Measuring Distance with Spectroscopic Parallax
Most stars are too far away to measure their parallax angles. So, how do we determine
the distance to these stars? A method, known as spectroscopic parallax is used. The
method is as follows:
1)
2)
3)
4)
measure the brightness of a main sequence star
determine the star’s temperature from its spectral type
knowing the star’s temperature, use the HR diagram to estimate its luminosity
use the brightness and luminosity to calculate the distance to the star
In this lab activity, we will use the method of spectroscopic parallax. You are given the
brightness and spectral type for a number of stars. You will use the method outlined
above to find the distance to these stars.
Finding the Temperatures of the Stars
In Table 1 are data for several main-sequence stars, including their brightness (as viewed
from Earth) and spectral type. This is the kind of data astronomers can obtain for far
away stars. Use the spectral types of the stars and the table of temperatures provided in
Appendix 1 to determine the temperatures of these stars. Record the temperatures in
Table 1.
Finding Luminosity Using the HR Diagram
At the end of this activity packet is an HR diagram that you made earlier in this course.
The Luminosity of the stars (in units of Suns) is plotted versus the Temperature of the
stars in Kelvin (in reverse order). When using this graph, remember that the vertical axis
is plotted on a logarithmic scale, and note that the tick marks on the horizontal axis are
each worth 500 degrees K.
1. Print out the HR diagram.
2. Using a pen or pencil, draw a smooth best-fit curve that runs through the middle
of all of your main sequence stars. Just ignore the red giants and white dwarfs
for this activity. Note that this will not be a straight line; it will curve slightly.
And, it will not go through all the points. Just get it as close as you can to as
many of the points as possible.
3. Now, note the temperature you recorded for Star #1 in Table 1. Find this
temperature on the horizontal axis of the HR diagram. Then, move straight
upward on the graph until you get to the line you drew through the main
sequence. On the vertical axis, read off the luminosity, in Suns, for this star with
this temperature. Record this luminosity in Table 1.
4. We will now convert the luminosity in Suns to units of Watts. To do this, just
multiply the number in Suns by the luminosity of the Sun, which is 3.846 x 1026
Watts, and record this in the next column of Table 1.
5. Repeat these steps for the rest of the stars, so that you have all of their
luminosities in Watts.
Finding the Distances to the Stars
Using the data you have so far, you can determine the distance to each of your stars.
Recall that there is a relationship between brightness, luminosity, and distance.
B
L
4 d 2
This can be rearranged such that, if you know the brightness and luminosity, you can
calculate the distance,
L
,
d
4 B
Where L is in Watts, B is in Watts per square meter, and d comes out in meters.
1. Using the given brightness (in Watts per square meter) and the luminosities you
found (in Watts), calculate the distance to each star and record the distances (in
meters) in Table 1.
2. There are 9.46×1015 meters in one light-year. Convert your distances to lightyears by dividing the distance in meters by this number.
3. Recall that our Milky Way galaxy is 100,000 light-years across. For each of your
stars, use the space below to explain whether it is most likely inside our galaxy or
outside our galaxy.
Table 1 – Star Properties
Star
Spectral
Type
Temperature
(K)
Brightness
(Watts/m2)
#1
B2
4.00×10−10
#2
A0
3.42×10−10
#3
G0
1.37×10−10
#4
B5
1.90×10−15
Luminosity
(Suns)
Luminosity
(Watts)
Distance
(meters)
Distance
(lightyears)
Table 2 – Approximate Temperatures of Main-Sequence Stars
Spectral
Type
O5
O6
O7
O8
O9
B0
B1
B2
B3
B5
B6
B7
B8
B9
A0
A1
A2
A3
A4
A5
A7
F0
F2
F3
F5
F6
F7
F8
Temperature
(K)
54,000
45,000
43,300
40,600
37,800
29,200
23,000
21,000
17,600
15,200
14,300
13,500
12,300
11,400
9600
9330
9040
8750
8480
8310
7920
7350
7050
6850
6700
6550
6400
6300
Spectral
Type
G0
G1
G2
G5
G8
K0
K1
K2
K3
K4
K5
K7
M0
M1
M2
M3
M4
M5
M6
M7
M8
Temperature (K)
6050
5930
5800
5660
5440
5240
5110
4960
4800
4600
4400
4000
3750
3700
3600
3500
3400
3200
3100
2900
2700
100000
10000
1000
10
1
0.1
0.01
0.001
0.0001
0.00001
25000
20000
15000
10000
Surface Temperature (K)
5000
0
Luminosity (Suns)
100