Astronomy 120 "Galaxies and the Universe"                Spring 2011
Homework Assignment #9  LAST ONE!!       DUE: Wednesday Apr 20, 2011


HOMEWORK PROBLEMS:

1. (51 points)
You have discovered a protogalaxy at z=9.87 on the WIYN telescope!
(Yale partly owns the WIYN telescope, which is a 3.5-meter optical
telescope located on Kitt Peak in Arizona).

a.) The light from this protogalaxy contains the H-alpha emission line,
whose rest wavelength (or emission wavelength)is 0.656 microns, in the 
red optical part of the spectrum. Calculate the wavelength at which 
we would observe the H-alpha line from this protogalaxy. 

b.) Can an optical-infrared telescope on earth's surface (like 
the WIYN telescope) observe its H-alpha line, if the telescope can 
observe from 2.2-0.3 microns? If not, what kind of telescope would be 
required to observe it, and where should the telescope be located?

c.) The present separation of the Milky Way Galaxy and the 
Andromeda Galaxy (M31) is 2 million light years.
If you assume that the only motion of the galaxies is due to the
expansion of the universe, how far apart were these 2 galaxies 
at the time that the light from the z=9.87 protogalaxy was emitted?

d.) How do these distances (at z=0 and z=9.87) compare to the present
size of the Milky Way Galaxy?  What does this suggest about the size of
the proto-Milky Way Galaxy at z=9.87?

e.) How dense is the present Milky Way Galaxy, compared to the present 
average mass density of the universe? Assume that the Milky Way has 
a mass of M=10^12 Msun and the same radius you used in part d.
Give your answer in the form of a ratio.

f.) How dense is the present Milky Way Galaxy, compared to the average mass 
density of the universe at z=9.87?  Give your answer in the form of a ratio.

g.) What does the change in the density ratios in parts e and f tell you 
about the formation of structure in the universe?

h.) What was the temperature of the cosmic background radiation
at the time corresponding to z=9.87?



2. (21 points)
a.) What was the peak wavelength in the spectrum of the Cosmic Background 
radiation at a time in the universe corresponding to a redshift z=1100?

b.) What is the wavelength of a photon which has just enough
energy to ionize a Hydrogen atom? 
[There is no calculation for part b. Just look up answer. See Section 5-8]

c.) Given that these are different, why is the Cosmic Background
radiation at z=1100 able to ionize all the Hydrogen? 
[HINT! The ratio of the number of cosmic photons to protons is relevant!]
[ANOTHER HINT!! Do all the photons have the same energy?]
[NO MORE HINTS!!!]


3. (28 points)
a.) What is the peak wavelength of the cosmic background radiation
for an observer at rest with respect to the cosmic background radiation?
Calculate this (to 4 signficant figures) from the present temperature 
of the cosmic background radiation and Wien's Law.

b.) Suppose you live in a galaxy which is orbiting at high
speeds through a cluster, and is therefore moving at speeds 
of 1555 km/s with respect to the cosmic background radiation. 
[Ignore the effects of the rotation of the galaxy.]
What is the peak wavelength of the cosmic background radiation measured
from a point on the sky which is in the direction of motion? 

c.) For the observer moving at 1555 km/s with respect to the cosmic 
background radiation, what is the peak wavelength of the cosmic 
background radiation measured from a point on the sky in the direction 
which is opposite that of the direction of motion?

d.)  For the observer moving at 1555 km/s with respect to the cosmic 
background radiation, what is the peak wavelength of the cosmic background 
radiation, in a direction which is 90 degrees (at right angles)
from the direction of motion?