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PHY 150 - Astronomy
Homework Assignment #6
November 27, 2007
1)
Why does the mass of a star play such an important role in determining the star’s evolution?
The mass determines the gravitational pressure at the core of the star. The greater the mass the
greater the pressure, the greater the temperature, the greater the luminosity, the faster the
burning of the star’s fuel, the heavier the elements that can ultimately be burned in the core, and
the ultimate end state of the star when all the fusion processes are exhausted.
2)
On a H-R diagram, sketch the evolutionary
track that the Sun will follow from when it
leaves the main sequence to when it becomes
a white dwarf. Approximately how much
mass will the Sun have when it becomes a
white dwarf? Where will the rest of the mass
go?
Probably about 10 to 20% of the mass will be
blown off after leaving the main sequence, probably
becoming a planetary nebula. The white dwarf will
probably be about 0.8 MSun.
3)
Why do you suppose that all the white dwarfs
known to astronomers are relatively close to
the Sun?
While white dwarfs are hotter than the sun they are also much smaller than the sun, thus, their
luminosity is much less than the sun. This means they cannot be seen at great distances because
their apparent magnitude would be too low.
4)
Suppose that the red-supergiant star Betelgeuse, which lies some 1400 light-years from the
Earth, becomes a Type II supernova.
(A) At the height of the outburst, how bright would it appear in the sky? Give your
answer as a fraction of the brightness of the Sun (bSun).
(B) How would it compare with the brightness of Venus (about 10-9 bSun)?
(A) From Figure 20-22 we see that a typical Type II supernova reaches a maximum luminosity of
L
LSun
= 5 × 108 . The conversion factor for 1 ly = 63239 A.U. The relative brightness of the
supernova is
b
bSun
2
 L   dSun  2
1

8 

=
 = 5 × 10 
 = 6.4 × 10− 8
 63239 × 1400 
 LSun   d 
(
)
(B) Apparently, the supernova would be 64 times brighter than Venus.
5)
In what way are the orbits of stars in the galactic disk different from the orbits of planets in
our solar system?
Astronomers conclude that there are vast quantities of dark matter surrounding our Galaxy
because the rotation curve is fairly flat. This curve requires that a large amount of dark matter lies
outside of the Sun’s orbit.
6)
How do astronomers conclude that vast quantities of dark matter surround our Galaxy?
How is the dark matter distributed in space?
Kepler’s Law of Periods (derived from Newton’s 2nd Law) relates the period of an object to the
radius of the object when the object is circling some massive object, i.e. T 2 ≈ r 3 . Most of the
mass in the Milky Way galaxy lies in the galactic nucleus. Thus, stars in the spiral arms can be
envisioned as circling the galactic center the same way planets circle the sun, i.e. the farther away
from the nucleus the longer the period of rotation about the nucleus, all obeying the same
relationship T 2 ≈ r 3 . This is not observed to be so and it is suggested that the explanation for
this phenomena could be explained by large amounts of dark matter in the Milky Way, outside the
nucleus, which makes this relationship inapplicable.
7)
Why are Cepheid variable stars useful for finding the distances to galaxies? Are there any
limitations on their use for this purpose?
Cepheid variable stars are useful for finding distances because they are are very luminous, they re
recognizable due to their variation, and a definite relation exists between their periods and their
luminosities. Their use is limited to the range where they can be seen as individual stars.
8)
Some galaxies in the Local Group exhibit blue- shifted spectral lines. Why aren’t these blue
shifts violations of the Hubble law?
The Hubble law applies only to galaxies that are not gravitationally bound to the Milky Way.
Therefore some of the local group galaxies show small blue shifts.
9)
As Figure 19-19 shows, there are two types of Cepheid variables. Type I Cepheids are
metal-rich stars of Population I, while Type II Cepheids are metal-poor stars of Population
II.
(A) Which type of Cepheid variables would you expect to be found in globular clusters?
Which type would you expect to be found in the disk of a galaxy? Explain your
reasoning.
(B) When Hubble discovered Cepheid variables in M31, the distinction between Type I
and Type II Cepheids was not yet know. Hence, Hubble thought that the Cepheids
seen in the disk of M31 were identical to those seen in globular clusters in our own
Galaxy. As a result, his calculations of the distance to M31 were in error. Using
Figure 19-19, explain whether Hubble’s calculated distance was too small or too large.
(A) Cepheids are metal-rich stars associated with young star groups (galactic clusters) such as
those found in the Population I stars in the galactic disk. Type II Cepheids are metal-poor stars
associated with older star groups (globular clusters) such as those found in the Population II stars
in the galactic halo.
(B) M31, the Andromeda galaxy, is a spiral galaxy like our own. Thus, the Cepheids in the
galactic disk of M31 are probably Type I Cepheids and intrinsically brighter than the Type II
Cepheids found in globular clusters of our Milky Way Galaxy by a factor of about 3. By
assuming these stars were dimmer to start with, he would have concluded that they were closer
than brighter stars further away. Thus, he would have concluded that M31 was closer by a factor
of 3 .
10) Do Starry Night exercise 24-61.
My best guess:
M87 giant elliptical galaxy, E0
M101 normal spiral, Sc
M104 normal spiral, Sa
M102 elliptical, E7