**Problem 1:**

The Crab pulsar has the fastest spin-down rate of any known radio pulsar, 3.7x10^{-10} Hz/s. Its period is 33 ms. What is the spin-down upper limit on the gravitational-wave amplitude assuming that all energy goes into GW emission? Compare with your answer to problem 1 from assignment 2.

**Problem 2:**

Repeat the calculation of Roche lobe overflow and tidal disruption radius sketched out in Lecture 4. What black-hole mass would disrupt a Sun-like star exactly at the innermost stable circular orbit (ISCO)? A white dwarf? A neutron star? [What does this say about tidal disruptions of stars by massive black holes? LISA EMRI sources? LIGO sources?]

**Problem 3:**

Consider a low-mass interloper with velocity v_{int} that comes within a semimajor axis of a hard binary with more massive components and orbital velocity v_{orb} >> v_{int}. Carry out a Newtonian analysis of the energetics of the interaction. By how much is the binary expected to harden?

Back to the course web page