Mathematics Question

Question 1 Main-sequence lifetime (3 points)Calculate the main-sequence lifetimes of stars with:a) 7 times the mass of the Sunb) 0.6 times the mass of the SunExpress your answers as multiples of the Suns main-sequence lifetime, as well as in units of years.Question 2 Stellar classification (7 points)Explain the following stellar classes from the point of view of stellar evolution.a) What is a T Tauri star?b) What is a brown dwarf? How is it different from a red dwarf?c) What is a red giant? How is it different from a blue giant?d) Describe the helium flash and why it occurs.e) What is a white dwarf?Question 3 21-cm radiation (6 points)What is 21-cm radiation? How is it detected? With which element is it associated? Why is useful to astronomers?The actual wavelength of the line is 21.1 cm. If this line is observed peaking at 21.2 cm from a dust cloud, atwhat fraction of the speed of light is the cloud moving relative to the observer? Towards or away from the observer?Question 4 Binary stars (8 points)Eclipsing binary stars are also spectroscopic binary stars, as we see the orbit edge-on. For an imaginary binary starsystem with a red dwarf and a blue giant, assign mass values to the two stars consistent with their type. If the starsare in a circular orbit, separated by 15 AU:a) What is their orbital period?b) What is the orbital speed of each star?c) Draw three diagrams as a function of time, ordered vertically so the time axis lines up between them:1. Radial speed of the more massive star2. Radial speed of the less massive star3. Apparent brightnessLabel the primary eclipse and the secondary eclipse.Make sure the eclipses line up correctly in time with the radial speed diagrams, with the correct orbital period.1Question 5 Globular cluster (6 points)a) Copy the following H-R diagram into your solutions file, and label the different parts:i) Main sequenceii) Red giant branchiii) Turnoff pointiv) Stragglersb) Determine the age of this globular cluster.c) Why is the presence of blue stars in this cluster surprising at first sight? What is the most likely explanation?

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