Presets
Playback
Parameters
Model checks
The science
Pulsars as lighthouses
A pulsar is a rotating, magnetised neutron star. Its radio beam is emitted along the magnetic axis, which is tilted by an angle α from the spin axis, so each rotation the beam sweeps a cone through space. An observer at angle ζ from the spin axis sees a pulse only when the angle θ between the beam axis and the line of sight is below the beam half-opening ρ, where cosθ = cosα cosζ + sinα sinζ cosφ. The visible duty cycle is therefore arccos[(cosρ - cosα cosζ)/(sinα sinζ)]/π.
Spin-down
Magnetic dipole radiation slows the star: the period grows at the rate Ṗ. For braking index n = 3, PṖ is constant, so P(t) = √(P0² + 2P0Ṗ0t). The characteristic age is τ = P/2Ṗ, the dipole surface field is B ≈ 3.2×1019√(PṖ) gauss and the spin-down power is É = 4π²IṖ/P³ with moment of inertia I = 1045 g cm².
Honest simplifications: the field and age formulas assume a vacuum dipole and braking index 3 (measured indices of real pulsars are mostly lower, 0.9 to 2.9), the true age can differ a lot from τ, the beam is a single Gaussian cone, and the death line is a rough pair-production boundary. The labelled catalogue points are rounded textbook values. The animation spins the star at a fixed slow rate for visibility, not at the real rotation frequency.
What to try
- Pick the Crab-like preset and compare the age, field and power readouts with the published values.
- Increase the observer angle away from the magnetic inclination until the pulse vanishes: the beam then misses us.
- Move the point along a constant-B line to see how a pulsar ages and approaches the death line.
- Select the millisecond preset: a tiny Pdot means a very old, weakly magnetised, recycled star.