Astronomy 122 mid Term Exam
Name: __________________________
Please confine your answers to the space provided and make sure to write legibly.
Remember to show all work. There are a total of 171 points on this exam. This exam
consists of three parts:
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Part 1: 12 Short Questions @3 points each
Part 2: 7 Medium Answer Questions @5 points each
Part 3: 10 Longer Answer Questions @10 points each
Part 1: Each Question in this Section is worth 3 points: (36 points total)
1. If a 10000 K blackbody has a wavelength of peak emission at 3000 angstroms,
what would be the wavelength of peak emission for a blackbody at a temperature
of 2500 K?
As blackbodies get hotter, more of their emitted radiation shifts to shorter
energy. The shift is directly proportional to wavelength. Therefore, if a 10000K
blackbody has a wavelength of peak emission of 3000 angstroms a 20000K (i.e.
hotter) would be shifted to even short wavelengths (in this case peak emission would
be at 1500 angstroms) and a cooler 2500K radiation would shift toward
redder/longer wavelengths, or more exactly 12,000 angstroms. (3000 x 4)
2. If a 1 solar mass main sequence star has a hydrogen burning lifetime of 1010 years
then what would the hydrogen burning lifetime of a 10 solar mass star be?
The lifetime of a star is Mass divided by the rate at which the fuel is burned.
The rate at which is fuel is burned is the luminosity of the star. Hence the
lifetime of a star is
M/L
Since L M4 (mass luminosity relationship) the lifetime can be expressed as
M/M4 or 1/M3
Thus a 10 solar mass star has a main sequence lifetime 103 times less than a 1 solar
mass star. 1010 yrs divided by 1000 would be 10 million years.
3. Star A has a surface temperature of 20000 degrees (K). Star B has a surface
temperature of 10000 degrees (K). Both stars have the same radius. What is the
luminosity ratio of Star B to Star A?
For blackbodies the energy emitted
th
goes as Temp to the 4 power (T^4) so A emits 2^4 times more = 16
4. You make parallax measurements of two stars. Star A is observed to have a
parallax of 1/8 of an arc second. Star B is observed to have a parallax of 1/2 of an
arc second. What the ratio of distance of Star A to Star B?
Star A is 4 times farther away
Questions 6 – 10 refer to the above diagram.
5. Which star has the highest luminosity? 1
6. Which star has the longest main sequence lifetime? 6
7. Which star is fusing Helium as its primary energy source? 2 (red giant)
8. Which star is now in its last evolutionary phase? 5 (it’s a white dwarf)
9.
Which star would appear to be the reddest? 2 or 6
10. Which star might be starting its Post Red Giant Phase of evolution? 8
11. Which star would most likely have strong hydrogen absorption lines in its
atmosphere? 4 (10,000 degrees = A star = strong hydrogen lines)
12. Which star is most like our Sun? 3
Part 2: Each Question in this Section is worth 5 points: (35 points total)
1. Explain why it is difficult to make accurate distance measurements to nearby stars by
using ground based telescopes.
Because atmospheric motions smears the stellar image on the detector thus
introducing positional uncertainty for each individual exposure. So you have to
take many years of observations to average out this error.
2. List two physical characteristics that are common for all main sequence stars,
independent of their mass
A) Pressure = Gravity; stable
B) They all fusion hydrogen in their cores
3. Briefly explain how stellar masses can be determined.
Stellar masses can only be DIRECTLY obtained by measuring the orbital periods of
binary stars around one another.
You observe 4 stars in the sky. Their properties are summarized in the table below:
Star
Flux on Detector
Distance
(Arbitrary Units) (Light Years)
Observed
Color
A
4
2
Blue
B
8
4
Red
C
10
4
Very Blue/White
D
32
1
Yellow
4. Which of these stars has the coolest surface temperature and how do you know this?
B because its red
5. What would the flux of Star D be if it were located at a distance of 8 Light Years?
Moving it from 1 to 8 LY means moving it 8 times farther away. Therefore flux
goes done by 1/8^2 = 1/64. The on the detector from this star would then be 32
*1/64 = 0.5 units
6. What is the ratio of luminosities between Star B and Star A?
Move Star A to the distance of Star B. That moves it twice as far away so the flux
would be reduced by ¼ from its value at D=2. So the flux would be 1 unit at D=4
light years where as the flux of star B at D=4 light years is 8. So the luminosity ratio
has to be 8 (since both stars are now at D=4).
7. Shown below are two spectra of real stars. Explain how you can tell which of the
stars is the hottest?
A spectra is a plot of received energy vs wavelength. Since stars are blackbodies,
those that emit most of their energy at short wavelengths are hotter. The spectrum
of the lower star is hotter than the upper star (by rather a lot)
.
Part 3: Each Question in this Section is worth 10 points: (100 points total)
1. The above images show two exposures of the same star field. The exposure on the
right is 1 seconds, the exposure on the left is 50 second. Explain why you can more
easily detect the stars in the 50 second exposure than in the 1 second exposure.
Signal to noise increases with increasing exposure time.
2. Explain how astronomers determine the spectral type of a star
By doing exactly what the students did in homework 3. Measure the strength of the
hydrogen lines relative to calcium lines.
3. A simplified atom has 4 energy states in it. The ground state has zero energy, the first
excited state has energy = 5 units above the ground state, the second excited state has
energy = 8 units above the ground state, and the third excited state has energy 10
units above the ground state.
a. draw a sketch of these energy states
b. If an electron resides in the third excited states, list all possible kinds of
photon emission and/or absorption that could be associated with an electron in
that energy level
Well done, not going to answer here.
4. Explain why the main sequence lifetime of a star is strongly dependent on its mass.
Stars need to be stabilized against G. So need to generate core pressure via core
temperature increases until P=G. Each mass has a unique value of G so requires
a unique core temperature for stabilization. The nuclear reaction rate is very
sensitive to core temperature. Hence massive stars require higher core
temperatures for stabilization and subsequently burn up their fuel much faster.
5. Circle the correct choice in each triplet option (bold face in parentheses) in the
paragraph below: Correct choices are de-bolded below and this conceptual story
applies to all the question on stellar evolution in this exam.
If the temperature in the core of a star decreases, the pressure in the core
would (decrease, remain unchanged, increase). In this case, the pressure
will be (less than, the same as, greater than) the gravity. So the core of
the star will (contract, not change, expand). As a result the temperature
in the core will (decrease, remain unchanged, increase). In this case the
rate of energy generation in the core will (decrease, remain unchanged,
increase) and the pressure in the core will (decrease, remain unchanged,
increase).
6. You observe a stellar cluster and make an HR diagram of the stars in it. From that you
notice that the most massive star that is still on the main sequence is 2 solar masses.
What is the approximate age of this cluster and how is this age determined?
The main sequence lifetime of a 2 solar mass star is about 1/8 that of a 1 solar mass
star. So the cluster is about 1 billion years old. If it were older, then 2 solar mass
stars would no longer be on the main sequence. If it were younger then more
massive stars would still be on the main sequence. This material is clearly covered
in the module on Stellar Clusters. (4A)
7. Explain why low mass stars such as the sun can never produce any elements heavier
than Carbon or Oxygen.
Low mass stars can do not have enough self gravity to ever generate the required
core temperature for the fusion of Carbon/Oxygen as those nuclei have too many
protons in them and require a temperature that is too high for these kinds of stars to
ever produce.
8. Briefly explain why the luminosity of a star begins to increase as it evolves from the
main sequence to the red giant phase of stellar evolution.
The helium core collapses and heats. The heat is spread to a thin shell of hydrogen
which beings to fuse at a rate that is greater than the rate of hydrogen fusion in the
core. So the luminosity increases as this shell gets hotter and hotter.
9. Explain the post main sequence evolutionary process of a star that leads to most of
the mass of the star being lost and to the brief appearance of the planetary nebula
phase of stellar evolution.
Same process as in the previous question – only now the collapsing carbon core heats a
double shell source of helium+hydrogen burning. The subsequent huge pressure from that
double-shell source drives the outer layers of the star complexly away, exposing the core.
10. Explain why, in a randomly selected sample of stars, the most common star that we
would expect to find is a low mass main sequence star.
A) Nature creates mostly low mass stars
B) Low mass stars live a very long time