9 Astrophysics: Neutron Stars and Black Holes

Neutron Stars

  • Formation

    • End of life of massive star leads to core collapse.
    • Iron core collapses to the size of Milwaukee (approx. 20 km or 13 mi in diameter).
    • Energy released during collapse is 100 times greater than the energy emitted over the star's lifetime.
    • Results in a neutron star, an object composed almost entirely of neutrons, akin to a giant atomic nucleus.

  • Historical Context

    • Lev Landau (1930) proposed that stellar core pressure could lead to the conversion of electrons to neutrons, forming neutron stars.

  • Characteristics

    • Radius: Approximately 10 km (1/1000 the Earth's radius).
    • Density: Over 1 billion tons per teaspoon of neutron star matter.
    • Mass: Approximately 1.4 solar masses.

  • Energy Considerations

    • Gravitational energy released during neutronic formation is about 1 billion times the energy emitted by the Sun throughout its lifecycle (Baade & Zwicky, 1933).

Discovery of Pulsars

  • Initial Speculation

    • 1966: Shklovsky suggested a bright X-ray source was a neutron star accreting matter from a companion star.

  • Notable Discoveries

    • Jocelyn Bell (1967) used a radio antenna to identify pulsars—regularly pulsing sources of radio waves, which were later identified as neutron stars.
    • Pulses detected from pulsars exhibit extreme regularity (e.g., PSR B0329+54, period: 0.7 s).

  • Pulsar Characteristics

    • Pulsars are neutron stars emitting beams of radiation due to intense rotating magnetic fields.
    • Magnetic fields around pulsars: approximately 10^{12} times stronger than Earth's.
    • Pulsars must rotate at a period < 1.3 seconds to avoid disintegration.

Black Holes

  • Formation of Black Holes

    • If a neutron star exceeds approximately three solar masses, the nuclear forces can no longer withstand gravitational collapse, leading to the formation of a black hole.

  • Escape Velocity

    • To escape a neutron star: approx. 100,000 km/s (one-third the speed of light).
    • Once escape velocity exceeds light speed, everything, including light, is drawn in.

  • Historical Origin

    • John Michell (1784) and Pierre Simon Laplace (1799) theorized about black holes using gravitational attraction properties.

  • Properties of Black Holes

    • Event Horizon: Boundary where escape from the black hole becomes impossible.
    • Nothing inside the event horizon can communicate or emit information outside.

Spacetime and Relativity

  • Galilean View vs. Einstein’s Revolution

    • Galilean: Absolute time and flat space.
    • Einstein: Space and time are interwoven; speed of light is constant regardless of observer.

  • Special Relativity Concepts

    • Laws of motion apply differently based on the observer's frame of reference.
    • Time and space are not absolute quantities; they relate to the observer's state.

  • General Relativity

    • Mass and energy warp spacetime, creating a curvature in the fabric of the universe.
    • Black holes represent extreme spacetime curvature, where light cannot escape.

Gravitational Waves

  • Existence

    • Predictions derive from general relativity, signaling ripples in spacetime caused by massive objects in motion.

  • Detection of Gravitational Waves

    • Anticipated from ambitious observatories (e.g., LIGO), which aim for early detections by measuring minute changes in distances caused by passing waves.

Hawking Radiation

  • Phenomenon
    • Derived from quantum mechanics principles; particles at black hole event horizon can induce radiation, resulting in black hole 'evaporation.'
  • Evaporation Timescale
    • A solar mass black hole takes 2 imes 10^{67} years to evaporate; smaller black holes evaporate faster; thus, very small black holes could explode with tremendous energy practically instantaneously.