- Generalized Oort "Constants"
The Oort constants are commonly defined and employed in the solar
neighborhood, but of course their definition could be applied to any
location in the galaxy, or for that matter, to any galaxy.
In addition to flat rotation curves, many galaxies show a region of
"solid body" rotation. Consider a galaxy whose rotation curve is
|V = mR||for||R < R0|
|V = Vf||for||R > R0|
- A. Derive expressions for A(R) and B(R).
- [Hint: what is m in terms of Vf and R0?]
- D. Use the result from (A) to find the orbital
and epicyclic frequencies. Sketch a graph of these.
- C. Consider a pattern like a bar or spiral arms.
Can these be composed of the same stars? (It helps to think of the
spiral arm as a solid piece of string winding out from the center.)
What happens to such a structure in each regime?
- Comment on the identification of Oort's constant A with "shear"
and the description of this rotation curve as "solid body".
- A. Binney & Merrifield 4.12
- B. The current record holder for the most distant quasar is
J2329-0301 at z = 6.43.
Its apparent brightness is J = 21.56.
What is the absolute magnitude of this object?
(The solar absolute magnitude in J is 3.66. You may ignore the K-correction,
but not cosmology:
See BM eqn 7.7. Assume and Ho = 72 km/s/Mpc and qo = 0.)
How does the luminosity of this object compare to that of the Milky Way?
By how much does this change if instead we assume qo = 1/2?
How far off would we be if we ignored cosmology entirely and just used the
usual Euclidean distance modulus?
- C. Using the results of (A) & (B), what is the minimum mass of
the black hole required to power this object?
- Is the Local Group Bound to the Virgo Cluster?
Binney & Tremaine 10-8
It may help to know that Ωo = 0.25.
- Build your own rotation curve
Build your own model galaxy by combining an
exponential disk with an NFW halo.
Plot the rotation curve
showing the disk, halo, and total rotation curve.
What parameters do you have to specify to do this?
Tweak it until your model looks realistic...
How easy is it to get a rotation curve in that is flat
the outer parts of the disk?