Astrophysics (Index) About

### 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 × 1019 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 1019 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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