The Final States

Section 2 of 6

Pulsars

Part 2: Pulsars — Cosmic Lighthouses

The observational puzzle

Some radio sources pulse so regularly they act like cosmic clocks. The first known pulsar, discovered by Jocelyn Bell Burnell and Antony Hewish in 1967, had a period $P = 1.337\,\mathrm{s}$ . Many pulsars have periods from milliseconds to seconds — which immediately constrains the source to be compact enough to rotate that quickly.

Pulsar

A rotating, magnetized neutron star observed through regular pulses of radiation as its beam crosses our line of sight. The pulse period is the star’s rotation period — not a blinking on and off.

The Lighthouse Model

In the lighthouse model, a neutron star has a strong magnetic field, rapid rotation, charged particles accelerated near its magnetic poles, and radiation beams that need not align with the rotation axis. As the star rotates, the beams sweep through space.

Lighthouse model

The model in which a pulsar’s radiation beam sweeps across Earth because the neutron star’s magnetic axis is misaligned with its rotation axis. We see a pulse each time the beam points at us — the pulse period is the rotation period.

NASA JPL infographic on dark background showing three panels: Magnetar (left) with intense magnetic field lines, Pulsar (center) with twin beams of radiation sweeping from magnetic poles misaligned with the rotation axis, and Magnetar plus Pulsar (right) combining both properties. Each panel includes a brief description and illustration. — Figure 3What to notice: pulsars emit beams from magnetic-pole regions, and we see pulses only when the rotating beam crosses Earth. Magnetars are neutron stars with especially strong magnetic fields; the categories describe observed behavior, not separate kinds of matter.NASA/JPL-Caltech

Compactness from pulse periods

A rotating object cannot have its surface moving faster than light. The equatorial speed is $v = 2\pi R/P$ ; requiring it to stay below $c$ gives a maximum radius $R_{\max} = cP/(2\pi)$ . For a millisecond pulsar with $P = 1.0 \times 10^{-3}\,\mathrm{s}$ ,

R_{\max} = \frac{(3.0 \times 10^{10}\,\mathrm{cm\,s^{-1}})(1.0 \times 10^{-3}\,\mathrm{s})}{2\pi} = 4.8 \times 10^6\,\mathrm{cm} = 48\,\mathrm{km}.

A millisecond pulsar must be only tens of kilometers across — neutron-star scale, not normal-star scale.

Problem

A pulsar has $P = 5\,\mathrm{ms}$ . (1) Should its maximum radius be larger or smaller than the $1\,\mathrm{ms}$ case? (2) Use $R_{\max} = cP/(2\pi)$ to estimate it. (3) Why does this rule out a normal star?

Pulsar spin-down

Most isolated pulsars gradually slow down, losing rotational energy through magnetic fields, particle winds, and radiation, so their periods increase over time. Young pulsars tend to spin rapidly; old isolated pulsars spin more slowly; and old neutron stars in binaries can be spun back up by accreting matter from a companion. These spun-up old neutron stars are millisecond pulsars.

Millisecond pulsar

A rapidly rotating neutron star with a period of a few milliseconds, typically an old neutron star spun back up by accreting matter from a binary companion.