Pulsar Timing Simulator: Spin Period, Dispersion & Magnetic Fields

simulator intermediate ~10 min
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τ = 2.5 Myr — characteristic age of B0329+54

PSR B0329+54, a well-known pulsar with period 714 ms, has a characteristic age of about 5.5 million years and a surface magnetic field of ~10¹² Gauss, typical of normal radio pulsars.

Formula

τ_char = P / (2 Ṗ) (characteristic age)
B_surf = 3.2 × 10¹⁹ √(P · Ṗ) Gauss
Δt_DM = 4.15 ms × DM × (f_lo⁻² - f_hi⁻²)

Cosmic Lighthouses

Pulsars are rapidly rotating neutron stars — city-sized remnants of supernova explosions — that emit narrow beams of radio emission from their magnetic poles. Jocelyn Bell Burnell discovered the first pulsar in 1967, initially dubbed 'LGM-1' for 'Little Green Men' due to its clock-like regularity. The discovery revealed a new class of stellar object and confirmed the existence of neutron stars predicted by Baade and Zwicky in 1934.

The Spin-Down Clock

Pulsars gradually lose rotational energy through magnetic dipole radiation, causing their period to increase over time. The period derivative Ṗ, measured in seconds per second, encodes the pulsar's energy loss rate. Combined with the period, it yields the characteristic age τ = P/(2Ṗ) and the surface magnetic field strength B ∝ √(PṖ). Young pulsars spin fast with strong fields (~10¹² G); recycled millisecond pulsars have weaker fields (~10⁸ G) but extraordinary rotational stability.

Interstellar Dispersion

Radio pulses traveling through the ionized interstellar medium experience frequency-dependent delay: lower frequencies arrive later than higher ones. The dispersion measure DM — the integrated electron column density — quantifies this effect. De-dispersing the signal (removing the frequency-dependent delay) is essential for achieving the sharpest pulse profiles and the most precise timing measurements.

Pulsar Timing Arrays

Millisecond pulsars are so rotationally stable that an ensemble of them can serve as a galaxy-scale gravitational wave detector. Pulsar timing arrays (PTAs) search for correlated timing residuals caused by nanohertz gravitational waves — the rumble of merging supermassive black holes. In 2023, NANOGrav and partner collaborations reported compelling evidence for this gravitational wave background, opening a new window on the universe.

FAQ

What is a pulsar?

A pulsar is a rapidly rotating neutron star that emits beamed radio waves from its magnetic poles. As the star rotates, the beam sweeps past Earth like a lighthouse, producing regular radio pulses. Over 3,000 pulsars are known, with periods ranging from 1.4 milliseconds to several seconds.

What is dispersion measure?

Dispersion measure (DM) quantifies the total column density of free electrons along the line of sight, in units of pc cm⁻³. Radio pulses at lower frequencies arrive later because the interstellar plasma slows them more, and the delay is proportional to DM/f².

How is pulsar age estimated?

The characteristic age τ = P/(2Ṗ) assumes the pulsar was born spinning much faster than its current period and has been spinning down due to magnetic dipole radiation. It provides an order-of-magnitude estimate but can differ significantly from the true age.

What is a pulsar timing array?

A pulsar timing array (PTA) monitors dozens of millisecond pulsars to detect correlated timing residuals caused by passing gravitational waves. In 2023, NANOGrav and other collaborations reported evidence for a gravitational wave background from supermassive black hole binary mergers.

Sources

Embed

<iframe src="https://homo-deus.com/lab/radio-astronomy/pulsar-timing/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub