Ay 127
Midterm Exam
Due: Tuesday May 7, 2013 to Chris Hiratas Mailbox (3rd floor Cahill)
TIME LIMIT: 3 hours
RULES:
Closed books, Internet, etc.
Open course lecture notes, your own notes, and

SOLUTIONS TO MIDTERM PROBLEMS
1. Short calculations.
(a) The peculiar velocity is 400 km/s so in order for this to induce no more than 10% error the galaxy
should have a Hubble ow velocity of 4000 km/s. For a Hubble constant of 70 km/s/Mpc this would impl

Ay 127 - Spring 2013
Solution Set 4
TA: Allison Strom
1. Diusion damping in the CMB analytical background. [25 points]
(a) The intensity from CMB photons with a small perturbation in the z -direction is
I (x, n) = I0 [1 + 4eikz ()].
Now consider the relat

Ay 127 - Spring 2013
Solution Set 3
TA: Allison Strom
1. Starbursts and the cosmic far-infrared background. [20 points]
(a) Physical energy density scales as (1 + z )4 , so we can write
uCIB (1 + z )4 =
N L t
,
Vz=3
which means that the total number of st

Ay 127 - Spring 2013
Solution Set 2
TA: Allison Strom
1. Cosmic recombination. [15 points]
(a) We start with the Peebles-Zeldovich ODE, which was given in Chris lecture notes
on recombination:
3/2
+ 3 8HxHI
dxHI
me kT
Ly nH
=
eI/kT xHI .
B xe xp nH
2
8H

Ay 127 - Spring 2013
Solution Set 1
TA: Allison Strom
1. Age of the Universe. [10 points]
(a) We can write an expression for the age of the Universe as
a
a
da
=
a
tage =
0
0
da
.
a H (a )
The next question is what the analytical form of the Hubble constan

AY 127 SOLUTIONS TO FINAL EXAM
1. Short questions. [24 pts]
(a) [6 pts] Suppose the correlation function of galaxies is approximated by (r) =
(r/r0 ) where r0 is the correlation length. Two types of galaxies (sample 1
and sample 2) have biases b1 and b2 .

1. Short questions. [24 pts]
(a) [6 pts] Suppose the correlation function of galaxies is approximated by (r) =
(r/r0 ) where r0 is the correlation length. Two types of galaxies (sample 1
and sample 2) have biases b1 and b2 . What is the ratio of their cor