Gravitational-wave astronomy -- assignment 3
- 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?
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