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Astronomy Assignment

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Lab # 6 : 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).

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 in table below, the other two columns will be done later. The colour index or CI is found by the following equation:

CI = B – V

 

Photometric Data for Pleiades (M45):

Star no. V mag

(mV) B Mag CI = B – V

Abs V

(MV)

1 10.44 11.06 2 7.52 7.62 3 6.60 6.57 4 7.97 8.15 5 5.09 5.01 6 3.64 3.56

7 8.12 8.34 8 11.35 12.13 9 6.95 7.07 10 10.91 11.77 11 9.05 9.54 12 10.02 10.58 13 8.27 8.63 14 9.25 9.80 15 9.88 10.42 16 7.66 7.87 17 10.48 11.12 18 6.81 6.87 19 2.87 2.78 20 6.29 6.31 21 8.25 8.51 22 8.69 9.15 23 7.26 7.31 24 6.99 7.02 25 6.82 6.84 26 12.61 13.79 27 9.46 9.93 28 8.37 8.67 29 9.29 9.75 30 12.12 13.14 31 11.71 12.58 32 10.42 11.06 33 11.34 12.20 34 12.89 13.68 35 7.35 7.45 36 7.96 8.28 37 4.18 4.12 38 9.70 10.25 39 5.76 5.72 40 6.43 6.41 41 8.60 8.95 42 11.27 12.19 43 3.88 3.81 44 7.18 7.34

45 9.45 9.97 46 10.55 11.22 47 10.13 10.75 48 8.04 8.25 49 7.85 8.05 50 4.31 4.20 51 10.39 11.02 52 5.46 5.42 53 8.58 8.92 54 11.40 12.25 55 3.71 3.60 56 10.81 11.61 57 11.93 12.87

2. Plot your results as an “X – Y” scatter plot, using “V mag” 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 mag”, the higher up the axis it is (in spreadsheet reverse order of values). Ensure that you have clearly marked the scales. Give yourself enough room above and below your vertical scale values to add additional data later.

Questions after done the plot:

1. What is the trend of the majority of stars in the Pleiades cluster?

2. In blue, circle the most massive star/s on your Colour-Magnitude plot, these are to the left.

3. In red, circle the least massive group of stars on the diagram, these are to the right.

4. Draw a curve to the trend of these stars, name this trend “Main Sequence” (it should look like an “S” shape)

5. Look on the Internet for a color image of the Pleiades Cluster (M45). Comment on the neatness of the image. Are they young or old? How can you tell? Explain: (hint: see the presence of molecular dust/gas around them)

6. Look at the photo of the Pleiades below.

The Pleiades Open Cluster, M45.

Is there any visible evidence to support your answer to questions 5? What does

this evidence suggest about the origin of stars? (think on molecular clouds)

7. In this exercise, you have plotted apparent magnitude V-mag (or mv), rather than absolute magnitude, Mv, or Luminosity on the vertical axis. Let’s make a strong assumption about the stars in the Pleiades cluster that it is about 126 parsecs away from us (observers). Results from the European astrometry satellite, HIPPARCOS, gave a distance of 116 parsecs to the Pleiades. So, using the distance modulus equation:

𝑀 = 𝑚 − 5   ∙   log ( ! !” )

Calculate the Absolute (visual) Magnitude, M of each of the Pleiades stars, in table above (5th column)

8. Make a new plot with the vertical axis (the scale) using the Absolute Magnitude (5th column entries). Again, lower number up and higher numbers down (reverse axis values – flip).

9. The value ”m – M” is called the distance modulus. What is the value for all the Pleiades stars? (calculate the distance modulus for five rows in table above)

10. Would the value of the distance modulus for a more distant cluster be higher or lower? (Example: use distance 200 pc equation above). Explain:

11. The relationship between Colour Index (CI) 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 values on your plots (x-axis) from steps 2 and 8.

Spectral Class B – V

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

12. On your plot, write in the colour (eg, red) beneath the corresponding spectral class (see charts in textbook chapter 13)

13. Using capitals SUN, mark in where the Sun would be on your plot (use plot in step 8).

14. Draw and label three regions on your plot to show where red giants, red supergiants and white dwarfs would be found in both plots

15. Below is a colour-magnitude diagram for the globular cluster, M5.

Credit: SEDS (C-M diagram) and AAO (image)

Is the globular cluster older or younger than the open clusters? Justify your answer:

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