Download Homework #7 (Ch. 19)

Astronomy 120
HOMEWORK - Chapter 19
Star Formation
Use a calculator whenever necessary.
For full credit, always show your work and explain how you got your answer in full, complete
sentences on a separate sheet of paper.
Be careful about units!
Please CIRCLE or put a box around your final answer if it is numerical.
If you wish, you may discuss the questions with friends, but please turn in your own hand-written
solutions, with questions answered in your own way.
1. Chaisson Review and Discussion 19.1
Briefly describe the basic chain of events leading to the formation of a star like the Sun. (4
points)
Star formation starts with an interstellar cloud of low density and temperature, tens of
parsecs in diameter. It becomes unstable to gravitational collapse and starts to fragment.
Anywhere from dozens to thousands of fragments are produced, each collapsing even further
on its way to forming a star. In a fragment, the collapse raises the central temperature to
10,000 K but the exterior remains cool and is able to radiate its energy. As the collapse
continues, the central density and temperature increase until the fragment can start to trap
its own radiation. The object, now known as a protostar, begins to heat up rapidly and give
off infrared light. The protostar is hundreds of times larger than the Sun and its luminosity is
thousands of times larger; however, its surface temperature is still relatively cool, and most
of the light given off is not visible. The collapse slows as internal pressure builds. The
luminosity of the protostar decreases as it shrinks, while the central temperature gradually
increases. While still several times larger and brighter than the sun, the central temperature
reaches 10 million K and hydrogen fusion begins, and the protostar becomes a star.
Continued slow contraction raises the central temperature to about 15 million K and the star
finally becomes a main sequence star.
2. Chaisson Review and Discussion 19.2
What is the role of heat in the process of stellar birth? (3 points)
The temperature of the gas must be initially low enough so that the gravity can overcome the
individual speeds of gas molecules, and collapse the cloud. Initially, the cloud radiates away
its gravitational energy and does not heat up much. However, as the cloud gets smaller and
denser, radiation cannot escape so easily and the interior of the cloud starts to heat up.
Slowly at first, and then with increasing speed, internal pressure builds and pushes against
gravity and slows the collapse of the protostar. The collapse does not stop, however, and
gravity continues to compress the gas and heat it until finally the core temperature reaches
10 million K, which is sufficient to initiate hydrogen fusion. The object is now a star.
3. Chaisson Review and Discussion 19.3
What is the role of rotation in the process of stellar birth? (3 points)
As an interstellar cloud collapses, it must spin faster as it conserves angular momentum. This
can actually hinder star formation, as the rotation wants to fling material out of the cloud,
opposing gravity. Thus, a rotating cloud needs a stronger gravitational pull, and thus more
mass, to be able to collapse than a cloud that is spinning slowly or not at all. Rapid spin
also causes the cloud to flatten into a disk. Although most of the mass is still concentrated in
the center, the material in the disk could form into planets.
4. Chaisson Review and Discussion 19.6
Why do stars tend to form in groups? (3 points)
During the process of star formation, large interstellar clouds collapse under the influence of
gravity. They are so massive that they fragment into small clouds, each of which may
eventually form a star. Therefore a cluster of stars will be formed rather than just single
stars. The number of fragments depends on the mass of the original clouds, and to some
degree on random chance.
5. Chaisson Review and Discussion 19.8
In what ways do the formative stages of high-mass stars differ from those of stars like the
Sun? (2 points)
High mass stars form much faster and are much more luminous than lower mass stars during
formation. Otherwise, the processes are very similar.
6. Chaisson Review and Discussion 19.9
What are brown dwarfs? (3 points)
If a cloud fragment has a mass less than about 8% of the mass of the Sun, gravity will not be
able to collapse the cloud enough to begin nuclear fusion. Internal pressure is too great for
the weak gravity to overcome, and the collapse halts before the critical temperature of 10
million K is reached. The “failed star” radiates off its excess energy from formation, and is
known as a brown dwarf.
7. Chaisson Review and Discussion 19.12
At what evolutionary stages must astronomers use radio and infrared radiation to study
prestellar objects? Why can’t they use visible light? (3 points)
Radio and infrared observations are used in the study of the initial stages of star formation
because the entire process occurs deep inside a molecular cloud, which itself is deep inside a
dark, dense dust cloud. Visible light cannot escape from this environment but long
wavelength radio and infrared light can. Also, prior to the onset of nuclear fusion,
protostars are typically so cool that they generate primarily infrared light.
8. Chaisson Review and Discussion 19.14
What is a shock wave? Of what significance are shock waves in star formation? (3 points)
Many processes, such as supernova explosions, spiral density waves, and radiation from hot
stars in an emission nebula, can push shells of gas outward at high speed. As these waves of
matter crash into the material nearby, that material gets compressed to unusually high
density. The sheet of gas that “plows” through the surrounding material is called a shock
wave, and they could play a major role in initiating star formation by increasing the local
density of material, giving gravity a hand.
9. Chaisson Review and Discussion 19.17
What do star clusters and associations have to do with star formation? (3 points)
Since the large clouds that stars form from tend to fragment into many pieces, stars tend to
form in groups. Also, star formation in one part of a cloud can induce star formation in
other parts, due to the powerful shock waves caused by the stellar winds generated by
newborn stars. For these reasons, stars rarely (if ever) form alone. Star clusters and
associations can break up over time, however, as individual motions of stars become more
important than the uniting force of gravity.
10. Chaisson Review and Discussion 19.18
Compare and contrast the observed properties of open star clusters and globular star clusters.
(4 points)
Open clusters are young, with many bright main sequence stars, as well as dim, low-mass
stars. Typically there are a few hundred to a few thousand stars, and they have no real
arrangement. These clusters are found in the plane of the Milky Way. Globular clusters are
very old, and contain no bright main sequence stars and numerous red giants. They contain
hundreds of thousands of stars in a roughly spherical shape and are found in the halo of the
Milky Way.
11. Chaisson Review and Discussion 19.19
How can we tell whether a star cluster is young or old? (3 points)
The age of a star cluster is determined by the type of star that is about to leave its main
sequence. The more massive a star is, the faster it uses up its hydrogen fuel on the main
sequence. As the cluster ages, the more massive main sequence stars become red giants and
die out, leaving only the fainter, lower mass main sequence stars. So we locate the most
massive stars in the cluster that are still on the main sequence, and the main sequence
lifetime of such a star is the cluster’s age.
12. Chaisson Review and Discussion 19.20
In the formation of a star cluster with a wide range of stellar masses, is it possible for some
stars to die out before others have finished forming? Do you think this will have any effect on
the cluster’s formation? (3 points)
Low mass stars evolve at a slower rate than high mass ones; this principle applies equally to
the process of formations. If a star cluster forms any O or B stars, they will use up their
hydrogen and die out before many of the lowest mass stars have time to evolve onto the main
sequence. The powerful solar winds from these massive stars as they live or supernova blasts
as they die can significantly affect further star formation, disrupting it in some places and
initiating it in others.
13. Chaisson Problem 19.9
What is the luminosity of a brown dwarf whose radius is 0.1 solar radius and whose surface
temperature is 600 K (0.1 times that of the sun)? (4 points)
4
2
4
2
LBD  TBD   RBD   600   0.1 
6
We use the formula

 
 
 
  110 . So the brown dwarf is
L
T
R
5780
1
 


 
 
about a million times less luminous than the Sun.
14. A protostar can have a temperature of 600 K and luminosity 1000 times that of the sun.
a) At what wavelength is its peak emission? Use Wien’s Law. (2 points)
Wien’s Law:  max
2.9  10 3

meters
T
max =
2.9 x 10-3
600 K meters
max = 4.83 x 10-6 meters
b) What is its radius?
F  Teff 4 and L  4r 2  F . (8 points)
The first step is to find the flux at the star’s surface:
W
F = Teff4 = 5.6697 x 10-8 2 4 x (600 K)4
m K
F = 7.348 x 103 W/m2
Since L = 4r2 x F, then algebraically solve for r, the radius
r =
L
4F
r =
1000 x 3.9 x 1026 W
= 2.06 x 1012 m  3000 rsun !
3
2
4 x 7.348 x 10 W/m