# Colour - Magnitude Diagram for M 45 (Pleiades)

## Introduction

The Pleiades is a relatively close open cluster. The six or seven stars visible to the naked eye form a tight grouping of stars (an asterism) near the even closer Hyades cluster. They are easily visible in the summer months from the southern hemisphere. In this exercise, you will determine the colour of many cluster members and plot them on a Colour-Magnitude diagram. This is just a type of Hertzsprung-Russell (HR) diagram in which we plot Colour Index rather than Spectral Class on the horizontal axis; and use the apparent visual magnitude, V, for the vertical axis.

## Procedure

Photometric measurements of the Pleiades cluster can be used to determine the age of the cluster and its distance. By taking images of the stars through separate blue (B) and visual (V) filters we can measure the apparent magnitude of each star in each waveband colour. In this exercise this stage has already been done, presenting you with a table with two magnitude values for each star. You may recall that a visual or V filter approximates the spectral response of the human eye and is most sensitive in the yellow part of the spectrum. A blue filter, B, which corresponds to the sensitivity of photographic film (hence photographic magnitude).

or:
Download the data as an csv file for use in spreadsheets such as Excel worksheet file here.

The data reductions and plotting below can be done either manually or using a spreadsheet.

1. Calculate and record the Colour Index for each star. The colour index or CI is found by the following equation:

CI = B - V
2. Plot your results as an X- Y scatter plot, using V for the vertical axis and B - V for the horizontal axis. Remember to draw your vertical scale so that the lower the value of V, the higher up the axis it is. Ensure that you have clearly marked the scales. Give your self enough room above and below your vertical scale values to add additional data later.

## Questions

1. What type are the majority of stars in the Pleiades cluster?
2. In blue, circle the most massive star/s on your Colour-Magnitude plot.
3. In red, circle the least massive group of stars on the diagram.
4. What is the source of fuel for all the stars shown on the diagram?
5. Comment on the relative age of the stars. Are they young or old? How can you tell?
6. Look at the photo of the Pleiades below. Is there any visible evidence to support your answer to question 5? What does this evidence suggest about the origin of stars?

7. Where in the galaxy would you typically expect to find open clusters like the Pleiades?
8. In this exercise, you have plotted apparent magnitude V or mv, rather than absolute magnitude, Mv, or Luminosity on the vertical axis. What assumption about the stars in the Pleiades cluster must be made for this to be valid?
9. Results from the European astrometric satellite, HIPPARCOS, gave a distance of 116 parsecs to the Pleiades. Using the distance modulus equation:

m - M = 5log10(d/10)

Calculate the Absolute (visual) Magnitude, M of each of the Pleiades stars (easy if your data is already on a spreadsheet). You will have to rewrite the equation first.

10. On the right hand vertical axis of your plot, recalibrate the scale using Absolute Magnitude rather than V.
11. The value m - M is called the distance modulus. What do you notice about this value for all the Pleiades stars? What is the value for M 45?
12. Would the value of the distance modulus for a more distant cluster be higher or lower? Explain.
13. The relationship between Colour Index and Spectral Class for Main Sequence stars (ie those of Luminosity Class V) is shown in the table below. Use it to mark in the values for spectral class beneath those of colour index on your plot.

Luminosity Classes of Stars
Spectral Class B - V
O5
-0.35
B0
-0.31
B5
-0.16
A0
0.00
A5
+0.13
F0
+0.27
F5
+0.42
G0
+0.58
G5
+0.70
K0
+0.89
K5
+1.18
M0
+1.45
M5
+1.63
14. On your plot, write in the colour (eg, red) beneath the corresponding spectral class.
15. Using a capital S, mark in where the Sun would be on your plot (use M).
16. Draw and label three regions on your plot to show where red giants, red supergiants and white dwarfs would be found.
17. Below is a colour-magnitude diagram for the Hyades, the nearest open cluster to Earth. Compare this with the one you have plotted for the Pleiades. Which of the two open clusters, the Pleiades or the Hyades is older? How can you tell?

Credit: Johnson, H. L.; Mitchell, R. I.; Iriarte, B., Astrophysical Journal, vol. 136, p.75
The Color-Magnitude Diagram of the Hyades Cluster.
18. Below is a colour-magnitude diagram for the globular cluster, M5. Is the globular cluster older or younger than the open clusters? Justify your answer.

Credit: SEDS (C-M diagram) and AAO (image)
Colour-magnitude diagram for and image of the Globular Cluster M5.
19. Why may white dwarfs be under represented on the globular cluster diagram?
20. Is there likely to be any difference in the initial composition of stars in the globular cluster to stars in the open clusters? Explain your answer.

You can download an Excel spreadsheet solution for the data and the plot here (28 Kb xls worksheet).

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