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1. a. A white dwarf
becomes a "black dwarf" when its surface temperature decreases to
the point where its wavelength of maximum emission is in the infrared region
(say, 10000 Angstroms). Use Wien's Law to compute the temperature at which
that occurs.
HINT: This is an application of Wien's Law, except that we are looking for temperature instead of
lambda-max.
b. From the time the
white dwarf "starts out" (ie, its star
dies) at an initial temperature of 50,000K, how long does it take to
"vanish" if we assume that they cool down at a rate of 2 X 10-5
K per year?
HINT: There is no equation for this problem. Just figure out
how far the temperature must drop from the original value, then use the
information in the problem to compute how many years required for the
temperature to drop that far! Should be a LOT of years!
2.
The prominent "Balmer Alpha Line," caused
by the Hydrogen atom, was first seen in the Sun, and has been found in all
stars. The rest wavelength of this line is 6563 Angstroms. Use the Doppler
Effect to compute the direction and value of the line-of-sight velocity (in
km/sec) of stars where this unmistakable line is seen at
- 6561.2 Angstroms
- 6571.5 Angstroms
- 6595.7 Angstroms
HINT: This problem asks you to utilize the Doppler Effect. The first step is always to
calculate the Doppler Shift, the difference between the observed wavelength
and the "rest" wavelength. By looking at the sign of that
difference (- is a blueshift, + is a redshift), you
can immediately tell whether the object is coming towards us or moving away
from us. Divide the shift by the rest wavelength, and then multiply by c, the
speed of light, to get the speed of the star. The units for the velocity of
the star will be the same as the ones you chose for the speed of light.
3. Below are two tables of star data, one for the nearest
stars, the other for the brightest
stars. The tables contain information on the stars' temperatures as
well as information on their absolute magnitudes. Absolute magnitude is
a measure of how truly bright a star is. The absolute magnitude system
is a "backward" system: the smaller the value of
absolute magnitude, the brighter the star is.
a. Make a large, whole-page graph with
temperature on the x-axis and absolute magnitude on the y-axis. In one
color (say, pencil) put the nearest stars on this graph. Then, in a
different color (say, blue ink) put the brightest stars on the graph.
There is no need to label the points.
b. Are the stars evenly distributed on the
graph? Are there any obvious patterns? Describe these patterns,
if any.
c. Of the nearest stars, are the majority
dimmer than the Sun, or brighter?
d. Of the nearest stars, are the majority
hotter than the Sun, or cooler?
e. Most of the brightest stars are more
luminous than the Sun. Are most of these stars hotter than the Sun, or
cooler? Explain how this makes sense, in view of the relationship
between luminosity and temperature.
f. There are a some very luminous stars
that are cooler than the Sun, yet more luminous than the Sun. Looking
at the formula for luminosity, explain how
this can be so.
The
Nearest Stars
|
Name of
star
|
Absolute
magnitude
|
Temperature
|
|
Sun
|
+4.85
|
5700 K
|
|
Proxima Centauri
|
+15.5
|
2600 K
|
|
Alpha Centauri A
|
+4.4
|
5800 K
|
|
Alpha Centauri B
|
+5.7
|
4000 K
|
|
Barnard's Star
|
+13.2
|
2600 K
|
|
Wolf 359
|
+16.7
|
2400 K
|
|
Lalande 21185
|
+10.5
|
3100 K
|
|
Sirius A
|
+1.4
|
9500 K
|
|
Sirius B
|
+11.2
|
28,000 K
|
|
Ross 154
|
+13.3
|
2650 K
|
|
Ross 248
|
+14.8
|
2500 K
|
|
Epsilon Eridani
|
+6.1
|
4500 K
|
|
Ross 128
|
+13.5
|
2600 K
|
|
Luyten 789-6
|
+14.6
|
2500 K
|
|
61 Cygni
A
|
+7.6
|
4000 K
|
|
61 Cygni
B
|
+8.4
|
3700 K
|
|
Epsilon Indi
|
+7.0
|
4000 K
|
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Procyon A
|
+2.6
|
6500 K
|
|
Procyon B
|
+13.0
|
7000 K
|
The
Brightest Stars in the Sky
(Based on apparent brightness, not luminosity)
|
Name of
Star
|
Absolute
Magnitude
|
Temperature
|
|
Sirius
|
+1.4
|
9500 K
|
|
Canopus
|
-3.1
|
6400 K
|
|
Alpha Centauri A
|
+4.4
|
5800 K
|
|
Arcturus
|
-0.3
|
3900 K
|
|
Vega
|
+0.5
|
9700 K
|
|
Capella
|
-0.7
|
5000 K
|
|
Rigel A
|
-6.8
|
11,000 K
|
|
Rigel B
|
-0.4
|
10,000 K
|
|
Procyon A
|
+2.6
|
6500 K
|
|
Betelgeuse
|
-5.5
|
2700 K
|
|
Achernar
|
-1.0
|
13,500 K
|
|
Hadar
|
-4.1
|
20,000 K
|
|
Altair
|
+2.2
|
7700 K
|
|
Acrux A
|
-4.0
|
19,500 K
|
|
Acrux B
|
-3.5
|
16,500 K
|
|
Aldebaran A
|
-0.2
|
3500 K
|
|
Spica
|
-3.6
|
19,500 K
|
|
Antares A
|
-4.5
|
2700 K
|
|
Pollux
|
+0.8
|
4100 K
|
|
Updated 5/22/02