Notes for Lecture 13
Lecture 14, March 31, Anatoly Spitkovsky
Homework #4 is due on Thursday, April 2. The problem session for this will happen in McDonnell A02 on Wednesday, April 1.
 No stars appear to form with mass more than about 150 solar masses.
 More massive stars would be so luminous, that the pressure from all
 that light coming out would overwhelm the gravity, and blow the star
 apart.

 One model for Gamma-ray bursts is a pair of merging neutron stars.
 Another scenario has a neutron star orbiting a black hole; it gets
 torn to pieces by the tidal forces from the black hole.
 Another model is the formation of black hole inside a massive
 star as it explodes in a supernova. The accretion onto black hole
 leade to jets along the axis of rotation. Gamma ray bursts come in different
 flavors, and all models may have some applicability. This is still an 
 active area of research.

 We finished the discussion of stellar evolution, and now move on to galaxies,
 beginning with our own Milky Way. 

The Milky Way galaxy has several components.  It consists of a very
thin disk, almost circular, but with a thickness (1000 light years)
1/100 that of its diameter (100,000 light years).  The Sun lies in 
the disk, about 28,000 light years from the center.  There
is also a central bulge of stars near galactic center.   The disk 
of the galaxy is the place where stars are most actively forming.   
 We are inside this structure, seeing it
edge-on; it appears as a band of light across the sky.   The "holes"
or gaps apparent in the Milky Way are due to the obscuration of dust
in the Interstellar Medium. 

 The Milky Way also has a halo: a thin sprinkling of stars which
surround it in a roughly spherical distribution.  The halo includes
globular clusters, which are spherical groupings of up to a million
stars.  Over 100 globular clusters are known, and they are distributed
more-or-less symmetrically around the center of the Milky Way.  The
stars in most globular clusters are quite old, up to 13 billion
years.


 The disk has a spiral structure if seen from above.  Sorting this
 out has not been easy, as we're inside this spiral structure, and
 the dust obscures our view.

 In addition to the stars, we see clouds of gas and dust, called
 "nebulae", which come in different types:

   -Emission nebulae, or ionization nebulae: gas that is ionized by
   ultraviolet light from hot stars.  They tend to be quite colorful,
   due to emission lines from various elements (especially red, which
   is largely due to hydrogen, and green, due to oxygen).  A famous
   example is the Orion Nebula.   They indicate regions in which
   stars have recently formed,  as it requires young, hot stars to
   ionize gas.

   -Reflection nebulae: gas and dust around lower-mass stars: the light isn't
   energetic enough to ionize the gas, but the dust does reflect the
   light.  The dust is more effective at reflecting blue light, so
   the nebula looks blue (i.e., the same reason that the sky is
   blue).   An example is the Pleiades star cluster, which has
   a reflection nebula around it.

   -A dark nebula, a region in which the dust is so thick that it
   simply appears dark on the sky.  A famous example is the "pillars
   of creation" inside the Eagle Nebula, M16.

 The interstellar medium is the raw material out of which new stars
form.  Gravity brings together enormous (many light years across)
clouds of the interstellar medium.  Dense regions of the ISM, where
stars might form, and where there will be a lot of dust, are apparent
as dark clouds which block the light of stars behind them.  It turns
out that dust is largely transparent to light of longer wavelengths,
and so observations in the infrared reveal new-born stars inside these
clouds.

 Most of this star formation happens in the spiral arms of the disk.
 A spiral arm is a propagating density wave passing through the disk
 of the galaxy. 

 As stars give off planetary nebulae or explode as supernovae, they
 give their material (now enriched in heavy elements) back to the
 interstellar medium, and the material can then be incorporated into
 the next generation of stars.   This is indeed where all the heavy
 elements on Earth come from: they were all created in the interiors
 of stars.

 Mapping the structure of the galaxy requires measuring distances to
 its stars.  The first approach: look at the distribution of stars
 along the Milky Way; we see roughly similar number of stars in every
 direction.  So are we in the center?  No, because we're not taking
 into account the obscuring effects of dust.  When you correct for
 that, you see the Milky Way is quite lop-sided, as you would expect
 if we're actually far from the center.

 In the 1920's, Harlow Shapley mapped out the distribution of
 globular clusters, and saw that they were centered not on us, but on
 a point about 28,000 light years away (modern value); the
 interpretation is that the globular clusters are centered around the
 center of the Milky Way.

 So how do we measure all these distances?  Within our own solar
 system, we use radar (bouncing radio waves off Venus in particular)
 and measure the round-trip travel time to determine distances; this
 is how we know that 1 AU is 150,000,000 km.  We can use parallax to
 measure distances to stars within perhaps 1000 light years.  To
 measure stars further away, we use the inverse square law:

  b = L/(4 pi d^2)
If we know the luminosities of stars (from their color or spectrum, we
get their temperature; assuming they are main sequence stars, the HR
diagram gives us their luminosity), and we measure their brightness,
we can infer their distance.  A star or other object whose luminosity
you know or can infer, is called a "standard candle".  Indeed, if
you're looking at a *cluster* of stars, you can use the whole HR
diagram of all the stars in it to measure the distance to the cluster.

 The Milky Way disk rotates.  The Sun goes around the center of the
Galaxy once every 250 million years; this corresponds roughly to a
speed of 220 km/s.  Yes, we are all moving that fast, right now!
This means that in the age of the Sun (4.5 billion years) it has 
traveled 18 times about the galactic center -- the Sun is 18 
"galactic years" old!

 Stars in the bulge are also in orbits around the center of the Milky
 Way, but they are not all moving in the same plane, like the stars of
 the disk.

 We can use Newton's law of gravity to calculate the mass of the Galaxy.
From the speed and radius of the Sun's orbit around the Galaxy; we get
a value of 100 billion solar masses.  This refers to the mass of the
material within the Sun's orbit, and does not include any material
outside that orbit.

Kepler's law tells us that the mass enclosed by a circular orbit of
radius r on which a body with velovity v moves is: M=r v^2/G, where G is
the Newton's constant. We can infer the rotation velocity in the Galaxy
from measuring Doppler shifts of stars and gas in different directions. 

 It is interesting to measure the rotation speed of the Milky Way
at different points as a function of distance from the center of the
Galaxy.  We would naively expect that far from the center, the
gravity, and therefore the speed, should fall off with distance, as
Kepler's law implies.  In fact, we find that the speed remains nearly
constant, as far as we can measure it.  Our interpretation: the mass
of the Galaxy within a distance R is proportional to R, even out where
there are essentially no more stars.  The mass of the Galaxy is
dominated by what we call dark matter.  There is no hint yet of a real
edge to the Milky Way; its total mass is at least 10^12 solar masses,
of which probably only 10% or less is made of stars. 
The Galaxy is sitting in a large "halo" of dark matter which provides 
the graviatational potential to hold the Galaxy together.
Notes for Lecture 15