Stars

Key physical properties of the ultra-dense compact objects shown in the image:

1. Pulsar

A highly magnetized, rapidly rotating neutron star that emits beam radiation along its magnetic poles.

• Composition: Degenerate neutron matter core with a solid iron-rich outer crust.
• Magnetic Field: 10^8 to 10^{12}\text{ Gauss} (10^4 to 10^8\text{ Tesla}).
• Rotation Period: Ranges from milliseconds (ms pulsars rotating up to \sim700\text{ Hz}) to a few seconds.
• Mass & Radius: Typical mass of 1.4\text{ M}_\odot to 2.1\text{ M}_\odot; radius of \sim10\text{--}12\text{ km}.
• Key Mechanism: Acts as a cosmic lighthouse—pulses are detected when the magnetic axis sweeps past the observer's line of sight.

2. Magnetar

A type of neutron star characterized by an extraordinarily powerful magnetic field.

• Composition: Degenerate neutron matter under extreme magnetic pressure.
• Magnetic Field: 10^{14} to 10^{15}\text{ Gauss} (10^{10} to 10^{11}\text{ Tesla})—roughly 1,000 times stronger than a typical pulsar.
• Rotation Period: Slower rotation than most pulsars, typically 2\text{ to }10\text{ seconds}.
• Mass & Radius: Typical mass around 1.4\text{ M}_\odot to 2.0\text{ M}_\odot; radius of \sim10\text{--}12\text{ km}.
• Key Mechanism: Energy output is driven by magnetic field decay rather than rotation, leading to intense X-ray and gamma-ray bursts ("starquakes").

3. Quark Star (Strange Star)

A hypothetical compact object resulting from ultra-dense nuclear matter collapsing past the neutron-degeneracy point into deconfined up, down, and strange quarks (Strange Quark Matter / SQM).

• Composition: Quark-gluon plasma / deconfined u, d, and s quark matter.
• Density: Exceeds nuclear saturation density (> 3 \times 10^{14}\text{ g/cm}^3).
• Stability: Theorized under the Bodmer-Witten hypothesis to be the absolute ground state of hadronic matter.
• Mass & Radius: Predicted mass up to \sim2.3\text{--}2.5\text{ M}_\odot; radius slightly smaller than a standard neutron star (\sim8\text{--}11\text{ km}).
• Key Feature: Sharper density gradient at the surface compared to standard neutron stars, with high potential rotational speeds without disruption.

4. Black Hole

A region of spacetime where gravitational pull is so intense that nothing, including light, can escape from within its event horizon.

• Composition: All mass is concentrated into a gravitational singularity (zero volume in classical GR, or bounded by quantum gravity scales).
• Key Boundaries:
  • Event Horizon (R_s): R_s = \frac{2GM}{c^2} for a non-rotating (Schwarzschild) black hole.
  • Photon Sphere: Region at 1.5 R_s where light orbits in unstable paths.
  • Accretion Disk & Gravitational Lensing: Surrounding hot matter emitting radiation, visually bent around the black shadow via intense spacetime curvature.
• Mass & Radius: Stellar-mass black holes range from \sim3\text{ M}_\odot to tens of M_\odot; event horizon radius scales linearly with mass (\sim3\text{ km} per solar mass).
• Fundamental Parameters: Defined entirely by three macroscopic properties according to the No-Hair Theorem: Mass (M), Spin/Angular Momentum (J), and Electric Charge (Q).