Download Problem 4 : a. (20 points)

Problem 4 : As discussed in class, recent observations of stars within 0.1 pc of the center of our
galaxy show that they move with speed approximately 300 km/sec.
a. (20 points) Assuming circular orbits about the galactic center, calculate the mass within 0.1 pc
of the center. Express your answer in terms of solar masses.
As we’ve discussed many times in class, for a mass m moving with speed v in a circular orbit of radius r about a much larger mass M, F=ma is written as
v2
GMm
-------------- = m ----r
r2
which tells us that the “mass in the middle” is
36
6
v2r
M = -------- = 4.2 ×10 kg = 2.1 ×10 solar masses
G
b. (5 points) Argue that it is very unlikely for this mass to be made up of ordinary stars.
From Table A4-1, the nearest star to us is 1.31 pc, so the local density of stars is
something less than one per cubic parsec. This is consistent with one of our past
studio exercises (on interstellar reddening) where we were told that the local density
of stars is something like 0.1 per cubic parsec.
If the center of our galaxy were made up of ordinary stars, this problem suggests a
stellar density of 2 million per 0.13 cubic parsecs, or about 20 billion times the local
stellar density. This would be like having several suns within the size of our solar
system, which is much larger than we see anywhere else in the galaxy.
Instead, we believe the center of our galaxy is occupied by a giant black hole.
Problem 3 (25 points): Five galaxies are listed. (All are Messier objects). Five answer columns
are also listed, corresponding to the five descriptive phrases listed below. Put a check (✓) in the
corresponding box if that descriptive phrase applies to that galaxy. (One point for each box.)
Galaxy
M31
A
C
✓
D
✓
✓
M32
M77
B
✓
M82
M87
✓
E
✓
✓
✓
✓
✓
✓
✓
A.) Spiral galaxy
B.) Elliptical galaxy
C.) Active galaxy
D.) Significant (typical or greater) star formation in progress
E.) Member of the local group
Note that Appendix 1 lists the Messier objects, including their type. Note also that
M82 is a “starburst” galaxy, which the text associates with being an “active galaxy”.
If you didn’t check box C for M82, you’ll still get credit if you explained why not.
Problem 2 (25 points): Use Zeilik Table 24-1 and Figure 24-2 to determine the distance to the
Seyfert galaxy Markarian 79. Clearly indicate the values you assume for any other parameters.
According to the figure caption, the prominent emission lines in Figure 24-2 are Hβ,
and two lines of OIII. These can be associated with the lines listed in Table 24-1 if
we allow for some redshift:
Line
Hβ
OIII
OIII
λ0
4861
4959
5007
λ
5050
5150
5200
z=(λ−λ0)/λ0
0.0391
0.0385
0.0386
Each line is consistent with a redshift z ≈ 0.039. According to Hubble’s Law, the
distance to the galaxy is given by Equation 22-3c, namely
cz
d = ----- = 156 Mpc
H
where we’ve assumed a value of H = 75 km/sec•Mpc.
Problem 1: The spectral type of a certain main sequence star is precisely determined to be F5. Its
apparent visual magnitude is 14.90 and its apparent blue magnitude is 15.85.
a. (20 points): Find the distance to the star, accounting for interstellar reddening.
Table A4-3 (in the appendix) tells us that an F5 star has absolute visual magnitude
MV=3.4 and an intrinsic color index B−V=0.45. The observed color index is taken
from the apparent magnitudes given, namely B−V=15.85−14.90=0.95, where the
difference between intrinsic and observed is due to interstellar reddening.
The “color excess” is CE=0.95−0.45=0.50 (Zeilik Eq.19.3) and the total visual
absorption is AV≈3×CE=1.5 (Eq.19.4). We can then determine the distance from
m V – M V = 5 log d – 5 + A V
(Eq.19.2), and therefore logd = (14.90−3.4+5−1.5)/5 = 3 or
d = 10 3 pc = 1 kpc
b. (5 points): Does it seem that you are viewing the star through a dense dust cloud, or simply
through the average interstellar medium? Explain your answer.
It appears that we are viewing this cloud through the average interstellar medium.
From the average amount of dust in the galactic disk, we expect to see between one
and two magnitudes of visual absorption per kpc. (See class notes, or Zeilik page
369.) In this problem, the absorption is 1.5 magnitudes over 1 kpc, which is just
what you’d expect if there were no extra-dense clouds in the way.
Exam #3
79205 Astronomy
Fall 1996
NAME:
Solution Key
You have two hours to complete this exam. There are a total of four problems and you are
to solve all of them. All the problems are worth the same number of points.
You may use your textbook (Zeilik), workbook (Hoff), and class notes and handouts, or
other books. You may not share these resources with another student during the test.
Indicate any figures or tables you use in your calculations. Show all Work!
GOOD LUCK!
Problem
Score
Worth
1.
25
2.
25
3.
25
4.
25
Total Score:
100