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