Download Distances to the Stars in Leo

Summary
The student determines the distances to seven of the brightest stars in the
constellation Leo using the method of spectroscopic parallax and
compares the results to the more accurate distances derived from measured
trigonometric parallaxes.
Background and Theory
If the distance to the star is known via its measured parallax (as it was discussed in class), it is a somewhat easyl
matter for astronomers, or anyone else for that matter, to determine the absolute magnitude of the star using the
distance-magnitude relation. However, most stars are too far away to have a measurable parallax. In these cases,
the distance to the star must be determined by some other method.
We can use our knowledge of the Hertsprung-Russell (or H-R) Diagram and our analysis of a star's spectrum to
determine stellar distances. The H-R Diagram is a graph measuring a star's absolute magnitude or brightness
against its temperature and colour. Below is an example of the diagram:
L stands for luminosity (or brightness) and T stands for temperature (in Kelvins or K, a different unit like
Celsius). The light from a star can be analysed using a spectrum diagram on the next page:
From the strength of the lines in a star's spectrum, we can give it a spectral type (O, B, A, F, G, K & M) and
luminosity class. We can use the luminosity to find its absolute magnitude and thus its distance. Finding the
distances to stars based upon their spectral type and luminosity is known as spectroscopic parallax (even
though no parallax determination or trigonometry is involved). This method is neither easy nor exact; however,
it has proved to be one of the best ways to learn about the more distant stars.
The first part of this method involves determining the star's spectral type and luminosity class.
Procedure
Table 1 lists the 14 stars Leo in order of their apparent magnitude. Seven of the stars have already been
classified, and their absolute magnitudes and distances calculated. Your mission is to fill in the details for the
other seven stars.
1. Use the Internet to find the spectral type (O, B, A, F, G, K & M) of the seven stars (Wikipedia contains
this information; see Mr. Jennings if you have difficulty finding the information). Fill in column 3.
2. Use the Internet to find the absolute magnitude of each star. Fill in column 6.
3. Solving for the distance in the distance-magnitude relation, we get:
d  10 ( m  M 5)5
Solve for the exponent of 10 first, then use either the inv log; keys or the 10x key on your calculator.
Calculate the distance to each of the seven stars based upon the absolute magnitude (M) from
spectroscopic parallax.
4. For the seven unclassified stars, fill in column 9 in Table 1 for the distances determined from the
parallax values, where d = 1/parallax (d is in parsecs for parallax measured in seconds of arc).
Table 1 - Distances to Stars in Leo Worksheet
Fourteen Stars in the Constellation Leo
Star ID
Star Name
 Leo
Regulus
 Leo
Denebola
 Leo
Al Geiba A*
 Leo
Zozma
 Leo
Spectral Luminosity
Type
Class
Apparent
Magnitude
M from
d from Spec.
Spectroscopic
Parallax
Parallax
Measured
Parallax
(arc sec)
d from
Parallax
V
1.36
V
2.14
III
2.14
V
2.55
Ras Elased
Australis
II
2.98
0.009
 Leo
Chort
V
3.34
0.036
 Leo
Al Geiba B*
III
3.39
0.036
 Leo
Aldhafera
F0
III
3.44
~1
32
0.025
40
 Leo
30 Leonis
A0
I
3.48
~ -5
500
N/A
**
 Leo
Subra
V
3.52
B1
I
3.85
~ -6
900
N/A
**
K2
III
3.88
~2
25
0.025
40
B9
V
4.05
~2
25
0.017
59
III
5 - 10
-1 to +4
160
N/A
**
1
2
 Leo
 Leo
Ras Elased
Borealis
 Leo
R Leo
A3
A5
***
0.038
~2
10
0.076
13
0.036
~1
20
0.040
25
0.034
* Visual Binary
** Distance is too far for a measurable parallax
***Variable Star
M = absolute magnitude of the star
Luminosity class symbols: V = dwarf, IV = subgiant, III = giant, II = luminous giant, I = supergiant.
1. As part of this exercise, you determined the distances to these stars based on the method of spectroscopic
parallax. In your own words, summarize why the method is an important tool for astronomers.
2. Compare the two values for the distance to each of the seven stars. Do certain spectral types or luminosity
classes lead to larger differences between the two values?
3. Comment on the accuracy of the spectroscopic parallax method vs. the trigonometric parallax measurements
(i.e. the difference in columns 7 & 9).
© 2000 University of Washington
Revised: 11 July, 2000