When astronomers measure the period, or spin-rate of the rotation of a pulsar, they find that pulsars are slowing down, usually at a very consistent rate. This “spin-down” is thought to be due to braking caused by the rotating pulsar’s magnetic field, and this information can be used to determine an approximate age for the pulsar, known as the *characteristic age*.

A radio pulsar’s characteristic age *τ* is usually defined as:

where *P* is the pulsar’s period, and the dot represents the period derivative (the rate the pulsar is slowing). The characteristic age provides an approximate measure of a pulsar’s true age, and the calculation is reasonably valid under three assumptions:

- The pulsar’s initial spin period was very much smaller than that observed today.
- There is no magnetic field decay.
- The magnetic braking can be approximated by the energy loss a spinning dipolar magnet would experience in a perfect vacuum (in this case, the braking index,
*n*= 3.)

The “correct” formula explicitly includes *n* and allows for a finite initial spin period *P _{0}* and derivative.

It is important to use the same units for period and age and to check the period derivative is dimensionless.

In 2007 the Crab pulsar had a period of 0.0331 sec and a period derivative of 4.22×10^{-13}s/s. The characteristic age is around 1240 years. The supernova that produced the pulsar was in 1054 AD, yielding an age of ~950 years.

Study Astronomy Online at Swinburne University

All material is © Swinburne University of Technology except where indicated.