Astronomy 100, Fall 2013, E. Pierpaoli
Homework 4. Due Thursday, December 5
Make sure that you give a short explanation of your answers. Answers that consist of two or three words
will not receive full credit. Some of your explanations would almost certainly bene±t if you drew diagrams.
Where a calculation is involved, you must show your working, and add some written lines of reasoning to
the calculation. This homework comprises both quantitative problems [marked with an asterisk [
⇤
], and
non-quantitative problems. The
theoretical
maximum total of points is 58. However, to allow for the
diverse backgrounds of the students in this course, you only need to get 46 points in order to have a perfect
score. You may attempt, and submit more than 46 points worth of problems, and you will not be penalized,
except that if your score exceeds 45, then it will be set equal to 46.
Before you do this homework please read the comments on the syllabus concerning ac-
ceptable and unacceptable levels of collaboration.
You should also be aware of potential
consequences of inappropriate behavior, as stated in the student conduct (see web link on
blackboard’s course site).
If, after trying on your own, you have trouble completing the homework, please ask me, or the TAs, for
help. This is all right. All what counts with homework is that you completely understand your answer.
BUT: Only by documenting this in your own words you can convince the grader that you have
understood.
1
⇤
) By looking at ±gure 25.1 in your book, provide an estimate for the mass of NGC4984 inside 20 kpc.
Please explain your reasoning. (5 points)
2
⇤
) Calculate the average speed of hydrogen nuclei in a gas with a temperature of 2
⇥
10
7
K (recall MP8.1).
Now compare this answer with the speed of a galaxy moving in a circular orbit of radius 1 Mpc around a
galaxy cluster of mass 10
14
M
±
. (6 points)
3
⇤
) What is the current temperature and peak wavelength of the cosmic microwave background (CMB)?
Knowing that the peak wavelength scales as the inverse of (1+
z
) where z is the redshift, while the temperature
scales as (1 +
z
), calculate the peak wavelength and temperature at matter-radiation decoupling (
z
'
1000).
Will most of the CMB photons, at the time of decoupling, have enough energy to ionize hydrogen atoms?
So does it make sense to you that scientists say that the Universe ”recombine” at this redshift (that means
electrons ”attach” to protons to form neutral hydrogen)? (
Hint: you may want to refresh your memories of
chapter 4 and MP 4-1; as well as of Chapter 3, MP3-2.
) (7 points)
4
⇤
) Assuming that a quasar which emits at a rate of 10
41
W has an e
f
ciency for conversion of mass into
energy of 10%, calculate how much accreting mass the quasar would need to continue burning for 10 billions
years. Do we currently believe quasars last for so long? (5 points)
5
⇤
) According to the big bang theory presented in chapter 26, what is the maximum possible age of the
Universe if there is no cosmological constant and: a)
H
0
= 60
km/s/Mpc
,b
)
H
0
= 70
km/s/Mpc
,c
)
H
0
= 80
km/s/Mpc
? (4 points)
6) Summarize the current theories for galaxy formation. Describe what top-down and bottom up theories
are. How long ago (and how long after the Big Bang) did galaxies form? Did di
↵
erent types of galaxies form
in di
↵
erent moments? (4 points)
7) Summarize, brie²y, how the matter in the universe is distributed (clusters, superclusters and voids). What
are the typical sizes of these structures? If the expansion of the universe continues forever, how would you
expect the distribution of matter to evolve? (6 points)
8) What is Olbers paradox and what does it tell us about the universe? (4 points)