An Introduction to Modern Astrophysics · Problem 16.22

General Relativity and Black Holes — Carroll & Ostlie

Physics — Astrophysics · pulsar-age

Problem

(a) Integrate Eq. (16.32) to obtain an expression for a pulsar's period

P

at time

t

if its initial period was

P_0

at time

t = 0

. (b) Assuming that the pulsar has had time to slow down enough that

P_0 \ll P

, show that the age

t

of the pulsar is given approximately by

t = \frac{P}{2\dot{P}},

where

\dot{P}

is the period derivative at time

t

. (c) Evaluate this age for the case of the Crab pulsar, using the values found in Example 16.7.1. Compare your answer with the known age.