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2nd Astronomy Exam Fall 2015
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1
1. A star leaves the main sequence when
A. it stops fusing hydrogen in its core.
B. neutrinos can no longer escape the star.
C. its core of iron can no longer support itself and it collapses catastrophically
D. the t-Tauri winds clear the nebula of gas and dust terminating planet formation.
2. When a star like the Sun ceases to produce energy in its core and energy production begins in a shell outside
the core, its envelope
A. Collapses and heats up.
C. Expands and heats up.
B. Collapses and cools down.
D. Expands and cools down.
The HR Diagram at right is provided to assist with answering the following two questions.
Spectral Type
O5
B5
A5
F5 G5
K5
M5
Blue Giants
10,000
Red Giants
a
d
Luminosity (solar units)
1,000
-5
b
100
10
1
Absolute magnitude
3. Which is hotter, a main sequence star with
an absolute magnitude of M= -5 or a Red
Giant.
A. The main sequence star
B. The red giant
C. They have the same temperature.
D. There is insufficient information to
determine this.
0
Main
Sequence
e
5
.1
.01
4. Which statement is the most correct about
c
.001
the comparison between a K5 main sequence
White Dwarfs
.0001
star and a Red Giant
A. The K5 star is less luminous, smaller,
20,000
10,000
and will not live as long as the Red
Giant star.
Temperature (K)
B. The K5 star is less luminous, smaller,
and will live longer than the Red Giant star.
C. The K5 star is less luminous, larger and will not live as long as the Red Giant star.
D. The K5 star is more luminous, smaller, and will live longer than the Red Giant star.
f
10
15
5,000
5. The element iron in the hemoglobin of your blood was formed
A. in our Sun.
B. in the chemistry of Giant Molecular Clouds
C. at the instant of the Big Bang.
D. in a distant galaxy in a different part of the early universe.
E. by the explosive death of a massive star.
6. The object to the right is an example of which of the following
A. It is the outflow of gas from the envelope of a sun-like star that
marks the end of the star’s energy production.
B. It is the peculiar morphology associated with the collision of two
galaxies
C. It is the giant molecular cloud from which protostars form
D. It is what is left when a white dwarf star explodes as a supernova.
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7. Which of the following lists, in the correct order, a possible evolutionary path for a sun-like star (i.e. 1 solar
mass)?
A. Main sequence, horizontal branch star, red giant, red supergiant, white dwarf
B. Main sequence, red giant, horizontal branch star, red supergiant, supernova
C. Main sequence, proto-star, red giant, white dwarf
D. Main sequence, red giant, horizontal branch star, red supergiant, white dwarf
E. Main sequence, red giant, white dwarf, supernova
Refer to H-R diagram illustrating the evolutionary track
of a 1 solar mass star to the right to answer the following
questions.
8. Which of the objects listed below would be observed
along the portion of the track marked (e)?
A. White dwarf
B. Horizontal Branch Star (a.k.a.Yellow Giant)
C. Planetary Nebula
D. Red Giant Star
E. None of the above
e
-10
d
-5
0
M
b
c
+5
a
+10
+15
+20
9. Which of the methods of energy production is at
active along the portion of the track marked (d)?
A. Core H-burning
B. Core He-burning
C. Shell H-burning
O
B A
F G
K
M
D. Shell He-burning
E. Proton-proton chain
10. In a few sentences, define an HII region and an OB Association. Also describe the relationship between the
two of them.
An OB Association is a small group of brand new O & B main sequence stars. An HII region is a
cloud of ionized hydrogen gas that glows red as electrons recombine with the hydrogen nucleus. The
HII requires a power source to excite and ionize the hydrogen. The power source is the UV photons
from the very hot O and B stars. The OB association creates the HII region and maintains it.
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11. The 3-D HR diagram
to the right displays
the abundance of
stellar types in a
typical million cubic
parsec volume of the
galaxy. As this figure
indicates, the most
common types of stars
in a typical location of
the galaxy are M main
sequence stars (a.k.a.
Red Dwarfs).
A. List two reasons
why the most
common stars in
the galaxy are M
main sequence
stars.
1.
2.
M stars form more often from a GMC because the Birth Function dictates that there are
hundreds of times more smaller (≈ 0.1 solar masses) than there are lager fragments and the
smaller fragments from the M main sequence stars.
The M main sequence stars have very long lifetimes…longer than the Universe is old. The
lifetime of an M main sequence stars is over 1 trillion years. Thus every M main sequence
star that has ever formed in the history of the universe is still an M main sequence star. They
never die…we’ll not yet anyway. So their numbers just continue to build up.
B. State why there are so relatively few Giant and Supergiant stars.
Giant and supergiant stars are so rare because their lifetimes are so short. Giant stars as a class
only exist for a few percent of their main sequence lifetimes. Their numbers never have an
opportunity to grow due to their high “death rate”.
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12. The HR Diagram to the right is
of an open cluster. Note the
horizontal axis is labelled as B-V
which is another way in which
temperature is expressed.
Suffice it to say that hot is to the
left and cool is to the right as in
our usual practice of drawing HR
Diagrams. The main sequence is
clearly outlined.
A. Carefully sketch in the
ZAMS line and define what
the acronym ZAMS means.
The ZAMS line lies to the
lower left of the main
sequence and represents
the point on an HR
diagram where conditions
within the core of the star
are sufficient to initiate
fusion.
ZAMS is an acronym for Zero Age Main Sequence.
B. The five stars that appear in nearly a straight line in the lower left of the HR diagram are what type of
objects?
These five objects are white dwarf stellar remnants the “tombstones” of low mass stars (M < 9 solar
masses).
13. Our Sun is halfway through its main sequence lifetime. During the first half of its main sequence lifetime,
the Sun’s luminosity was expected to be
A. Greater than it is now
B. The Same as it is now
C. Less than it is now
D. No predictions of past conditions are possible.
5
14. The evolutionary track of a protostar
evolving toward the main sequence is
shown on the HR diagram to the right.
A. Describe the changes in the protostars luminosity, temperature and
radius as it evolves through the two
points marked by the circles labeled
A and B.
B
A
From point A to point B the
 Luminosity of the proto-star
is nearly constant,
 Temperature is increasing,
and
 Radius must be decreasing
following the Stefan-Boltzmann Law. (If L is constant then since an increasing T would
drive up the luminosity, the radius must be decreasing to counteract the effect of
temperature.
B. If nuclear fusion has not yet started in this proto-star, then what is the source of energy that is causing
B
A
the temperature to change? Answer in a sentence.
The proto-star is generating energy by converting gravitational potential energy into thermal energy.
In other words, it is creating heat as it collapses and compresses itself.
15. The following four sketches represent the four types of binary stars. Note that the spectral type and
distances are provided for each star in the sketch. Write the type of binary star the picture represents under
the appropriate sketch.
A2
210 ly
F0
85 ly
Optical Double Star
K2
35 ly
G3
35 ly
True Binary Star
A0
60 ly
K5
60 ly
G0
100 ly
B5
100 ly
Spectroscopic Binary Star Eclipsing Binary Star
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16. One of the sketches of binary stars from the previous problem represents an eclipsing binary star. What
information, besides the combined mass of the system, can be extracted from an eclipsing binary star
system? Answer in a sentence.
The diameters of both the primary and secondary star in an eclipsing binary star system can be extracted
from the light curve of the two stars.
17. The image to the right shows several Bok Globules.
A. What is the mass limit for the smallest globule
that will form a star and why can no smaller
fragments form stars? Answer in a sentence.
The smallest mass fragment that can go to
form a star is about 0.1 solar masses. If a
cloud fragment is less massive than 0.1 solar
masses, then it will not have sufficient
temperature sand density to initiate fusion in
its core when it has collapsed fully.
B. Why is the largest fragment that will form a star limited to 100 solar masses? Answer in a sentence.
The largest fragment that will form a star limited to 100 solar masses because any larger mass
fragment will generate so much energy as it collapses that it literally blows itself apart into
smaller fragments.
18. In the August 2015 edition of Physics Today magazine, a new book is advertised as
being available. Its cover is shown on the right. This book will no doubt challenge
what empirical law that predicts how a Giant Molecular Cloud fragments? Just
name the empirical law that predicts how a giant molecular cloud should break up.
The Birth Function or The Initial Mass Function
7
The following question requires a detailed quantitative answer.
19. Describe the nature of the bright stars in the night sky, contrasting
their properties with the Sun. Be quantitative in your description.
An HR diagram of the brightest stars in the sky appears to the right
to assist your memory.
Points to mention
The Bright Stars are
 All more luminous than the Sun.
 Either hotter main sequence stars or cooler giants.
 The hotter main sequence stars are mostly B and A stars
with temperatures around 15,000 K and luminosities
between 50 and 5,000 solar luminosities,
 The cooler giant stars are mostly K and M giants with
temperatures around 5,000 K to 3,000K and luminosities
between 50 and 5,000 solar luminosities.
 The stars are all larger in radius than the Sun, being
between 1 and 100 solar radii.
 All these stars will have very short lifetimes compared to
the Sun. The main sequence stars will have lifetimes less
than 1 billion years and the giants are at the end of their
lives with perhaps as little as100,000 years left.
 It is not shown in this HR diagram but the bright stars
are about a few hundred light years away on average
and half of them are in multiple star systems, unlike the
Sun.
 Taken as a class, the bright star are more luminous,
larger and shorter lived that the Sun and are in different
orbital geometries.
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20. The spectrum of a star appears below.
Maximum intensity at about 600 nm
A. Estimate the wavelength at which the star emits its maximum intensity.
The wavelength at which the star emits its maximum intensity is about 600 nm.
B. Using your estimated wavelength of maximum emission, calculate the temperature of this star. (Note:
If you did not estimate the wavelength of maximum emission in part A, then use λMax = 950 nm for this
part B. It is not the right answer to part A, but will allow you to do this part B.)
T
2.9  106 K  nm
Max

2.9  106 K  nm
 4,833 K (3,053 K)
600 nm
The temperature of the star is about 4,833 K. (3,053K)
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C. The luminosity of the star is known to be 100 solar luminosities. What is the radius of the star
compared to the Sun’s radius? (Note: If you did not calculate the temperature in part B, then use T =
2,500 K for this part C. It is not the right answer to part B, but will allow you to do this part C.)
Use the Stefan-Boltzmann Law to solve for the radius of this star relative to the Sun
Stefan Boltzmann Law:
L  4R 2  T 4
2
2
4
2
4
2
4
 RStar
  TStar
  R  T 
LStar 4RStar
 TStar
RStar
 TStar




 2
  2    4    Star    Star 
2
4
4
LSun
4RSun  TSun
RSun  TSun  RSun   TSun   RSun   TSun 
2
4
4
 R  T 
L
 Star   Star    Star 
LSun  RSun   TSun 
Now, that we have a simple expression with ratios, we’ll fill in the known ratios and find the unknown
ratio
2
 R   4,833 
100   Star   

 RSun   5,800 
4
2
R 
100   Star   0.482
 RSun 
The star has a radius14.4 times that of the Sun.
2
R 
  Star   207
 RSun 
RStar
 14.4
RSun
21. The orbit of the binary star Kruger 60 is shown to the right. The radius of the companion star’s orbit is 8.9
AU and the period of the companion star’s orbit is 44. 6 years.
A. What is the combined mass of the two stars in the Kruger
60 binary system?
a 3 8.9 AU 

 0.35 solar masses
P 2 44.6 yr 2
3
m1  m2 
The combined mass of these two stars is about 0.35 solar
masses.
B. Assuming that both stars in the system are main sequence
stars, what would be a reasonable guess as to their spectral
types given the value of the combined mass?
Since the combined mass is only 0.35 solar masses both stars must be very low mass stars that
would be consistent with M main sequence stars. I would guess that bot these stars are some subclass of M main sequence star.
10
Use the HR diagram to the right to answer the following questions. Note: The only calculations needed are to
convert absolute magnitude into solar luminosities. Most answers can be read off the HR Diagram.
22. The bright star Deneb has a luminosity of 54,000
solar luminosities (M = -7.0) and a temperature of
8,525 K (spectral type A2). What is its approximate
radius?
HR Diagram
The radius of this star is about 60 solar radii.
30,000 K
-10
9,500 K
7,200 K
6,000 K
5,250 K
3,800 K
1,000 R
60 M
-5
17.5 M
100 R
23. The star nearest the Sun is an M5.5 V star. What are
its luminosity and its radius, approximately?
The absolute magnitude of this star is about 12
which corresponds to a luminosity of
2.5124.812  0.00132 LSun
The radius of this star is about 0.2 solar radii.
24. The companion star to the brightest star in the sky is
designated Sirius b. It has a spectral type of A2 and
has a radius of 0.01 that of the Sun. What is its
approximate luminosity?
Absolute Magnitude
5.9 M
2.9 M
0
1.8 M
10 R
1.2 M
0.1 R
1.0 M
5
Sun
.67 M
1 R
0.01 R
10
.21 M
0.001 R
15
20
O
B
A
F
G
K
M
Spectral Type
The absolute magnitude of this star is about 12 which corresponds to a luminosity of
2.5124.812  0.00132 LSun
25. What would be the spectral type of a main sequence star with 10 times the mass of the Sun?
The spectral type of a main sequence star with 10 times the mass of the Sun would be about a B3 main
sequence star.
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26. The core of a high mass star at the end of its energy production lifetime is composed of which of the
elements listed below?
A. Hydrogen
C. Carbon
E. Silicon
B. Helium
D. Oxygen
F. Iron
27. In a sentence or two, explain what a “standard candle” is and why are supernova’s considered very good
“standard candles.”
A standard candle is any astronomical object of a priori know luminosity (i.e. the luminosity is known
as soon as the object is identified).
Type II supernova are goods standard candles because they all seem to have the same peak luminosity
(about M = -17) and that peak luminosity is VERY luminous allowing supernovas to be observed at
very great distances.
28. Why do high mass main sequence stars like O and B stars go on to fuse heavier elements in their cores,
while stars of lower mass, like the Sun, stop with the fusion of helium? Answer in a couple sentences.
High mass main sequence stars like O and B stars go on to fuse heavier elements in their cores, while
stars of lower mass, like the Sun, stop with the fusion of helium because the high mass stars have
higher central temperatures and densities in their core that can overcome the electrostatic barriers to
fusion that heavier elements like carbon, oxygen, neon etc. present. The larger central temperatures
and pressure allow more types of fusion to occur in these higher mass stars.
29.The image to the right illustrates a typical open cluster of stars. In a
few sentences, describe what an open cluster of stars is giving typical
dimensions and stellar content. Answer in a few sentences.
An open cluster is a brand new group of stars fully emerged from
the Giant Molecular cloud it formed from. An open cluster may
contain 100’s to 1,000’s of visible stars. The visible stars are
mostly B and A main sequence stars but there are far more
invisible K and M main sequence stars whose luminosities are too
low to allow us to see them. The typical Open Cluster is about 15
light years across.
30. On Tuesday 06 Oct 2015, The Royal Swedish Academy of Sciences
has decided to award the Nobel Prize in Physics for 2015 to Takaaki Kajita of University of Tokyo,
Kashiwa, Japan and Arthur B. McDonald of Queen’s University, Kingston, Canada “for the discovery of
neutrino oscillations, which shows that neutrinos have mass.” For a little extra credit, in what area of study
did we encounter the issue of neutrino oscillations?
We encountered neutrino oscillations in our study of the Sun’s source of power.
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Astronomy Formula and Constants Sheet for Exams
Conversions
Formulas
A
L

2D
360 
Main Sequence Lifetime t 
M
1010 yr
L
13