Astro 1050     Fri. Mar. 5, 2004
   Today: More Ch. 10: The Deaths of Stars
Homework #5
Extra Credit articles

Homework 5 solutions
Q1. 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 = mass/volume
Mass is the same, volume of sphere = 4/3 π R3
Radius increases by 20, R3 and the volume increases by 203 = 8000, so density decreases by 8000
Q2. In an H-R Diagram, stars with the largest radius are found in the upper right of the diagram. (Fill in the blank.)
Q3. The lifetime of high temperature main sequence O and B stars is much shorter than the lifetime of low temperature K and M stars. (Fill in the blank.)

Homework 5 solutions
Q4.  Spectroscopic parallax.  (Apparent) magnitude = 5.4 for an O6 V star.  How far away is it?  First need to get an absolute magnitude.  Can estimate it several ways (H-R diagrams, mass-luminosity relation).  I used M = -5.6.  So:
d (pc) = 10 (m-M+5)/5 = 103.2 = 1585 parsecs
Q5. 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 (pc) = 10 (m-M+5)/5 = 108.2 = 1.6x108 pc x 1Mpc/106pc = 160 Mpc
Q6.  The “Blade Runner Question.”  A star that burns half the lifetime of the sun does not burn twice as bright.  How bright (luminous) is it?
  Lifetime in solar units = M-2.5 (solar m)
0.5 = M-2.5
M2.5 = 2
M  =  (2)1/2.5 = 20.4= 1.3 solar masses
L in solar units = M3.5 (solar units)
Luminosity = (1.3)3.5 = 2.6 solar

Homework 5 solutions
Q7. Sunsets appear red for the same reason that some stars in space appear red -- they are both seen through dust particles. Why does this make them appear red?  b. The dust scatters blue light more than red light, such that more of the red light passes directly though the dust.
Q8. What do we see in the Orion nebula that indicates it is a region of new star formation?
a. Hot O stars   b. Herbig-Haro Objects   c. Dust Disks around stars   d. All of the Above   e. None of the Above
Q9. The Pleadies is an open star cluster not too far from us. It also represents a textbook example of a type of nebula. Which type is it?  C. A reflection nebula

Complications in Stellar Evolution
Pressure forces other than thermal gas pressure
Reminder:  We’ve been assuming that when star loses energy it contracts and actually heats up.  Clearly not all objects do this (e.g.  Earth)
Convection bringing in fuel from outer regions
Mass loss from stellar wind, or mass gain from nearby star

Pauli Exclusion Principle
From quantum rules, electrons don’t like to be packed into a small space, either in atoms or in ionized gas
At normal ionized gas densities, electrons are so spread out quantum rules don’t matter.
As high enough ionized gas densities, quantum rules need to be considered, just has they have been in atoms
Think of each “atom sized” region of space having a set of energy levels associated with it  (although it is really more complicated)

Effect of Degenerate Electron Pressure
Loss of energy does not reduce pressure
Star does not contract in response to loss of energy
Gravity not available as energy source to heat up star
Electrons are already in lowest energy states allowed
(equivalent to atoms in ground state) so no energy available there
If there is no other energy source, as energy is lost nuclei move slower and temperature drops.

Degenerate Pressure Can End Fusion
Degenerate Electron Pressure limits contraction and core temperature
“Stars” with M < 0.08 MSun never burn H    (brown dwarfs)
Stars    with M < 0.4   MSun never burn He   (red dwarfs)
Stars    with M < 4      MSun never burn C     (but do make red giants)
Stars    with M > 4      MSun do burn elements all the way to Fe
What happens to these objects?
Brown dwarfs never become bright – sort of giant version of Jupiter
Red dwarfs have such long lives none have yet exhausted H
Red giants are related to white dwarfs
Massive stars explode as supernova

Effects of Convection
Energy can be moved by radiation or convection
Convection in core brings in new fuel
Cooler material more opaque
 making radiation harder and convection more likely
Choice also depends on energy flux

Mass Loss from Giant Stars
Envelope of red giant very loosely held
Star is so big, gravity very weak at the surface
Degenerate core makes nuclear “thermostat” sluggish
Core doesn’t quickly expand and cool when fusion is to fast
Energy can be generated in “thermal pulses”
Low temperature opaque envelope can also “oscillate”
Energy is transmitted in “pulses” as envelope expands and contracts
Main cause of “Variable Stars”

White Dwarfs

Simple Planetary Nebula
IC 3568   from the Hubble Space Telescope

Complicated P-N in a Binary System
M2-9 (from the Hubble Space Telescope)

A Gallery of P-N from Hubble

Complications in Binary Systems
Can move mass between stars
1st (massive) star becomes red giant
Its envelope transferred to other star
Hot (white dwarf) core exposed
2nd star becomes red giant
Its envelope transferred to white dwarf
Accretion disk around white dwarf
Angular momentum doesn’t let material fall directly to white dwarf surface
Recurrent nova explosions
White dwarf hot enough for fusion, but no Hydrogen fuel
New fuel comes in from companion
Occasionally ignites explosively,
 blowing away remaining fuel

Is a star stable against catastrophic collapse?
Imagine compressing a star slightly (without removing energy)
Pressure goes up (trying to make star expand)
Gravity also goes up (trying to make star collapse)
Does pressure go up faster than gravity?
If Yes:  star is stable – it bounces back to original size
If No:   star is unstable – gravity makes it collapses
Ordinary gas: P does go up fast –  stable
Non-relativistic degenerate gas:   P does go up fast –  stable
Relativistic degenerate gas: P does not go up fast –  unstable
Relativistic:   Mean are the electrons moving at close to the speed of light
Non-relativistic degenerate gas:   increasing r means not only more electrons, but faster electrons, which raises pressure a lot.
Relativistic degenerate gas:   increasing r can’t increase electron velocity (they are already going close to speed of light) so pressure doesn’t go up as much

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
Supernova

Supernova
When the degenerate core of a star exceeds 1.4 MSun it collapses
Type II:  Massive star runs out of fuel after converting core to Fe
Type  I:  White dwarf in binary, which receives mass from its companion (collapse ignites carbon burning).
Events:
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)
pulsars
Accelerates nearby charged particles

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