

23 4. Cosmic Microwave Background The CMB is the most persuasive evidence in favor the Big Bang. It is the natural consequence of very hot, dense phase (blackbody) of the early U. The expansion of the U results in the cosmological redshift of all the photons of the Planck radiation to the equivalent of a 3 o K Blackbody seen today. 4a) Blackbody shape (difficult to explain in other theories) 4b) Temperature consistent with the pure theory of Alpher & Gamow(1948) 4c) Radiation is very smooth (1 part in 10 5 ) The CMB was discovered in 1965 by Penzias and Wilson with a horn antenna at Bell Labs.

24 4. Cosmic Background Radiation Blackbody radiation is described by the Planck distribution where u is the energy density per unit volume (ergs/cm 3 ) over an interval of wavelength close to λ: u(!) =! 5 [e 8"hc hc!kt #1] λ = wavelength T = temperature ( 0 K) c = speed of light h = Planck s constant =6.625x10-27 erg/s k= Boltzmann constant = 1.38x10-16 erg/k enclosed box with uniform temperature T tiny hole radiation inside has Planck distribution

25 4. Cosmic Background Radiation NOTES - pg 411 BB: 1) Maximum of distribution is at λ = 0.2 hc/kt 2) Total energy density summed over all λ: " U = u(!)d! = # 0 8$ 5 kt 4 15(hc) 3 = at 4 a=radiation density constant = 7.56x10-15 erg/cm 3 o K 4 Raleigh-Jeans Limit For T=2.7 o K U=4x10-13 ergs/cm 3 ~ 1/4 ev/cm 3 ~ Milky Way starlight 3) for long wavelengths λ, e hc/λkt -1 ~ hc/ λkt so that u(λ)~8πkt/ λ 4 4) Since from redshift λ (1+z) -1 and T λ -1 (1+z), then since U T 4 ==> U (1+z) 4 in RADIATION. U was very hot in the past. Moreover since matter scales by volume and thus (1+z) 3, the energy density in radiation will always dominate over matter at high enough z

26 John Mather, Nobel Prize Physics 2006

27 5. Helium and Deuterium Abundance P P N N P N Helium (He) Deuterium (D) Normal Hydrogen (H) A hot, dense U can easily make such light elements during the expansion phase, but not heavier elements. Stars can make some helium from hydrogen, but destroys Deuterium. Astronomers find that ~25% He and ~0.01% Deuterium almost everywhere. This is hard to explain with star formation but is natural for the Big Bang model. Deuterium abundance is consistent with the amount of ordinary matter (protons and neutrons) actually seen in the Universe. P