# Name: Partner(s): 1102 or 3311: Desk # Date: NGC 6633

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1 Name: Partner(s): 1102 or 3311: Desk # Date: NGC 6633 Determining the Age of a Cluster Purpose Understand how HR diagrams reveal information about stellar evolution Use an HR diagram to determine the age of a star cluster Use RR Lyrae variable stars to determine the distance to a star cluster Equipment Spreadsheet Data file (cluster_data.csv) Question 1: Review of the HR diagram. You already know that we can determine the spectral type of a star by analyzing its light with a spectrograph. We can then classify stars by spectral type. a) What is the relation between the OBAFGKM sequence of spectral types and surface temperature? b) Using the diagram below, which star is bluer, Spica or the Sun? c) Which star has the largest luminosity, Dened or Sirius? d) Which star is bigger (i.e. larger diameter), Betergeuse or Procyon B? Astronomy 1102/3311 Cluster Ages - 1

2 e) Using the diagram below, make a rough estimate of the colour, luminosity and size of a low mass star (one solar mass) at five different stages of its evolution (you can give a range of values if needed.) Answer in the table provided. Stage Colour Luminosity Size (in solar radius) Main sequence Helium flash Ejection of outer layers White dwarf f) Using the diagram below, make a rough estimate of the colour, luminosity and size of a massive star at different stages of evolution. Answer in the provided table. Stage Colour Luminosity Size (in solar radius) Main sequence Supernova Astronomy 1102/3311 Cluster Ages - 2

3 You know how to find the spectral type (and temperature) of a star using a telescope and a spectrograph. But to find the position of a star in the HR diagram, you also need to measure its luminosity. g) What makes it so difficult to measure the luminosity of a star? h) How can we overcome this difficulty by studying a single cluster of hundreds of stars that were roughly born at the same time? Explain how you could determine the luminosity of the stars of the cluster after drawing the HR diagram of the cluster. Question 2: Cluster age. If you plot the temperature and apparent luminosities of all the star of a given cluster on a HR diagram, the more massive stars will have left the main sequence while the less massive ones will still be burning their hydrogen. Therefore the graph will exhibit a turnoff point Astronomy 1102/3311 Cluster Ages - 3

4 Here are HR diagrams for 4 star clusters. Rank each cluster from youngest to oldest and explain how you can determine the relative age of each cluster. Question 4: The Colour-Magnitude diagram of 47 Tuc and M45. HR-diagrams can be drawn in many different ways. The horizontal axis can be the spectral type, the surface temperature or the colour of stars. The vertical axis can be luminosity or brightness or magnitude of stars. For this part you will use a colour-magnitude diagram. To calculate the colour index of a star, the brightness of the star is measured through different colour filters. A filter only lets light of specific wavelengths through. a) If you were to look through a red filter, everything would appear different shades of red. Explain why. Astronomy 1102/3311 Cluster Ages - 4

5 Stars are blackbodies and will appear brighter in one filter than in another. The difference between these two measurements is the colour index of the star. For example, a massive blue star will let a lot of light through a blue filter and very little through a yellow filter. Its blue magnitude (B) will be a small number and its yellow magnitude (V) will be a large number (the brighter the star, the smaller the magnitude). So the colour index B-V will be small. During your last observing trip you collected data for the open cluster M45 and the globular cluster 47 Tuc. You measured the magnitude of the stars with a blue filter then a yellow filter. You calculated the difference between the two magnitudes: B-V. Being an experienced astronomer, you know that: the bigger B-V index, the redder the star and the smaller the B-V index, the bluer the star. You also measured the apparent magnitude of each star (here after referred as magnitude). The lifetime of main sequence stars: Spectral Type Colour (B-V) Lifetime (million years) O -0.4 Less than 1 B A F G K M 1.6 More than b) Plot magnitude versus B-V for each cluster. Use either a graph paper or a spreadsheet. Share the workload and draw one graph each. The data are here (Cluster_Data.csv) Your colour axis should run from -0.4 to +1.6 with divisions of 0.2. The vertical axis is different in each of the two graphs. Don't forget that magnitudes are backwards, so that smaller numbers mean brighter stars! c) Estimate the age of each cluster and explain your reasoning. d) Explain how you could use an HR diagram to calculate the distance to a globular cluster. Astronomy 1102/3311 Cluster Ages - 5

6 Question 5: Determining the distance to a globular cluster using RR Lyrae stars. RR Lyrae stars are old, low-mass stars that are variable: their luminosity is not constant. A single globular cluster may have dozens of RR Lyrae stars. The following graphs show light curves of four RR Lyrae in the Draco dwarf galaxy. The horizontal axis is time in days and the vertical axis gives the magnitude of each star. Notice the similarities between the four graphs. They have roughly the same variations of magnitude, both in amplitude (20.5 to 19.5) and period (0.56 days). All RR Lyrae stars having more or less the same average luminosity, astronomers can use them as standard candles. a) Explain to an apprentice astronomer how to determine the distance to Draco. Describe the method using either words or equations, but do not do any calculation. Explain every step in details: how many nights you need, what instrument your need (photometer, spectrometer, filters), how you will proceed with the data, etc. Justify your choices. This is not an easy question. Brainstorm with your partner, but also with other groups. Astronomy 1102/3311 Cluster Ages - 6

7 b) (ASTR1102 only) Knowing that: The average absolute magnitude M of a RR Lyrae is /- 0.2 There is dust on the line of sight between you and the cluster which increases the apparent magnitude m by 0.1 If the distance to the cluster d is expressed in parsecs: i) Calculate the distance to Draco in parsecs. " m = M + 5log d % \$ ' # 10& ii) Calculate the maximum upper and the minimum lower possible values for d. (Hints: What is the average value for m? What is the uncertainty in m considering you estimated the average by eye? What is the uncertainty in M?) iii) Write you answer in standard form. Example: d = ( )pc. Astronomy 1102/3311 Cluster Ages - 7

8 Here is an extract of the original scientific paper. Bonanos et al, The Astronomical Journal, volume 127 (2004), pages : We present the first CCD variability study of the Draco dwarf spheroidal galaxy. The data were obtained with the Fred Lawrence Whipple Observatory 1.2 m telescope on 22 nights, over a period of 10 months, covering a field centered at =17h19m57.5s, = (J2000.0). The analysis of the BVI images produced 163 variable stars, 146 of which were RR Lyrae: 123 RRab, 16 RRc, 6 RRd, and one RR12. The other variables include a SX Phe star, four anomalous Cepheids, and a field eclipsing binary. Using the short distance scale statistical parallax calibration of Gould & Popowski and 94 RRab stars from our field, we obtain a distance of 75.8+/- 0.7(stat) +/- 5.4(syst) kpc. iv) On an axis, draw the range of values found by Bonanos et al. and by you. Does your calculation agree with the results of Bonanos et al.? Comment and provide a detailed explanation Astronomy 1102/3311 Cluster Ages - 8

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