Introduction to Astrophysics II, 29:120
Spring, 2009
Fifth Homework Set...February 27, 2009. Due March 5, 2009

(1) The famous (and bright) pulsar 0329+54 has a period and period derivative of $P=0.7145$ seconds and $\dot{P}=2.050 \times 10^{-15}$. What is the luminosity, in some form of energy, of this pulsar? Note of Interest: The period and period derivative of this pulsar are known to many more significant figures than given above. Pulsar timing measurements are some of the most precision measurements made in all of physical science.

(2) In class I derived an equation for $\phi$, the angular deflection due to the gravitational deflection of starlight. This may be re-expressed as a differential equation for $\frac{d \phi}{dx}$, where $x$ is the distance along the undeflected ray path. Use this latter equation to obtain a complete expression for the total deflection of a ray which approaches an object with an impact parameter $b$. In other words, starting with $x=- \infty$, solve for $\phi(x=+\infty)$. The mass of the object is $M$. Hint: For this problem, you may make the very good approximation that $\phi \ll 1$.

(3) Use the expression from (2) to obtain a numerical value (in arcseconds) for the deflection of a ray which passes by the Sun with an impact parameter $b=2 R_{\odot}$. Compare this angle with the angular radius of a solar type star 10 parsecs away. This will allow you to determine if a gravitational arc would appear for a more distant star directly behind the solar type star.

(4) Consider a $0.6 M_{\odot}$ white dwarf star that is $10^{10}$ years old. What is its surface temperature?

(5) Consider a $1.4 M_{\odot}$ neutron star. Assume its radius is adjustable. At what radius is the neutron Fermi energy corresponding to the mean stellar density equal to the neutron rest mass? Is this radius larger or smaller than the true radius of such a neutron star? Comment on whether your answer makes sense.

(6) Problem 16.8 from the textbook.

(7) Problem 16.9 from the textbook

(8) Problem 16.14 from the textbook