Exam 1

Due: February 3, 1995

Answer 4 out of the 5 following questions. Show your work.

Show that the central pressure of a star is roughly given by P = GM**2/R**4. State your assumptions.
Using the expression for normal gas pressure, find an expression for the central temperature of a star. State your assumptions.
Use your result, estimate the central temperature of a star which is twice as massive as the Sun and two times the radius of the Sun.

Suppose that you want to determine the mass, temperature, diameter, and luminosity of a star. Which of these physical quantities requires you to know the distance to the star? Explain.
While we are on the subject, how does one go about finding the temperature of a star using its continuum emission? Its line spectrum?
Suppose that you observe a spectrum which shows strong hydrogen Balmer absorption lines and strong lines due to TiO (molecular lines). Explain why this is odd. How might you explain this result? How could you test your hypothesis?

Using your knowledge of hydrostatic equilibrium and thermal equilibrium, what would happen to the appearance of the Sun if the nuclear reactions in its core were to suddenly cease. Be sure to mention not only what would happen, but also on what time scales things would happen.

Stars are not distributed randomly in the Herzsprung-Russell diagram; they are confined to well-defined regions:

What do you conclude based on this result? Support your argument (1. do this by thinking up some objections to your picture and then, if you can, present arguments to counter these objections and; 2. think about whether the assumptions you made are valid).
Based upon the distribution of white dwarfs in the Hertzsprung-Russell diagram, can you infer anything about how white dwarfs evolve? Is your conclusion firm (is it supported by other observations)? If not, can you suggest an observation which could prove or lend strong support to your theory?