Question 5: The figure to the right shows an H-R diagram for the open cluster M67 at a distance of 860 pc. Plotted is the apparent visual magnitude (mv) versus the B-V color for individual stars in the cluster. The dark line marks the main sequence. The distance modulus for M67 (mv - MV = +9.7) can be used to change from apparent magnitude to absolute magnitude. Use the H-R diagram and the information in the table at the end of the homework to estimate the age of this star cluster. Explain your answer.
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For an open cluster like M67, the H-R diagram (or color-magnitude diagram) plots the apparent visual magnitude (mv) against the B-V color index for each star in the cluster. The main sequence is a continuous and distinctive band of stars that appears on the Show more…
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Use the H-R diagram to arrange the star clusters from youngest to oldest. Hertzsprung-Russell Diagram An H-R diagram shows the relationship between the temperature and luminosity of stars. The different branches indicate where the turnoff point of the stars in a star cluster fall in this diagram. The grey line represents the main.
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1. A star has a distance modulus of 0 magnitudes. What is its distance from the observer? (2 points) 2. Is a star with a distance modulus of -5 closer or farther away than 10 pc? (2 points) Explain your answer. (3 points) 3. Explain stellar parallax and how it varies with distance to the star. (5 points) 4. What is the dependence of the intensities of stars on parallax? (5 points) Hint: Consider the inverse-square law of light. 5. The stars in a CCD image include stars in a cluster and stars in front of the cluster. (I.e. That don't belong to it.) One group has parallaxes clustered around of 3 milli-seconds of arc (mas). The parallaxes of the other group range from 10 mas to 15 mas. Which group contains the stars in the cluster? ( 1 points) Explain your answer. (2 points) 6. Rewrite the distance modulus expression in terms of parallax, p. (5 points)
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Explain how an $\mathrm{H}-\mathrm{R}$ diagram of the stars in a cluster can be used to determine the age of the cluster.
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