ASTR 10, Vista College, Spring 2004 - Instructor: Dr. Korpela
Homework #5: Due May 13, 2004
Briefly explain all answers.
Galaxies: Origin and Evolution(25 points)
- Origin/Formation of our Galaxy:
- Draw an edge-on view diagram of our Galaxy. Label all
of the following: disk, halo, bulge, globular clusters, open clusters, and
the location of the Sun.
- How do the orbits, ages, and heavy-element abundances of
the different populations of stars support our basic understanding of
how the Galaxy formed? (i.e. How does the observational evidence match the
predictions of this theory?)
- What observations don't fit into this basic understanding?
- Why do we believe that galaxy collisions are likely, but
star collisions are not?
- What evidence do we have that galaxies collide and merge? Be specific.
Galaxies: Mass and Dark Matter (20 points)
- The gravitational influence of mass contained within an orbit of a
particular size determines the speed (and therefore period) of that orbit.
So by measuring the period and size of the orbit, we can determine
the mass inside the orbit. This is one method you can use to determine
the mass of Jupiter (by looking at the orbits of its moons).
(Mathematically, the expression for the mass enclosed within an orbit
of radius r is M = v2r/G, where G is Newton's
gravitational constant (numerically equal to
4.30 x 10-6(kpc/M
)·(km/s)2) and v is the orbital speed of a star at
distance r. This formula is essentially another way of writing Kepler's
Law Porb2 = constant * r3.)
This concept works equally well for the orbits of stars and gas within
spiral galaxies. By looking at the mass inside the orbit of stars or gas
at different distances from the center of the galaxy, the mass of a galaxy
as a funcion of radial distance from the center (the mass of a galaxy INSIDE
radius r) can be obtained from the rotation curve of the galaxy.
Basically, both when discussing the orbits of planets around a star, or
the orbits of stars around the center of the galaxy, the mass inside
the orbit determines, via gravity, the properties of the orbit. The
difference here is that if you look at a bigger orbit (farther from the
center), the mass inside that orbit is bigger than the mass inside the
smaller orbit (something that doesn't happen with different-sized orbits
around stars - remember that the mass of the planets is insignificant
compared to the mass of the star).
Measuring the Mass
Shown above are two possible rotation curves of the Milky Way Galaxy.
(Neither one is necessarily correct.)
- Compared with rotation curve B, does rotation curve A yield a larger,
or smaller, mass for the Milky Way Galaxy within a radius of 8 kpc? Why
(Hint: This is equivalent to asking, "What would happen to the
speed of the Sun's orbit around the Galactic Center if the mass enclosed
were larger or smaller than it is?")
( Bonus: By what factor? (You can use ratios to solve this, or
calculate the mass within 8 kpc in each case.))
- Once you look at stars which are far enough out that essentially all
of the mass is inside their orbit, what happens to the orbital velocity
of stars/gas as you keep looking at stars farther from the center? (Note that
the mass enclosed within radius r is no longer changing.) Which curve would
be true in this case? (Hint: Think about the orbital velocities of
planets at different distances from the Sun).
- We know that the luminous
material (stars, gas) in the Milky Way Galaxy extends out to a radius of
14 kpc, and becomes quite faint beyond that. Suppose rotation curve B is
correct. Does this match your prediction in part (b)? If not, what must
be true at radii larger than 14 kpc? Why?
(Hint: If the mass was traced by the luminous matter, how much would
the mass enclosed increase as you go beyond 14 kpc? What what would happen
to the velocity outside 14 kpc? Your answer to the part (b) of this
question will help here).
The rotation curve of the Milky Way Galaxy is
more like curve B than curve A! So there is matter that
we cannot see: Dark Matter! In fact, only about 1% to 10% of our Galaxy's
mass is luminous.
We have also applied this method to other spiral galaxies. We can estimate the
the expected mass of a galaxy based on its brightness and distance. This
gives us an estimate of the mass of the luminous matter in the galaxy.
curve method tells us the mass based on the gravitational influence of
all the mass in the galaxy. For most galaxies, the luminous mass is in
the neighbourhood of 10 times less than the mass determined from the
rotation curve method. Therefore, a significant fraction of the mass of
the galaxy must be in dark matter.
In the previous question, we learned that we infer the presence of dark
matter by measuring the mass of spiral galaxies. What is some additional
evidence for the presence of dark matter in galaxy clusters?
- Bonus: Discuss the similarities and differences
of at least 2 methods of measuring the masses of galaxies (eg: rotation
curve of spiral galaxy, width of absorption lines in galaxy spectrum,
motions of galaxies or gas in a cluster).
Galaxies: Distances (30 points)
- Determining Distances:
There are only two main methods of determining distances to galaxies
and galaxy clusters. We use either "standard candles" (like the peak
luminosity of white-dwarf supernovae) or "standard rulers" (like the
size of HII regions).
- For one of these, explain how we can use these objects to determine the
distances to galaxies. (What property of a standard candle (or ruler) allows
us to determine the distance, and how? What measurements must be made in
order to determine the distance?)
- Explain why calibrating these standard objects is required,
and what is involved. (Hint: We discussed this issue when we talked
about using spectroscopic parallax to determine the distances to stars.)
- Hubble's Law
Hubble's Law says that the expansion of space between the galaxies is
simply v = Hod, where v is the apparent recessional velocity
of a galaxy, Ho is the Hubble constant, and d is the distance
of the galaxy.
- What observations are necessary in order to determine the Hubble
constant? (Hint: What properties of galaxies do we need to measure?
For just one galaxy, or for many?)
- What sorts of observations do we need to make to determine these
quantities? Which is the most difficult to measure?
- Assume that you have now measured the Hubble constant. (In
essence, you have now calibrated Hubble's Law). How do
the large redshifts of quasars lead us to conclude they must be very
- If a star in our own Milky Way Galaxy is measured to have a
redshifted spectrum, can the redshift be used with Hubble's law to determine
the distance to that star?
Galaxies: Centers (25 points)
- Evidence for a theory: We believe (based on Hubble's Law) that the
large redshifts of quasars indicate that they lie at large distances from us.
We also believe that these objects are the bright active cores of distant
galaxies. What additional evidence do we have (beyond quasar
redshifts) that quasars occur in distant galaxies?
- Milky Way Galaxy:
Describe at least two observations of our
Galaxy's central region that support the hypothesis that it is occupied by
a supermassive black hole. How do these observations fit that theory?
- Unified Model of AGNs and Quasars:
- Briefly describe the unified model that explains Active
Galactic Nuclei and quasars. (i.e. What is causing the extraordinary
- In this model, what role do collisions and mergers play in triggering
- What evidence do we have that quasars must be triggered by collisions
- Bonus: Why are there few quasars at low red shifts and at high red
shifts, but many at red shifts of about 2?