Notes for Lecture 14
Lecture 15, April 2; Anatoly Spitkovsky
Those who might be interested in astronomy as a major are invited to an astronomy open house, in which the major will be discussed, starting at 4:30 PM on Monday in Peyton Hall.

If there is ten times more dark matter than ordinary matter in the
Milky Way, why isn't it obvious to us right here in the room?  Two
reasons:
  -The dark matter is dark because it doesn't interact (at least not
  very much) with ordinary matter and photons.  Like neutrinos,
  whatever particle the dark matter might be can pass right through us
  without us noticing.  In fact, people considered that neutrinos
  might make up the dark matter.  This turns out not to work for a
  variety of reasons. 
  -The density of dark matter is very small; given the mass and the
  size of the Milky Way, we can work it out.  It corresponds to a few
  million atoms per cubic meter.  That is appreciably more than the
  *average* density of normal matter in the Milky Way, but we don't
  live in an average place.  The density of stuff here on Earth is
  *much* larger than this, and so locally, the dark matter is a tiny
  fraction of everything around. 

Current ideas on the nature of dark matter include MACHOs (massive
compact halo objects) and WHIMPS (wheakly interacting massive
particles).  MACHOS are made of normal matter (protons, neutrons,
electrons) and may be compact objects, brown dwarfs, etc. However,
their contribution is not thought to be large enough to explain the
dark matter.  Exotic particles (WHIMPS) that are yet to be observed in
the laboratory are thought to provide the best explanation. However, this is
still a very active area of research. 

Our current (very incomplete) understanding of what the dark matter
might be suggests that we should be able to detect it directly, either
by building sufficiently sensitive detectors that can measure the rare
occasional dark matter particle which interacts with the material in
the detector, or by making dark matter particles directly in huge
particle accelerators like the Large Hadron Collider.  There is a
Nobel Prize waiting for the first successful such experiment. 

It was unknown before 1923 whether the "spiral nebulae" were
relatively small objects in the Milky Way, or were structures as
large as the Milky Way itself at much larger distances. In  1923,
Edwin Hubble resolved the outer part of the Andromeda Nebula into
stars.  He used the inverse square law to determine their distances.  

  Hubble found that the Andromeda nebula is indeed very
distant; the modern value is that it lies 2 million light years away,
and is as big as the entire Milky Way. Hubble used the Cepheid Variable
stars in Andromeda to measure the distance: period of pulsarion of 
Cepheids is tightly correlated with their luminosity, and by knowing how
 bright a star with known luminosity appears, we can obtain the distance. 

 The universe is *much* bigger than just the Milky Way; the Milky way
is only one of 10^{11} galaxies in the universe.  Note the dramatic
increase in the size of the known universe: before Hubble's discovery, most
astronomers knew only of the extent of the Milky Way, and what might
lie beyond it was completely unknown.  The MW is "only" 100,000 light
years across, while Andromeda is 2 million light years away, and some
galaxies are literally billions of light years away.  Note the
contrast with stars: the distance between stars (several light years)
is tens of millions times larger than the stars themselves, so stars
essentially never crash into each other.  But the distance between
galaxies is only 20 times their typical sizes, so galaxy collisions
are not uncommon. 

  Galaxies come in a variety of shapes, distributed broadly in three
categories: spirals (like the Milky Way, with a disk and young stars),
ellipticals (no disk, no interstellar medium, and no young stars) and
irregulars (which tend to be smaller and less luminous than the other
two).

  The spectra of galaxies look like those of stars, except that they
are *redshifted*, a seeming Doppler shift that makes them appear to be
moving away from us.

Edwin Hubble measured the distances of galaxies using the inverse
square law for individual stars inside them.  Comparing with their
recession velocities, he found a linear relationship:

    		v = H d

This is called the Hubble Law, and H is the Hubble Constant; units of
km/s/Mpc (Mpc stands for Megaparsec, or 10^6 parsec).

The Hubble Constant sets the scale of the universe.  With the Hubble
law, measurements of the redshifts of galaxies (relatively easy),
tell you their distance, up to the uncertainty in the Hubble
Constant. 

Let's think about the Hubble Law, v=H d.  How can we measure H?  By taking
the ratio of v to d for galaxies.  

The redshifts, or recession velocities are easy to measure, from the
spectra of galaxies.  The distances are the hard part.  There is a lot
of controversy about the accurate measure of distance; it is usually
done using the relationship between measurements of brightness and
luminosity; making sure you know what the intrinsic luminosity of the
stars you are looking at is not easy! Hubble Space
Telescope was used to do the best measurement of the Hubble's constant; 
the accepted value now is about 72 km/s/Mpc.

The Hubble Law tells us the universe is expanding uniformly.  Indeed,
it looks like we're at the center of this expansion, but what counts
here is *relative* motions between galaxies.  From the perspective of
an astronomer on any other galaxy, they will decide that they are the
ones at rest, and all the other galaxies are expanding uniformly with
respect to it.  The expansion has no center!  Indeed, the universe has
no edge either, think of it as infinite in extent, so no center can be
defined.

The expansion of the universe is relevant only on the scale of
galaxies.  Within a galaxy (in general, within structures held
together by gravity), the expansion is *not* taking place. 

  Consider two galaxies separated by a distance r.  They are moving
apart at a speed v, so at a time r/v = r/Hr = 1/H, they were on top of
each other.  This time is the same for any two galaxies; all the
galaxies were on top of each other at a time 1/H ago.  This is the
time corresponding to the Big Bang (an originally derogatory term from
Fred Hoyle in the 1950's).  Plugging in numbers, this time is 14
billion years ago.  

  This was Professor Spitkovsky's last lecture of the course.  Professor
Gott will start next Tuesday, discussing Einstein's ideas, and
fleshing out our understanding of cosmology.
Notes for Lecture 16