Pulsar
A pulsar is a highly magnetised, rapidly rotating neutron star that emits beams of electromagnetic radiation from its magnetic poles; when these beams sweep across Earth like a cosmic lighthouse, observers detect precise periodic pulses ranging from milliseconds to seconds. Pulsars are the remnants of massive stars (>8 M☉) that exploded as core-collapse supernovae, leaving behind an object ~20 km in diameter but with a mass of 1.4–2 M☉ and a density (~10¹⁷ kg/m³) comparable to atomic nuclei. The extreme regularity of pulsar timing makes them natural clocks used to test general relativity, detect gravitational waves, and probe the interstellar medium.
Key Formula
E_rot = (1/2) I Ω²; dE/dt = −I Ω (dΩ/dt)
LaTeX: E_{\rm rot} = \frac{1}{2}I\Omega^2, \quad \dot{E} = -I\Omega\dot{\Omega}
| Symbol | Meaning | Unit |
|---|---|---|
| E_rot | Rotational kinetic energy | joules (J) |
| I | Moment of inertia (~10⁴⁵ g·cm² for NS) | kg·m² |
| Ω | Angular velocity (Ω = 2π/P) | rad/s |
| Ω̇ | Spin-down rate (negative for slowing pulsar) | rad/s² |
Worked Example
Problem
The Crab Pulsar has a period P = 33 ms and a period derivative dP/dt = 4.2 × 10⁻¹³ s/s. Assuming a moment of inertia I = 10³⁸ kg·m², calculate the spin-down luminosity (energy loss rate).
Solution
Step 1 — Angular velocity: Ω = 2π/P = 2π / 0.033 ≈ 190.4 rad/s. Step 2 — Angular deceleration: Ω̇ = −(2π/P²)(dP/dt) = −(2π × 4.2 × 10⁻¹³) / (0.033)² ≈ −2.43 × 10⁻⁹ rad/s². Step 3 — Spin-down luminosity: Ė = −I Ω Ω̇ = −10³⁸ × 190.4 × (−2.43 × 10⁻⁹) ≈ 4.6 × 10³¹ W. Step 4 — Convert: 4.6 × 10³¹ W ≈ 1.2 × 10⁵ L☉.
Answer
Spin-down luminosity ≈ 4.6 × 10³¹ W ≈ 1.2 × 10⁵ L☉
Notable Pulsars and Their Properties
| Pulsar | Period (ms) | Magnetic Field (T) | Age Estimate (yr) | Discovery Notes |
|---|---|---|---|---|
| Crab Pulsar (B0531+21) | 33.1 | ~8 × 10⁸ | 970 (SN 1054) | First optically identified pulsar |
| Vela Pulsar (B0833-45) | 89.3 | ~3 × 10⁸ | 11,000 | Bright gamma-ray source |
| PSR B1919+21 | 1,337 | ~1 × 10⁸ | ~10⁷ | First pulsar discovered (1967) |
| PSR J0437-4715 | 5.76 (ms) | ~5 × 10⁵ | Recycled (~10⁹) | Nearest millisecond pulsar |
| Double Pulsar (J0737-3039) | 22.7 & 2,773 | Both ~10⁸ | ~210 Myr | Only known double pulsar binary |
Interactive Tools
ATNF Pulsar Catalogue
Comprehensive database of over 3,000 known pulsars with all measured parameters.
Open ToolWolframAlpha Pulsar Spin-Down
Calculate spin-down luminosity and characteristic age from period data.
Open ToolNASA Fermi Pulsar Wind Nebulae
Gamma-ray pulsar data and science from the Fermi Gamma-ray Space Telescope.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Chandrasekhar Limit
The Chandrasekhar limit is the theoretical maximum mass (~1.4 solar masses) that a white dwarf star can possess and still be supported against gravitational collapse by electron degeneracy pressure. Below this limit, degenerate electrons exert sufficient quantum mechanical pressure to halt collapse; above it, gravity overwhelms this pressure, triggering a Type Ia supernova or collapse to a neutron star. The limit was derived by Subrahmanyan Chandrasekhar in 1930 using special relativistic corrections to the equation of state of a degenerate electron gas, earning him the 1983 Nobel Prize in Physics.
Stellar Nucleosynthesis
Stellar nucleosynthesis is the process by which nuclear fusion reactions inside stars create heavier atomic nuclei from lighter ones, releasing energy that sustains the star against gravitational collapse. Main-sequence stars primarily fuse hydrogen into helium via the proton–proton chain or CNO cycle, while more massive stars in later evolutionary stages fuse helium, carbon, oxygen, and silicon up to iron (Fe-56), the most tightly bound nucleus. Elements heavier than iron are synthesised through neutron-capture processes (s-process in AGB stars; r-process in neutron star mergers and supernovae), making stars the principal factories of the chemical elements in the universe.
Binary Star System
A binary star system consists of two stars gravitationally bound to each other, orbiting their common centre of mass (barycentre) under mutual gravitational attraction. Binary systems are remarkably common, accounting for roughly half of all star systems in the Milky Way, and are the primary means of directly measuring stellar masses through application of Kepler's third law. Depending on orbital geometry, binaries may be classified as visual, spectroscopic, eclipsing, or astrometric, each revealing complementary information about the stellar components.
Portmanteau of "pulsating star," coined by science journalist Anthony Michaelis in 1968 after the discovery by Jocelyn Bell Burnell and Antony Hewish at Cambridge in 1967. Initial designations were LGM (Little Green Men) before a natural explanation was confirmed.