### pulsar characteristic age

**(τ, characteristic age)**
(approximate age determination of a pulsar based upon rotation rate)

The term **pulsar characteristic age** (typically symbolized by **τ**)
refers to a particular simplified determination of a pulsar's
approximate age, which can be thought of a as the timescale
of a pulsar's age. It presumes the pulsar was originally rotating
so quickly that its initial rotation period can be approximated
by zero, and the variation of its period derivative over its
lifetime is following a simple, typical pattern. (The slowing is
due to interactions of the pulsar's magnetic field and often
follows a particular simple pattern.)
The widely-used formula is:

τ = P / ( 2 dP/dt )

- τ -
*pulsar characteristic age*.
- P - period.
- dP/dt - period derivative: rate of change of the period.

Variants to this formula incorporating more data offer a closer,
more likely approximation.

Similarly, the **pulsar characteristic magnetic field** is
an approximation of a pulsar's maximum-possible magnetic field:

B = 3.3 × 10^{19} P dP/dt

- B -
*characteristic magnetic field* of a pulsar with such rotation as magnetic flux density at its surface.
- P - period in seconds.
- dP/dt - period derivative.

The constant 3.3 x 10^{19} was derived using plausibly
common (canonical) values for some pulsar characteristics such
as its radius.

A pulsar's **braking index** indicates a characteristic of the
pattern of its **spin-down** (the slowing of its rotation) over time:

n = Ω d²Ω/dt² / (dΩ/dt)²

- n -
*braking index*
- Ω - angular velocity, 2π/P, where P is the period.
- dΩ/dt and dΩ²/dt² - derivative and second derivative of angular velocity;

(*pulsars,age,rotation*)
**Further reading:**

https://astronomy.swin.edu.au/cosmos/p/Pulsar+Characteristic+Age

https://ui.adsabs.harvard.edu/abs/2013IJMPS..23...95J/abstract

https://www.cv.nrao.edu/~sransom/web/Ch6.html

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