Astro 7A 2017 – Problem Set 11

Astro 7A 2017 – Problem Set 11 Due Friday 12.1.17 by 5pm. Please turn homework into the box that corresponds to your discussion section. Homework questions? Post questions and search for answers on Piazza. 1 Evolutio ...

Astro 7A 2017 – Problem Set 11 Due Friday 12.1.17 by 5pm. Please turn homework into the box that corresponds to your discussion section. Homework questions? Post questions and search for answers on Piazza. 1 Evolution on the main sequence [28 points] Figure 13.1 in Carroll & Ostlie shows the tracks of stars of different masses in the Hertzsprung-Russell diagram. Table 13.1 gives the corresponding times during the different phases. (a) At point 3 the hydrogen in the core has been depleted. Assume that the core contains 10% of the total mass of a star. Calculate the total energy output for stars of all masses in Table 13.1 during their total time on the main sequence. [10 points] The total energy output for each star is simply given by the amount of energy released by the fusion of all the hydrogen in the core to helium. The energy released in the conversion of hydrogen to helium is 26.22 MeV per helium nucleus. Therefore, to compute the energy released on the main sequence for a star of given mass, assuming the core is 10% of the total mass, you need to perform the following calculation: E = 0.1(M/mHe) × 26.22 MeV where mHe is the mass of the helium nucleus. To convert to J multiply this expression by 106 × 1.602 × 10−19 . (b) Given their times on the main sequence, calculate the average luminosity in solar luminosities. [10 points] To find the luminosity, simply divide the energy by the time! However you need to be careful of units: make sure to convert time from Myr to seconds before dividing, so that you will get out the luminosity in W. Then divide by the solar luminosity (3.8 × 1026 W) to find the luminosity in solar luminosities. (c) Make a graph of luminosity L vs. mass M. What is the approximate relation between L and M (hint: make a logarithmic plot)? [8 points