1	Astr 1050 Fri., Nov. 22, 2002 Today: Astronomy Articles Review Homework #10 Finish Chapter 15, Cosmology A great webpage tutorial on cosmology. Recommended! http://www.astro.ucla.edu/~wright/cosmolog.htm
2	Homework #10 Q 1: If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.) D = 10^(m-M+5)/5, so 160 Mpc Q 2: If a galaxy has a radial velocity (redshift) of 5000 km/s, how far away is it? Assume a Hubble Constant of 70 km/s/Mpc. V = HxD, so D=v/H, or 5000/70 Mpc = 71 Mpc Q 3: A quasar is observed to have a redshift z=0.5. What recessional velocity does this correspond to? v/c = ((z+1)²-1)/((z+1)² +1) = 1.25/3.25 = 38% Q 4: If we take a spectrum of a quasar and see that the Lyman alpha line, observed in the laboratory at a wavelength of 121.6 nm, appears at a wavelength of 425.6 nm, what is the redshift of this quasar? Z = Δλ/λ = (425.6 -121.6)/121.6 = (425.6/121.6) – 1 = 3.5 – 1 = 2.5 Q 5: Quasars can be 1000 times more luminous than an entire galaxy. The absolute magnitude of such a luminous quasar would be about M = -28.5. If the black hole in the center of our galaxy became a quasar, and obscuring gas and dust did not dim it, what would the apparent magnitude of the galactic core be? Think about the answer and what that would look like in the sky. m – M = -5 +5logd, so m = -5 +5log8.5k + M = -13.9 (about like the full moon!) Q 6: If Galaxy A is four times more distant than Galaxy B, then according to the Hubble Law, the recessional velocity of Galaxy A is larger than that of Galaxy B by what factor? V = HxD which is a linear relationship, so V is 4 times larger.
3	First prediction from Big Bang model: Cosmic Background Radiation Look out (and back in time) to place where H became neutral Beyond that the high density ionized H forms an opaque “wall” Originally 3000 K blackbody radiation The material that emitted it was moving away from us at extreme speed That v produces extreme redshift (z=1000), so photons all appear much redder, so T appears cooler With red shift, get 2.7 K Planck blackbody Should be same in all directions
4	Cosmic Microwave Background Observations First detected by Wilson and Penzias in 1960’s Serendipitous detection – thought is was noise in their radio telescope but couldn’t find cause. Only later heard of theoretical predictions Best spectrum observed by COBE satellite Red curve is theoretical prediction 43 Observed data points plotted there error bars so small they are covered by curve. it is covered by curve. Isotropy also measured by COBE T varies by less than 0.01 K across sky Small “dipole” anisotropy seen Blue = 2.721 Red = 2.729 Caused by motion of Milky Way falling towards the Virgo supercluster.
5	Second prediction from Big Bang Model: Abundance of the light elements Big Bang Nucleosynthesis T, r both high enough at start to fuse protons into heavier elements T, r both dropping quickly so only have time enough to fuse a certain amount. Simple models of expansion predict 25% abundance He 25% is the amount of He observed Abundance of ²H, ³He, ⁷Li depends on r_{normal matter} Suggests r_{normal matter} is only 5% of r_critical But we need to also consider “dark matter” and its gravity
6	Main Tests of the Big Bang Hubble Expansion (not a test really, inspiration) Cosmic Microwave Background Abundance of light elements Refinements of Big Bang Still Being Tested Possible “cosmological constant” Very early history: particle/antiparticle asymmetry “inflation” -- Details of very early very rapid expansion small r, T fluctuations which lead to galaxies
7	Will the expansion stop? Is there enough gravity (enough mass) to stop expansion? Consider an simple model as first step (full model gives same answer) Treat universe as having center Assume only Newtonian Gravity applies Does a given shell of matter have escape velocity? Is v > v_esc ?
8	General Relativistic Description What we call “gravity” is really bending of our 3-d space in some higher dimension. Bending, or “curvature of space” is caused by presence of mass. More mass implies more bending. If bending is enough, space closes back on itself, just like 2-d surface of earth is bent enough in 3rd dimension to close back on itself.
9	Mass and the Curvature of Space First consider case with little mass (little curvature) Ant (in 2-d world) can move in straight line from point A to point B. Add mass to create curvature in extra dimension invisible to the ant. In trying to go from point A to point B, fastest path is curved one which avoids the deepest part of the well. Ant will be delayed by the extra motion in the hidden third dimension. Both effects verified in sending photons past the sun: Bending of starlight during solar eclipse Delay in signals from spacecraft on opposite side of the sun
10	How to test the amount of curvature Measure the circumference of a circle as you get farther and farther from the origin: Does it go up as expected from (2 p R)? It goes up slower in a positively curved world.
11	How high is the density? Not nearly enough normal matter to provide critical density We keep seeing effects of gravity from “dark matter” Higher rotation speeds in our own galaxy Higher relative velocities of galaxies in clusters Rate at which matter clumps together to form galaxy clusters Gravitational lensing from galaxies, clusters May be 10 to 100 times as much “dark matter” as visible matter What might make up the “dark matter”? Possibilities include MACHOs (massive compact halo objects) http://www.astro.ucla.edu/~wright/microlensing.html but ²H, Li, Be abundance suggest no more than 5% can be “baryonic” WIMPs (weakly interacting massive particles) predicted by some GUT’s Mass of neutrinos Mass equivalent of “cosmological constant” energy
12	Refining the Big Bang Flatness Problem – why so close to a critical universe? Horizon Problem – why is background all same T? SOLVED BY AN “INFLATIONARY UNIVERSE” “Grand Unified Theories” of combined Gravity/Weak/Electric/Nuclear forces predict very rapid expansion at very early time: “inflation” When inflation ends, all matter moving away with v=v_escape (flat universe – curvature forced to zero) Also solves horizon problem – everything was in causal contact
13	Implications of Slowing Expansion Rate Our calculation of age T=1/H_o = 13.6 billion years assumed constant rate Gravity should slow the expansion rate over time If density is high enough, expansion should turn around If expansion was faster in past, it took less time to get to present size For “Flat” universe T = 2/3 * (1/H_o) = 9.3 billion years contradiction with other ages if T is too small
14	Is the expansion rate slowing? Look “into the past” to see if expansion rate was faster in early history. To “look into the past” look very far away: Find “H_o” for very distant objects, compare that to “H_o” for closer objects Remember – we found H_o by plotting velocity (v_r) vs. distance We found velocity v_r from the red shift (z) We found distance by measuring apparent magnitude (m_v) of known brightness objects We can test for changing H_o by measuring m_v vs. z
15	Measuring deceleration using supernovae Plot of m_v vs. z is really a plot of distance vs. velocity If faint (Þdistant Þearlier) objects show slightly higher z than expected from extrapolation based on nearby (present day) objects, then expansion rate was faster in the past and has been decelerating Surprise results from 1998 indeed do suggest accelerating expansion May be due to “cosmological constant” proposed by Einstein AKA “Dark energy” or “Quintessence”
16	“Cosmological constant” General Relativity allows a repulsive term Einstein proposed it to allow “steady state” universe He decided it wasn’t needed after Hubble Law discovered Is the acceleration right? Could it be observational effect – dust dims distant supernova? Could it be evolution effect – supernova were fainter in the past? So far the results seem to stand up Still being determined: 1) density, 2) cosmological constant With cosmological constant included, can have a “flat universe” even with acceleration. Given “repulsion” need to use relativistic “geometrical” definition of flatness, not the escape argument one given earlier. Energy (and equivalent mass) from cosmological constant may provide density needed to produce flat universe.
17	Tests using the Origin of Structure Original “clumpiness” is a “blown up” version of the small fluctuations in density present early in the big bang and seen in the background radiation. We can compare the structure implied to that expected from the “Grand Unification Theories” Rate at which clumpiness grows depends on density of universe Amount of clumpiness seems consistent with “flat universe” density That means you need dark matter to make clumpiness grow fast enough
18	Acoustic Peaks in Background
19	Chapter 13: Galaxies Family of Galaxies Classification Properties of Galaxies Distance; The Hubble Law Size and Luminosity Mass (including Dark Matter) Evolution of Galaxies Clusters Mergers
20	Chapter 11: Neutron Stars & Black Holes Neutron Stars Pulsars (Radio pulsation, lighthouse model) Properties (size, density, composition) Black holes Schwarzschild Radius Properties Detection (Gravity, X-rays from Disks)
21	Review Chapter 12: Milky Way The discovery of the Galaxy Variable stars as distance indicators Globular clusters The size and overall structure of the Galaxy 21 cm Hydrogen emission Motions in the galaxy The Halo The Disk population Spiral Arms The Nuclear Bulge The Rotation curve and the Galaxy’s mass The origin of the galaxy The Galactic Center
22	Chapter 13: Galaxies Family of Galaxies Classification Properties of Galaxies Distance; The Hubble Law Size and Luminosity Mass (including Dark Matter) Evolution of Galaxies Clusters Mergers
23	Chapter 14: Galaxies with Active Nuclei Discovery of Active Galactic Nuclei (AGN) Seyfert Galaxies and Radio Sources The Unified Model Black Holes in Galaxies, disks, orientation, + Quasars Distances and Relativistic Redshifts Quasars as extreme AGN Evolution of Quasars/Galaxies Gravitational Lensing
24	Chapter 15: Cosmology The Hubble Expansion – review+ Olber’s paradox The Big Bang Refining the Big Bang Details of the Big Bang General Relativity Cosmological Constant Origin of Structure
25	Exam #3 on Mon., Nov. 25 20 multiple choice (3 pts each), 10 true/false (2 pts each), 2 essay (10 pts each). A larger fraction of fact-based questions. Two Essay questions drawn from these topics: Falling into a Black Hole The Milky Way galaxy The Hubble Law The Cosmic Microwave Background Radiation The Unified Model of Active Galaxies The Age of the Universe
26	Exam #3 on Mon., Nov. 25 Sample questions. True/False: The radio lobes of radio galaxies arise from 21 cm radiation. The Milky Way galaxy is only a small member of the Local Group. Neutron stars can be found in supernova remnants. The Magellanic Clouds are irregular galaxies. The Cosmic Microwave Background Radiation is blackbody radiation. The more luminous a Cepheid variable star, the shorter its period. Elliptical galaxies evolve into spiral galaxies.
27	Exam #3 on Mon., Nov. 25 Sample questions. Multiple choice: Which sequence below gives objects in order of decreasing size? A. Red Giant -> the Sun -> the moon -> white dwarf B. The Sun -> the Earth -> neutron star -> 3 solar mass black hole C. Red Dwarf -> white dwarf -> the Sun -> neutron star D. Red Giant -> white dwarf -> red dwarf -> neutron star The assumption of Isotropy states that A. The universe looks the same at all epochs. B. The universe looks the same from all locations over large enough distances. C. The universe looks the same in all locations over large enough distances. D. All of the above. E. None of the above.
28	Exam #3 on Mon., Nov. 25 Sample questions. Multiple choice: In order to determine the age of the universe, we require A. The universe to be flat. B. The amount of dark matter to be determined. C. The redshifts of galaxies in the Local Group to be measured. D. An accuration temperature of the background radiation. E. The Hubble Constant and the density of the universe to be determined. The center of our galaxy lies in the direction of the constellation of A. Ursa Minor. B. Ursa Major. C. Sagittarius. D. Orion. E. Andromeda.