Astronomy 106.02 Third Examination Monday, April 21, 1997

Name:___________________________________________________________

Honor Pledge:






This exam consists of 36 questions and is worth a total of 100 points.

This exam is due at 10:25. You may use a calculator, but no notes or reference books.

Part I. Multiple choice. Each question is worth 2 points.

1. An isolated black hole in space would be difficult to detect because
a. there would be no light source nearby.
b. it would not be rotating rapidly.
c. it would be stationary.
(d.) very little matter would be falling into it.

2. The density of a neutron star is
(a.) about the same as an atomic nucleus.
b. about the same as that of the sun.
c. about the same as that of a white dwarf.
d. so great that light cannot escape from a neutron star.

3. Compared to a main sequence star a red giant star is
a. smaller
b. hotter
(c.) more luminous
d. none of the above

4. ____________ show(s) that some quasars are further away than distant galaxies and that space time is curved by massive objects.
a. Double-lobed radio galaxies
(b.) The gravitational lens effect
c. Head-tail galaxies
d. Superluminal expansion


5. The center of our galaxy lies in the direction of
a. Ursa Major
b. Ursa Minor
(c.) Sagittarius
d. Orion

6. The _______________ is caused by gas and dust located in the disk of the Milky Way that absorbs light and doesn't allow us to see distant galaxies in line with the plane of the Milky Way.
(a.) zone of avoidance
b. Large Magellanic Cloud
c. hot inter cluster medium
d. Virgo cluster

7. Supernovae are important for stellar evolution because
a. they are the only way pulsars are created.
b. they produce shock waves which can trigger star formation.
c. they distribute heavy elements into the galaxy.
(d.) all of the above.

8. A megaparsec is equivalent to
a. 3.26 light-years.
b. 206,265 AU.
(c.) 3,260,000 light-years.
d. the diameter of the Milky Way galaxy.

9. Younger stars have more heavy elements because
(a.) heavy elements were made in previous generations of stars.
b. young stars burn their nuclear fuels faster.
c. old stars destroy heavy elements as they age.
d. all of these

10. The Chandrasekhar limit tells us that
a. accretion disks can grow hot through friction.
b. neutron stars of more than 3 solar masses are not stable.
(c.) white dwarfs must contain less than 1.4 solar masses.
d. white dwarfs must contain more than 1.4 solar masses.

11. Cepheid variables show a clear relationship between period and
a. temperature.
b. distance.
(c.) absolute magnitude.
d. age.




Part II: True/False. Each question is worth 2 points.


1. Stars support their weight by generating energy in their centers.

(T) F

2. When a large galaxy collides with a small galaxy, the smaller galaxy may be pulled apart by tidal forces.

(T) F

3. The rapid rotation in the outer disk suggests that our galaxy is more massive than previously thought.

(T) F

4. If the accretion disk around a black hole emits X rays outside the event horizon, the X rays can escape.

(T) F

5. The sun will eventually become a supernova.

T (F)

6. Elliptical galaxies contain more gas, dust and young stars than do Sa galaxies.

T (F)

7. Neutron stars were first discovered in the 1930's

T (F)

8. Giant and supergiant stars are rare because that stage of stellar evolution is short.

(T) F

9. The disk of the galaxy is older than the halo.

T (F)

10. Planetary nebulae are sites of planet formation.

T (F)




Part III: Calculations. Each question is worth 4 points. The formulae given at the bottom of the next page may be useful.

1. A star 0.1 pc (3 X 1012 km) from the center of the Milky Way has an orbital period of 850 years. What is its orbital velocity in km/sec?

V = (2 pi R ) / T
R = 3 X 1012 km
T = (850 years) (3.2 X 107 sec/year) = 2.78 X 1010 sec

V = (2) (pi)(3 X 1012 km) / ( 2.78 X 1010 sec)

[Answer: V = 690 km/sec]





2. A neutron star has a temperature 200 times that of the sun. If its radius is 10 km, what is its luminosity? Give your answer in terms of the luminosity of the sun.

Use the formula L / Lsolar = (R / Rsolar)2(T/Tsolar)4

T/Tsolar = 200
R = 10 km
R / Rsolar = 10 / 7 X 105 km = 1.42 X 10-5

(L / Lsolar) = (1.42 X 10-5)2 (200)4

[Answer: (L / Lsolar) = 0.33]


3. The star Capella has an absolute magnitude of -0.4 and an apparent magnitude of
+0.1. How far away is this star?

d = 10(mv - Mv + 5)/5
mv = 0.1 and Mv = -0.4

d = 10(5.5/5) = 101.2

[Answer: d = 12.6 pc]




4. The escape velocity of a black hole is greater than the speed of light. Would the sun be a black hole if it were compressed to a radius of 10,000 m?


Ve = ( 2 G M / r )1/2
G = 6.67 X 10-11
M = 2.0 X 1030 kg
r = 10,000 m

Ve = {(2)(6.67 X 10-11)(2.0 X 1030 kg) / (10,000 m)}1/2

Ve ={2.7 X 1016}1/2

Ve = 1.6 X 108 m/s

[Answer: Since the escape velocity is less than the speed of light, the sun would not
be a black hole.]




5. The Whirlpool galaxy has an angular size of 10 minutes of arc. It's diameter is 22 kpc. How far away is this galaxy? (You do not have to convert your answer to meters).

theta / 206,265") = (d / D)
D = (206,265")(d /theta )
D = (206,265")(22 kpc) / (600")

[Answer: D = 7.6 Mpc]




theta / 206,265") = (d / D) Ve = {(2)(6.67 X 10-11)(2.0 X 1030 kg) / (10,000 m)}1/2 G = 6.67 X 10-11
Mass of the sun = 2.0 X 1030 kg Speed of light (c) = 3.0 X 108 m/s
d = 10(mv - Mv + 5)/5 L / Lsolar = (R / Rsolar)2(T/Tsolar)4
v = d / t circumference of a circle = 2 pi R radius of sun = 7 X 105 km
1 year = 3.2 X 107 seconds 1 minute of arc = 60 seconds of arc
Part IV: Short answer. Each question is worth 3 points.

1. The H-R diagrams of three star clusters are shown below. Order the ages of the clusters from youngest to oldest.

Referring to the figure printed on the exam: The order is a - c - b (youngest to oldest)




2. Write down the classification (type) of each of the three galaxies marked in the diagram.


Referring to the figure printed on the exam:
a = E0 elliptical
b = Sa spiral
c = SBc barred spiral




3. Label the components of the Milky Way Galaxy as indicated on the figure.

Referring to the figure printed on the exam:
a = globular clusters
b = nuclear bulge
c = disk




4. What type of pressure supports each of the following against compression by the star's gravity? Main sequence star; white dwarf; black hole.

main sequence: radiation pressure
white dwarf: electron degeneracy
black hole: nothing; it collapses to a singularity




5. What are the first three elements used as fuel in a massive star?

hydrogen, helium and carbon




6. List three types of active galaxies.

blazars, quasars, double lobed radio source, Seyfert galaxies.



Part V. Essay questions. Each question is worth 10 points.

Choose two of the four questions to write about.
Circle the numbers of the two questions you have chosen.
If you write on one or both of the two questions not circled, you can earn as much as 10 points total extra credit.

Write as much as necessary for each of the questions. Your score will be based on completeness, clarity and correctness of your response.

1. Discuss the steps in the evolution of a 10 solar mass star from Zero Age Main Sequence to black hole.

ZAM (zero age main sequence)
Hydrogen burning for approximately 30 million years as the star gets brighter and slightly cooler.
H-shell burning
Helium flash as the star becomes a giant
He burning
He-shell burning as the star expels a planetary nebula
Heavy elements are fused up to iron
Core collapses once iron is produced
Shock produces a Type II supernova
The supernova produces and expanding nebula
The core of the star collapses to form a black hole.





2. Describe the various ways astronomers determine the distances to galaxies.

Parallax and proper motion allow calibration of the distance scale.
Cepheid variables which have a direct relationship between period and absolute luminosity are observed in other galaxies. Knowing the absolute and apparent magnitude allows one to determine distance.
Other methods include measuring the apparent brightness of the brightest supergiants, measuring the brightness of supernovae, looking the size of the largest globular cluster or of young H-II regions.
For very distant galaxies one uses the relative size of galaxies or the brightest galaxy in a cluster.
The Hubble relation between distance and recession velocity allows one to estimate the distance to very distant galaxies.






Circle the numbers of the two questions you want counted as regular credit.

3. What are the differences between Population I and Population II stars?

Pop I stars are young and rich in metals. They are primarily in the disk and have circular orbits.

Pop II stars are older and contain mostly H and He. They are halo stars with elliptical orbits.




4. List as many differences as you can between a 0.2 solar mass star and a 10 solar mass star. You may want to consider lifetime, luminosity, temperature and evolution.

0.2 solar mass star is convective throughout, 10 solar mass star has convective core and radiative zone.
0.2 M star burns only hydrogen, while 10 M stars burns all elements up to iron.
0.2 M star will eventually become a white dwarf; 10 M star will go supernova and become a black hole.
0.2 M star has low luminosity and temperature, while 10 M star is hot and bright.
0.2 M star will live more than 100 billion years, while 10 M star will only live 30 million years.