Notes for Lecture 12

Lecture 13, March 26, Anatoly Spitkovsky

Homework #4 is due on Thursday, April 2.

We've seen that the life stages, and lifetime of a star depends on its mass.

Stars like the Sun can evolve to the point of having a core of Carbon
and Oxygen.

Stars more massive than 8 Solar Masses can burn Carbon and Oxygen.
The most common reactions involve integral numbers of helium nuclei
(i.e., elements that have even atomic numbers).  The odd elements are
created by absorption of a neutron, followed by various decays that
can get you to these odd elements.

 Energy is released when you fuse elements, until you get to Iron;
 you can't combine Iron with anything to get out energy.   So the
 star will have an onion shape, with Iron in the core.

 When the mass of Iron in the core gets above 1.4 solar masses, it
turns out that electronic degeneracy pressure can't hold the core
up any more.  So the core has no choice but to collapse, and collapse
fast.  Does it collapse forever?  Not necessarily; eventually all the
empty space in the atoms is squeezed out, and the nuclei of all the
atoms are squeezed out. Most of the nuclei in the core are turned 
into pure neutrons (protons combine with electrons to form neutrons + neutrinos); 
this forms a neutron star (i.e., a star made essentially purely of neutrons). 
When you get to that stage, the center bounces, and sends a huge amount of energy 
*outwards* in the star. This then drives a supernova -- the explulsion of the outer
layer, which leave at 10000 km/s. There is so much energy around that all
sorts of nuclear reactions go on, releasing lots of energy. Most of the 
nucleosynthesis beyond iron is done during this explosion in the expanding

 We actually detected the neutrinos from the famous supernova 1987A.
 We also saw emission lines (which turn out to be gamma rays) due to
 radioactive cobalt, which formed in the supernova explosion.

 In supernova remnants, we see spectroscopic evidence of large
 quantities of heavy elements, created in the supernova itself.

 Left behind after stars live their lives are very compact objects:
    -White dwarfs
    -Neutron stars
    -Black holes

These extreme objects test our understanding of the relevant physics.

*******White dwarfs
 Chandrasekhar was the first to apply the ideas of quantum mechanics
 to stellar structure, and in particular, he thought about the nature
 of degeneracy pressure.  The denser a star becomes, the faster the
 electrons move.  Eventually, the electrons are moving close to the
 speed of light; they can't go any faster than that.  So there is a
 *limit* to how strong the degeneracy pressure can go.  A white dwarf 
star is in  balance between gravity and degeneracy pressure, but if 
the mass is too large (greater than 1.4 solar masses, called the Chandrasekhar
 limit), the degeneracy pressure is not adequate to hold up the
 star, and the star collapses.

 Some white dwarf stars are in binaries, and their gravity will pull
 material from their companion onto them.  Because it has some
 angular momentum, the material will first form a disk orbiting
 around the white dwarf, and then by friction will spiral onto the
 white dwarf.

  This material is mostly hydrogen; as it falls onto a white dwarf,
it can get so hot and dense that it can suddenly set off thermonuclear
reactions in an explosion on the surface.  This is called a nova.

 Despite these explosions, the white dwarf will increase in mass,
eventually may reach the Chandrasekhar mass.  The white dwarf then
collapses.  The interior of the star heats up tremendously, the Carbon
starts to burn, and the whole star explodes to smithereens.  This is a
different kind of supernova than the one we saw before.  It is
tremendously luminous, something like 10^10 solar luminosities!

 You can tell the two types of supernova apart from the shape of
 their light curve (i.e., a plot of their brightness as a function of

*********Neutron stars
 In a massive star that collapses and explodes as a supernova, a
 neutron star is often left behind.  Roughly 1.4 solar masses within
 a radius of 10 kilometers!  Extremely dense, held up by *neutron*
 degeneracy pressure (just like electron degeneracy pressure, but now
 using neutrons).

 The densities are *far* larger than anything we can create in the

 The acceleration due to gravity on the surface of a neutron star is
 ~10^{12} m/s^2 (compare with the Earth, where it is 10 m/s^2).

 These stars tend to be rotating very fast; they can spin around in
 much less than a second.  They can have a magnetic field of 10^8
 Tesla, about a trillion times stronger than that on Earth.

 Neutron stars were first predicted by Fritz Zwicky in the 1930's.
 But they were first discovered observationally by Jocelyn Bell (her
 thesis advisor got the Nobel Prize, but not her!).  She
 discovered an object that was emitting radio waves every 1.337301
 second.  Extremely regular!  This turned out to be a pulsar, a
 rotating neutron star.   Given the fact that they are spinning so
 fast, they *have* to be small: anything larger will tear itself
 apart (remember Homework 3).

 So where do these pulses come from?  The strong magnetic field
rotates around and emits radio waves in only certain direction (along
the magnetic poles of the star).  As the star spins around, this beam
of radiation passes the earth (think of a lighthouse), giving you a
flash every time the star spins around.

 About 2000 pulsars have been discovered to date.

*******Black holes

 If the original star has a mass > 20 solar masses, the iron core
 will be > 3 solar masses, then even neutron degeneracy pressure
 can't hold up against the gravity of the core, and the core will
 collapse even further, to make a black hole.  The gravity is so
 strong that even light cannot escape.  So you can't see a black
 hole.  So how can they be discovered?
   You find a star in orbit around an invisible object, and you use
   Kepler's law to infer its mass.  If that mass is greater than 3-5
   solar masses, the object can't be a neutron star: it must be a
   black hole.  About 20 such are known now.

   Some of these objects are found because they emit X-rays: just as
   in the novae above, material from the companion star accretes onto
   the black hole, and forms an accretion disk.  It is moving
   extremely fast, close to the speed of light, when it is close to
   the black hole.  So it has *tremendous* kinetic energy, and gets
   enormously hot, 10^8 K.  Wien's law tells us that the blackbody
   that this emits peaks at very small wavelengths, X-rays!

   X-rays are absorbed by the Earth's atmosphere, and so you can only
   look for these X-rays with satellites in space.

******Gamma-ray bursts
 Another example of a serendipitous discovery, found by satellites
 checking whether the Russians were setting off atmospheric nuclear

 Noone knew what the nature of objects was, which suddenly give off a
 tremendous burst of gamma rays.  In particular, are they in our own
 Milky Way or much further away?   Turns out that they are *very*
 distant, associated with other galaxies.  We think (but are not
 sure) that these are due to massive stars collapsing and forming a
 black hole. We infer this because some of the gamma ray bursts seem to come 
 from regions in other galaxies which are full of star formation and massive
 stars. As the black hole forms inside of these rare supernovae (not every
supernova generates gamma ray bursts), the accretion disk in the middle of the 
star sends out a pair of jets, which pierce through the star, and this is 
when we observe a pulse of gamma rays. These bursts are highly collimated, so 
they have to be pointing at the Earth in order for us to see them. 
Alternative theory for gamma ray bursts involves a merging pair of neutron stars. 


Notes for Lecture 14

© Copyright 2009 Anatoly Spitkovsky and Michael A. Strauss