Astronomy Assignment #7: Structure of the Milky Way II
Your Name______________________________________
Your Class Meeting Time __________________________
This assignment is due on Monday 26, Oct and Tuesday, 27 October
Submit this cover sheet with your assignment.
Complete the assigned problems from the text listed below and address the Instructor Assigned Topic. Mathematical
problems may be hand written. Write out the problem, show your work in solving the problem and state your answer in a
complete sentence. Failure to complete all three of these tasks will result in less than full credit awarded.
1. What is the winding dilemma as it relates to spiral arms in galaxies and what does the winding dilemma forbid
regarding the speed or rotational period of spiral arms in galaxies?
The winding dilemma is the paradox created if we assume that spiral arms are simply a pattern of stars that
moves with the stars. If we assume that the spiral arm is just composed of a fixed set of stars that participate in
the galactic rotation, then these arms must “wind up” after just a few galactic rotations since the rotation curve
for spiral galaxies is so flat. The flat rotation cure demands that stars closer to the center complete one orbit
around the galaxy in a shorter time that stars farther from the center. Thus the inner portion of the spiral arm (if
it is just a group of stars) will complete one rotation is a shorter amount of time and the arms will “wind up” like
a clock spring and quickly lose their distinctive spiral appearance. The dilemma arises because we do not see
“wound up” spiral arms in other galaxies. This lack of observation implies that spiral arms are long-lived and
stable features of galaxies. Since spiral arms appear to be a stable then they must not be just a group of stars
rotating with the other stars. This is the winding dilemma – If spiral arms are just a group of stars they should
wind up and disappear, but spiral arms are long-lived stable structures in galaxies.
2. How does the density wave theory explain why stars form in
spiral arms?
The density wave theory proposes that spiral arms are a
manifestation of a density or compression wave that is
revolving around the galaxy. The shape of this density way is a
spiral as a result of the rotation of the stars in the galaxy. An
important fact regarding the density wave is that the wave
speed is slower than the orbital velocity of stars in the disk of
the galaxy. As a result of the slower wave speed, giant
molecular clouds that orbit with the stars move into the back of
the slower density wave. Within the density wave the GMC is
compressed and begin to collapse, fragment and form stars.
The short-lived very–luminous O & B stars define the beginning
of the spiral arms but do not live long. Where these short-lived
high-luminosity stars expire defines the end of the spiral arms. Other stars that formed from the GMC are much
less luminous and continue to revolve around the galaxy leaving the slower density wave that initiated their
formation behind. The figure to the right sums up the process and compares the GMC-Density Wave relationship
to a traffic jam.
3. In what way is a density wave like a traffic jam? What happens to a GMC as it moves into a density wave from
behind?
See the question 2 above. The figure in question 2 addresses this question.
4. How do astronomers know the dark matter halo (corona) exists if it does not radiate anything our telescopes can
detect?
The existence of dark matter is most firmly established in the interpretation of the galactic rotation curve. The
fact that the galactic rotation curve indicates that orbital speeds of stars and gas clouds DO NOT decrease as you
move away from the center of the galaxy indicates that the mass enclosed within orbits DOES NOT decrease as
the orbits get larger. This failure for that mass enclosed in these large orbits (greater than 18 kpc radius) cannot
be explained using the observed distribution of stars and gas clouds that clearly are decreasing with increasing
orbital radius. Thus there must be some unseen matter, a.k.a. dark matter, that we cannot detect any other way
except through its gravitational influence on the orbital velocity of stars.
There is other evidence for dark matter but it is always related to the gravitational influence dark matter exerts on
the system of objects under study. For example, other spiral galaxies also have flat rotation curves that indicate a
large amount of unseen mass in a halo around the galaxy. There are rich galaxy clusters whose individually
measured velocities are too large for the galaxies to be bound to the cluster. These high speed galaxies should
escape the cluster but, since they don’t, there must be unaccounted for invisible mass (i.e. dark matter) in the
galaxy cluster that provides the greater gravitational force to hold these galaxies in the cluster.
5. Scientists are advocating a focused search for extra-terrestrial intelligence that looks at stars relatively abundant in
elements heavier than helium because those are the elements from which life could possibly form. What part(s) of
the Galaxy would such stars be found and what are the distinguishing orbital characteristics of such stars?
In the beginning right after the Big Bang there was only hydrogen in the universe and the first stars were made of
only hydrogen. When the very first O and B stars supernova, they create all the elements on the Periodic Table of
Elements and disperse these newly formed elements into the interstellar medium (ISM e.g. space). These newly
created heavy elements mix with the primordial hydrogen to form Giant Molecular Clouds (GMC) that are now
just slightly enriched in these new heavy elements. A second generation of stars forms from this enriched GMC
and create stars slightly enriched in these heavy elements. The cycle repeats again and the supernovas from these
second generation stars produce and disperse more heavy elements into the ISM. New stars form with even a
greater enrichment of heavy elements and so the cycle continues where O & B stars create and disperse heavy
elements that then are incorporated into the next generation of stars.
The stars with the greatest enrichment of heavy elements will be those stars that have most recently formed and,
in the Milky Way galaxy, star formation is currently occurring only in the disk and bulge of the galaxy. These
enriched stars are called Population I stars. The stars in the disk of the galaxy are in circular orbit around the
center of the galaxy. In the bulge the stars are in randomly oriented elliptical
There is no star formation in the halo of the Milky Way so the stars there (mostly in globular clusters) are very
poor in heavy elements and are not likely to harbor life. These stars that are poor in heavy elements are called
Population II stars.
So…to get back to the question, you would look to find stars enriched in heavy elements in the disk and bulge of
the Milky Way and not in the Halo.
6. How do astronomers know that there is a very massive black hole at the center of the Galaxy?
There are two lines of evidence that a black hole exists in the center of our galaxy. First, the galactic rotation
curve allows astronomers to calculate the mass and therefore the density of matter as a function of distance from
the galactic center. These calculations indicate that the density of matter increases to a phenomenal value of
400,000 solar masses per cubic parsec (See the Milky Way Data Sheet) within the closest few parsecs of the
galactic center. This density corresponds to about 4 million main sequence M stars per cubic parsec which is an
unsustainably large density. Surely stars packed that close together (remember the density of stars around the
Sun is equivalent to about 1 main sequence M star per cubic parsec) would collide and merger into a larger
object. It is this very large density that suggests that a black hole resides in the center of the Milky Way galaxy.
The second and conclusive line of evidence that a black hole exists in the Milky Way galaxy derives from the orbit
of the star designated as S2. This star has been under close observation by astronomers since the 1990’s and they
have observed its orbit around a seemingly empty point in space designated as Sgr*. From the orbital period and
semi-major axis of S2’s orbit the mass of the central (invisible) object can be simply calculated. The result of that
mass calculation is that an object with a mass of several million solar masses (various estimates place the mass of
the object to be about 4.5 million solar masses) resides within the orbit of S2. The only type of object this could
be given its mass and the constraint on its size (less than a light day in diameter) is a supermassive black hole.
7. If there were no black hole in the center of the Galaxy, how would the orbits of the stars near the Sun be affected?
(Hint: compare the mass of the black hole to the total mass inside the Sun's orbit [black hole mass/total enclosed
mass]---would the gravity change significantly?)
Even though the mass of the supermassive black hole at the center of the Milky Way is severa; million solar
masses, the black hole represents only a small fraction of the mass within the Sun’s orbit. In fact the fraction of
the mass with in the Sun’s orbit attributable to the super massive black hole at the center is just
4.5 Million Solar Masses
 0.000045
100 Billion Solar Masses
This fraction of the mass within the Sun’s orbit that is attributable to the supermassive black hole is
extraordinarily tiny. Since the Sun’s orbit is determined by how far it is from the galactic center and the amount
of mass within its orbit around the galaxy, plucking out the supermassive black hole at the center of the galaxy
will have an immeasurably small effect on the Suns’ orbit.
8. Given that the period of the Sun’s revolution around the Milky Way galaxy is 240 Million years, calculate how
many times the Sun has completed an orbit around the galaxy since the Sun formed.
The number of times the Sun has completed a revolution around the galaxy in the Sun’s lifetime is given by the
ratio of the Sun’s age over the revolution period of the Sun:
4.6 Billion years
 19.2
240 Million Years
The Sun has completed about 19.2 revolutions around the galaxy since the Sun was created. Thus, you could say
that the Sun is about 19 galactic years old…just a teenager.
9. Besides revolving around the center of the Milky Way, the Sun is also bobbing or oscillating vertically as it
resolves (somewhat like a dolphin bobbing in and out of the ocean). Given that the period of the vertical
oscillation for the Sun perpendicular to the galactic mid-plane is 70 million years, (a) how many times does the
Sun pass through the galactic mid-plane in one orbit around the galaxy and (b) how many times as the Sun passed
through the mid-plane of the galaxy since the Sun was formed?
a) The number of time that the Sun has passed through the galactic mid-plane during one galactic revolution is
found by first finding the number of times the Sun has completed one vertical oscillation as completes one
revolution. The number of vertical oscillation the Sun completes in one galactic rotation is simply given from
the ratio of the oscillation period to the revolution period:
240 Million years
 3.43
70 Million Years
The Sun completes about 3.43 vertical oscillations during each galactic revolution. Here is the tricky part…the
Sun passes through the galactic mid-plane twice every vertical oscillation – once on the way up and once on the
way down. So the Sun then must cross the galactic mid-plane about 6.8 times during each galactic revolution.
b) To answer “How many times as the Sun passed through the mid-plane of the galaxy since the Sun was
formed?” we can repeat the calculation in part (a) but substitute the age of the Sun for the revolution period
of the Sun around the galaxy. Alternately, we can use the result of question 8 that tells us the Sun has made
19.2 revolutions around the galaxy and during each revolution around the galaxy the Sun passes through the
galactic mid-plane 3.43 times (part (a))to determine that Sun has passed through the mid-plane of the galaxy
19.2×3.43 = 65.9 times.
Instructor assigned topic.
1. Create a scale drawing edge-on and face-on of the Milky Way
using the parameters from the Milky Way Data Table at the
right. Also include (to scale) the limit of visibility in the disk of
10,000 ly. You may choose your scale and the size of paper
you which to use. Points awarded for accuracy to scale.
Diameter of Galactic Disk
36 kpc
Thickness of Galactic Disk
600 pc
Diameter of Central Bulge
3 kpc
Galactic Bar Length
8 kpc
Angle of Galactic Bar to the Line
between the Sun and Galactic Center
44 ± 10
Diameter of Halo
30 kpc
Distance of Sun from Center
9 kpc
Distance of Sun above Galactic Plane
14 pc