pulsar characteristic age

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 as the timescale of the 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. (Such slowing is due to interactions of the pulsar's magnetic field and often approximates a fairly 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. Another calculated value, 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 third calculated value, the 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 d²Ω/dt² - derivative and second derivative of angular velocity;