Pulsars and magnetars are extreme neutron stars left behind after some massive stars explode as supernovae. This cheat sheet helps students connect observations, such as pulses and X-ray bursts, to physics ideas like rotation, magnetic fields, and energy loss. It is useful because these objects test gravity, electromagnetism, nuclear matter, and high-energy astronomy in one compact topic.
The most important ideas are that pulsars are rapidly rotating neutron stars whose beams sweep across Earth like a lighthouse. Their measured period P and period change dP/dt reveal their age, energy loss rate, and magnetic field strength. Magnetars are neutron stars with magnetic fields far stronger than ordinary pulsars, so their activity is powered mainly by magnetic energy rather than rotation.
Key Facts
- A neutron star is typically about 1.4 solar masses compressed into a radius of about 10 to 12 km.
- A pulsar is observed when a rotating neutron star's radiation beam crosses Earth once each rotation, so pulse period equals rotation period P.
- Rotation frequency is f = 1/P, where f is in hertz if P is in seconds.
- The characteristic age of a pulsar is tau = P/(2 dP/dt), assuming steady magnetic braking and a much smaller birth period.
- The spin-down luminosity is E_dot = 4 pi^2 I (dP/dt)/P^3, where I is the neutron star moment of inertia.
- A common magnetic field estimate for a rotating dipole pulsar is B = 3.2 x 10^19 sqrt(P dP/dt) gauss.
- Ordinary radio pulsars often have magnetic fields near 10^11 to 10^13 gauss, while magnetars often have fields near 10^14 to 10^15 gauss.
- Magnetar flares and bursts are mainly powered by magnetic field stress and crust cracking, not by nuclear fusion or normal stellar burning.
Vocabulary
- Neutron star
- A neutron star is the ultra-dense collapsed core of a massive star after a supernova explosion.
- Pulsar
- A pulsar is a rotating neutron star seen as regular pulses because its radiation beam sweeps across Earth.
- Magnetar
- A magnetar is a neutron star with an extremely strong magnetic field that powers intense X-ray and gamma-ray activity.
- Period
- Period is the time for one rotation of a pulsar, usually measured from one pulse arrival to the next.
- Spin-down
- Spin-down is the gradual slowing of a neutron star's rotation as it loses rotational energy.
- Light cylinder
- The light cylinder is the distance from a rotating neutron star where co-rotating material would need to move at the speed of light.
Common Mistakes to Avoid
- Confusing pulse period with the time between different stars' pulses is wrong because P measures one neutron star's rotation, not a comparison between objects.
- Assuming every neutron star is a pulsar is wrong because a neutron star is only observed as a pulsar if its beam crosses Earth and is detectable.
- Treating magnetars as powered mainly by fast rotation is wrong because their bursts and persistent high-energy emission are usually powered by magnetic energy.
- Ignoring units in B = 3.2 x 10^19 sqrt(P dP/dt) is wrong because P must be in seconds and dP/dt must be in seconds per second to get B in gauss.
- Thinking a larger dP/dt always means an older pulsar is wrong because characteristic age tau = P/(2 dP/dt), so a larger dP/dt can mean a younger object if P is similar.
Practice Questions
- 1 A pulsar has period P = 0.50 s. What is its rotation frequency f?
- 2 A pulsar has P = 2.0 s and dP/dt = 1.0 x 10^-12. Estimate its characteristic age tau in seconds.
- 3 Using B = 3.2 x 10^19 sqrt(P dP/dt), estimate the magnetic field of a pulsar with P = 5.0 s and dP/dt = 2.0 x 10^-11.
- 4 Explain why a neutron star with no visible pulses might still be a real neutron star rather than not existing.