Introduction to Astrophysics II, 29:120
Spring, 2007
Seventh Homework Set...March 30, 2007. Due April 5, 2007
Nunc et in umbrosis, Fauno decet immolare lucis ...Horace

(1) Using an equation or graph of the initial mass function, calculate the fraction of stars with $M > 15 M_{\odot}$.

(2) Calculate the Kelvin-Helmholtz timescale for the Sun, using its present luminosity.

(3) Adopt the number in the book for the surface temperature of Sirius B, $T=27,000$ K. Using only this number, and the relative brightness of Sirius A and B, compute the radius of Sirius B.

(4) Generalize the derivation of the Fermi Energy presented in class to the case of a 2 dimensional star, i.e. particles are confined to a box of size $L$ in both the $x$ and $y$ directions. Compare your result to the equation derived in class for 1D, and the correct value for the Fermi Energy given in eq. 15.2 of the book.

(5) Problem 15.2 from the textbook.

(6) Problem 15.3

(7) Problem 15.5

(8) Problem 15.6