Download Question C:

Question C:
Describe the different features of the Milky Way Galaxy, as well as its nearby region. Include details such as
positions, distances, shapes, compositions, and ages of the various components.
Position
Distance/Size
Shape
Composition
Age
Center
8.5 kpc
“Sphere”
Pop I
Young & old
All around
50 kpc diam
Flat
Pop I / Dust
Young & old
In disk
We’re in one
“Spirals”
Pop I
Young
Globular
Clusters
“All over” 50-100 kpc diam
Spherical
Pop II
Old
Halo
“All over” 50-100 kpc diam
Sphere?
Pop II and
Dark Matter
Old
LMC. SMC,
Dwarfs
“All over” 15-100 kpc away
Blobs
Pop I /II ?
?
Bulge
Disk
Spiral arms
Question B:
Compare the light gathering power, diffraction-limited (theoretical) resolution, practical resolution (“seeing”),
and sensitive wavelength range for each of the following telescopes:
• The Keck Ten Meter Telescope
• The Hubble Space Telescope
• One Antenna in the Very Large Array
Note that the Keck has a 10m aperture, the HST is 2.4m (pg. 185 in Zeilik), and the VLA antennas are 25m in diameter (Fig.9-9). Also,
Light Gathering Power ∝ (diameter)2
Theoretical resolution ∝ λ/d
Practical resolution ≈ 1.0 arc second for optical wavelengths on earth
LGP
Theo Res’n
Prac Res’n
λ Range
Keck
≡1
0.01’’
(at 500 nm)
1.0”
“Visible”
HST
0.242=0.06
0.04”
(at 500 nm)
≡ Theo Res’n
“Visible” plus
Near IR and UV
VLA
2.42=6
2000”
(at 21 cm)
2000”
“Radio”
Part II Answer two of the following three questions. Each is worth 20 points.
Answer the questions in a complete but succint form. Justify your answers with numbers wherever possible.
Each can be answered in no more than one written page, but you may use more paper if you feel it is necessary.
Question A:
Discuss three different ways to plot an HR diagram. What are the advantages and disadvantages of each?
Advantages
Disadvantages
“Historical”:
Magnitude vs.
Spectral Type
Low-tech
Shows main features
Imprecise (Spectral Type)
“Practical”:
Color-Magnitude
(V vs. B-V)
Direct from observation
Well-defined quantities
Skews MS at low and high T
Needs sophisticated instruments
“Physical”:
Luminosity vs.
Temperature
Calculated quantities
Shows physical basis
Can’t measure either axis directly
Other different combinations would include absolute or apparent magnitude for the vertical axis,
along with some measure of temperature horizontally. Absolute magnitude is necessary to show
the important features, but requires that we know the distance to each star on the diagram.
Apparent magnitude does not require us to know the distance, but is only useful if all the stars on
the plot are at the same distance, such as in a cluster.
Problem 4:
a. (5 pt): An A0 star moves radially away from us at 300 km/sec. What is the observed wavelength of the Hα
Balmer absorption lines?
The wavelength shift ∆λ is given nonrelativistically by
3
∆λ
v
300 × 10
------- = -- = ------------------------ = 10 – 3 « 1
8
λ
c
3 × 10
which justifies the nonrelativistic approximation. Since the star is moving away from us, it is
“red” shifted, i.e. its wavelength increases, so
λ = λ 0 ( 1 + ∆λ ) = λ 0 × 1.001
where λ0 is the “laboratory” value for Hα radiation. You can either calculate this from Zeilik
Eq.8-25, or just read it from pg.159. The value is λ0= 656.3 nm so λ= 657.0 nm.
b. (5 pt): A B0 main sequence star has an apparent visible magnitude of +2.5. What is the star’s apparent blue
magnitude? (Zeilik Table 11-1 defines “visible” and “blue” in this context.)
The easy way is to look up B−V=−0.30 for a B0V star in table A4-3, so B=2.5−0.3=2.2.
The hard way is to first get the temperature of a B0 star from Figure 13-6 (25,000K), and calculate B−V=−0.52 using Equation 11-11a (although it is not meant for such hot stars).
c. (5 pt): In a certain star, hydrogen absorption lines are easily observed, but calcium and iron lines are also
obvious. Estimate the star’s surface temperature and spectral type.
In order for both hydrogen and Ca/Fe lines to be easily observed, you need a “middle temperature” star, either an A or F spectral type. (See Table 13-1.) From Figure 13-6, this would be
somewhere between 6000K and 10,000K.
Problem 3: Calculate the radius of a K5 giant star, using its spectral type and luminosity class,and the StefanBoltzmann Law.
This problem is done exactly as the example in the Week 4 Wednesday lecture (a G0 supergiant),
which is the same as Homework problem 13-15 (an M supergiant and M main sequence star).
Note that a “giant” star means Morgan-Keenan luminosity class “III”.
From table A4-3, a K5III star as
• T = 3700K
• MV = −0.3
• BC = −0.71
and therefore
MBOL = MV + BC = −1.01
log(L/LSUN) = 1.89 − 0.4MBOL = 2.29
L/LSUN = 102.29 = 195
Now use the Stefan-Boltzmann Law:
4
R 2 T
L
-------------- =  --------------  --------------
R
 T

L SUN
SUN
SUN
and the surface temperature of the sun (5780K) to write
5780 4
R 2
 ------------- = 195  ------------
 3700
R

SUN
which gives R = 34 RSUN. This is in good agreement with Table A4-3 which says R = 25 RSUN.
Problem 2: Using HR diagrams found in your textbook, estimate the distance to M3, including a rough estimate
of the range of acceptible values. Explain whether or not this distance makes sense, given the type of object
which is M3 and what you know about our galactic environment.
Zeilik, Fig. 13-10 is an HR (color-magnitude) diagram for the globular cluster M3.
At B-V=0.4, where there are some obvious main sequence stars, we read
18.5 ≤ mV ≤ 19.5
We can find the absolute magnitude MV at B-4=0.4 from a couple of places:
• Table A4-3 says that MV≈3.5
• The HR diagram used with the Hoff exercise on Distance to the Pleiades says MV≈4
• Fig. 13-15 implies that MV≈4 for Main Sequence stars
We therefore have a distance modulus
14.5 ≤ mV −MV ≤ 16.0
Since absolute and apparent magnitude are related by m-M=5logd-5, we write
19.5 ≤ 5logd ≤ 21.0 so that
7.9 kpc ≤ d ≤ 16 kpc
This range of distance makes perfect sense. Globular clusters are scattered symmetrically about
the galactic center, throughout the galactic halo. We are a distance of 8.5 kpc from the galactic
center, so M3 seems to be a relatively close globular cluster, and it is not surprising that it made
it into Messier’s catalog.
Part I: Answer all four problems in this part. Each is worth 15 points.
Indicate any figures or tables you use in your calculations. Show all Work!
Problem 1: Star #1 is 256 times brighter than star#2. They are at the same distance from us.
Parts (a) and (b) are based on the Stefan-Boltzmann Law, L=4πR2σT4. For two stars, this implies
2
4
L1
 R 1  T 1
------ =  ------  ------ = 256
L2
 R 2  T 2
a. (5 pt): If the stars have the same radius, what is the ratio of their surface temperatures?
R1 = R2 ⇒ T1/T2 = 2561/4 = 4
b. (5 pt): If the stars have the same surface temperatures, what is the ratio of their radii?
T1 = T2 ⇒ R1/R2 = 2561/2 = 16
c. (5 pt): If both are Main Sequence stars, estimate the ratio of their masses.
For Main Sequence stars, the “mass luminosity relationship” tells us that
L 1  M 1 3
------ ≈  --------
L 2  M 2
so M1/M2 ≈ 2561/3 = 6.3
Exam #1
79205 Astronomy
Fall 1996
NAME:
Solution Key
You have two hours to complete this exam. Part I has four problems, each worth 15 points. You are to
solve each of them. Part II has three “essay” questions, each worth 20 points, with more freedom in how you
may respond. You are to answer two of them.
You may use your textbook (Zeilik), workbook (Hoff), and class notes and handouts. You may not share
these resources with another student during the test.
GOOD LUCK!
Part I:
Problem
Score
1.
2.
3.
4.
Part II: Circle the two questions you chose to answer
Question
A.
B.
C.
Total Score:
Score