Astro 1050     Fri. Oct. 25, 2002
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      Homework #7 review
      Chapter 10: The Deaths of Stars
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Homework #7
Q1. We see the Crab Nebula is about 1.35 parsecs in radius and is expanding at a rate of 1400 km/s. Extrapolate backwards in time and estimate about when would the supernova creating the Crab Nebula have exploded?
Distance/rate/time problem so…
1.35 pc = 1400 km/s x time
Convert pc to km: 1pc = 3.09 x 1013 km
Time = (4.2x1013km)/(1400 km/s) = 3 x 1010 s
Convert to years: 31.5 million seconds in a year
Time = 950 years (if you don’t round get 920)

Homework #7
Q2. If the stars turning off the main sequence in the H-R diagram of a star cluster have masses of about 15 times solar, how old is the cluster?
The cluster will be about as old as the main sequence lifetime.  Can use lifetime (as fraction of solar lifetime) = 1/M2.5 and get 1/1000 of the solar lifetime or look up in the table in the slides.  15 solar masses is about a B star which have lifetimes of around 10 million years.

Homework #7
Q3. The Ring Nebula has an angular diameter of 72 arcsec, and we estimate it is 5000 light years away. What is its linear diameter?
Linear diameter = 5000 ly x 72/206265
Linear diameter = 1.7 light years
An aside.  Exansion rate is 15 km/s, so the age is approximately 34,000 years old.

Homework #7
Q4. If a type G star like the sun expands to become a giant star with a radius 20 times larger, by what factor will its density decrease?
Density is mass/volume.
Volume of a sphere is 4/3πr3.
If r increase by a factor of 20, volume increases by a factor of 20 cubed, or 8000.  Mass remains the same, so density decreases by 8000 times.

Chandrasekhar Limit for White Dwarfs
Add mass to an existing white dwarf
Pressure (P) must increase to balance stronger gravity
For degenerate matter, P depends only on density (r), not temperature, so must have higher density
P vs. r rule such that higher mass star must actually have smaller radius to provide enough P
As Mstar ® 1.4 MSun      velectron ® c
Requires much higher r to provide high enough P, so star must be much smaller.
Strong gravity which goes with higher r makes this a losing game.
For M ³ 1.4 MSun no increase in r can provide enough increase in P – star collapses

Implications for Stars
Stars less massive than 1.4 MSun can end as white dwarfs
Stars more massive than 1.4 MSun can end as white dwarfs, if they lose enough of their mass (during PN stage) that they end up with less than 1.4 MSun
Stars whose degenerate cores grow more massive than 1.4 MSun will undergo a catastrophic core collapse:
Neutron stars

When the degenerate core of a star exceeds 1.4 MSun it collapses
Type II: Massive star where it runs out of fuel after converting core to Fe
Type  I: White dwarf in binary, which receives mass from its companion.
Star’s core begins to collapse
Huge amounts of gravitational energy liberated
Extreme densities allows weak force to convert matter to neutrons
p+ + e-
®  n + n
Neutrinos (n) escape, carrying away much of energy, aiding collapse
Collapsing outer part is heated, “bounces” off core, is ejected into space
Light from very hot ejected matter makes supernova very bright
Ejected matter contains heavy elements from fusion and neutron capture
Core collapses into either:
Neutron stars or Black Holes (Chapter 11)

Supernova in Another Galaxy
Supernova 1994D in NGC 4526

Tycho’s Supernova of 1572
Now seen by the Chandra X-ray Observatory as an expanding cloud.

The Crab Nebula – Supernova from 1050 AD
Can see expansion between 1973 and 2001
Kitt Peak National Observatory Images

What happens to the collapsing core?
Neutron star (more in next chapter)
Quantum rules also resist neutron packing
Densities much higher than white dwarfs allowed
R ~ 5 km      r ~ 1014 gm/cm3   (similar to nucleus)
M limit uncertain,  ~2 or ~3 MSun before it collapses
Spins very fast (by conservation of angular momentum)
Trapped spinning magnetic field makes it:
Act like a “lighthouse” beaming out E-M radiation (radio, light)
Accelerates nearby charged particles

Spinning pulsar powers the
 Crab nebula
Red:  Ha
Blue:  “Synchrotron” emission from high speed electrons trapped in magnetic field

Review Chapters 7-10
Chapter 7: The Sun
Atmospheric Structure
Temperature, density, etc., with radius
Sunspots/Magnetic Phenomena
What are they?  Why do they exist?
Nuclear Fusion – proton-proton chain
What is it?  How does it produce energy?
Solar Neutrino “Problem”
What is it?  Is it still a problem?

Review Chapters 7-10
Chapter 7: The Sun – example questions
Q. The fusion process in the sun, the "proton-proton" chain, requires high temperatures because:
c of the ground-state energy of the Hydrogen atom.
c of the presence of Helium atoms.
c the colliding protons need high energy to overcome the Coulomb barrier.
c of the need for low density.
c the neutrinos carry more energy away than the reaction produces.

Review Chapters 7-10
Chapter 8: The Properties of Stars
Distances to Stars
Parallax and Parsecs
Spectroscopic Parallax
Intrinsic Brightness: Luminosity
Absolute Magnitude
Luminosity, Radius, and Temperature
Hertzsprung-Russell (H-R) Diagram
Luminosity Classes (e.g., Main Sequence, giant)
Masses of Stars
Binary Stars and Kepler’s Law
Mass-Luminosity Relationship

Review Chapters 7-10
Chapter 8: Properties of Stars--examples
True/False: The main determinant of the lifetimes of stars is their mass.
Q. A star’s luminosity depends only on the star’s:
c distance and diameter.
c temperature and distance.
c distance.
c temperature and diameter.
c apparent magnitude
Another version of the question\ can be made for apparent magnitude .
Short answer:  What are two methods for determining the distance to a star?
Another version of the question can be made for masses.

Review Chapters 7-10
Ch. 9: The Formation & Structure of Stars
Interstellar Medium
Types of Nebulae (emission, reflection, dark)
Interstellar Reddening from dust
Star formation
Protostar Evolution on H-R Diagram
Fusion (CNO cycle, etc.)
Pressure-Temperature “Thermostat”
Stellar Structure (hydrostatic equilibrium, etc.)
Convection, radiation, and opacity
Stellar Lifetimes

Review Chapters 7-10
Ch. 9: The Formation & Structure of Stars
Example questions
True/false: The sun makes most of its energy via the CNO cycle.
Short answer question: Explain what keeps the nuclear reactions in a star under control.

Review Chapters 7-10
Ch. 10: The Deaths of Stars
Evolution off the main sequence (=> giant)
Star Cluster Evolution on H-R Diagram
Degenerate Matter
Planetary Nebulae and White Dwarfs
Binary Star Evolution (Disks, Novae, etc.)
Massive Star Evolution and Supernovae

Review Chapters 7-10
Ch. 10: The Deaths of Stars—examples
Short answer: Describe the ultimate fate of stars as a function of their initial mass.
Q. Massive stars cannot generate energy through iron fusion because:
c iron fusion requires very high densities.
c stars contain very little iron.
c no star can get high enough for iron fusion.
c iron is the most tightly bound of all nuclei.
c massive stars go supernova before they create an iron core.