A neutron star's magnetic axis is tilted by obliquity χ from its spin axis and sweeps a cone once per rotation (the "lighthouse model"). Two beams stream out along the open dipole field lines above each magnetic pole. Earth sits at a fixed inclination ζ from the spin axis; a pulse is recorded whenever a beam sweeps within the polar-cap half-angle of that line of sight.
- Light cylinder: Rlc = cP / 2π — field lines that would need to corotate faster than light go "open" beyond this radius.
- Polar-cap half-angle: θpc ≈ asin(√(R/Rlc)) — the angular size of the open-field-line bundle at the surface.
- Spin-down luminosity: Ė = (2/3c³) μ² Ω⁴ sin²χ, with dipole moment μ = B₀R³/2 — the same magnetic-dipole-radiation formula used to derive the ~4.6×10³⁸ erg/s spin-down power of the Crab pulsar from its measured P and Ṗ.
R_lc = c·P / (2π)
θ_pc ≈ asin(√(R / R_lc))
Ė = (2/3c³)·μ²·Ω⁴·sin²χ