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

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.

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

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.

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 rnormal matter
Suggests rnormal matter is only 5% of rcritical
But we need to also consider “dark matter” and its gravity

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

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 > vesc ?

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.

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

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.

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

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=vescape  (flat universe – curvature forced to zero)
Also solves horizon problem – everything was in causal contact

Implications of Slowing Expansion Rate
Our calculation of age T=1/Ho = 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/Ho) = 9.3 billion years
contradiction with other ages if T is too small

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 “Ho” for very distant objects, compare that to “Ho” for closer objects
Remember – we found Ho by plotting velocity (vr) vs. distance
We found velocity vr from the red shift (z)
We found distance by measuring apparent magnitude (mv)
of known brightness objects
We can test for changing Ho by measuring mv vs. z

Measuring deceleration using supernovae
Plot of mv  vs. z   is really a plot of distance vs. velocity
If faint (Ţdistant Ţearlier) 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”

“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.

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

Acoustic Peaks in Background

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

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)

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

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

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

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

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

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.

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.

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.