World Science Scholars
2.2 Gravitational Wave Astrophysics
summary
Sources of gravitational waves

• In order to produce detectable gravitational waves, a source must have a large amount of mass and a very high acceleration.
• Binary neutron star or binary black hole systems are such sources. Both involve huge masses rapidly orbiting one another until they collide. The orbital motion and eventual collision provide enough acceleration to generate detectable gravitational waves.
• Lone neutron stars are also sources. As they spin around their axes, neutron stars can distort in shape, breaking their spherical symmetry and producing gravitational waves with constant frequency and amplitude.
• Supernovae are another source, since the explosion of a star will rapidly accelerate a huge amount of material very quickly.
• Even the Big Bang itself is a source of gravitational waves. These primordial gravitational waves, produced immediately after the Big Bang and totally unaffected by matter, can tell us about the earliest moments of the universe.

Einstein’s ambivalence

• Gravitational waves were first introduced in Einstein’s landmark 1916 paper on general relativity, though he did not produce a correct formulation of them until 1918.
• Their existence troubled Einstein, and he submitted a retraction in 1937 saying that he was wrong about the existence of gravitational waves. Later that year he retracted that retraction, and subsequently never published about gravitational waves again.
• Einstein thought that even if they did exist, gravitational waves were too small to have any practical purpose. Doubts about their importance and indeed their existence persisted in the scientific community into the 1950s.

Mounting observational evidence

• Black holes (called “dark stars” at the time) were predicted by Swarszchild in 1916, shortly after Einstein unveiled general relativity. The first black hole was discovered in 1971.
• Neutron stars were first proposed in 1934. In 1967 rotating neutron stars, called pulsars, were proposed. They were predicted to emit a rotating beam of EM radiation that would be detectable from Earth, and in fact the first pulsar was observed that same year.
• In 1974 two astronomers (Hulse and Taylor) discovered a pulsar that was in a binary system with another neutron star. Years of observation showed that the two stars were getting closer together.
• The shrinking orbit of this binary system perfectly matched predictions of general relativity, which says that the two stars will lose energy as they radiate gravitational waves. This observation was the first indirect evidence for the existence of gravitational waves.

Defining gravitational waves

• In the mid-1970s Kip Thorne and others began to seriously work on the problem of calculating gravitational wave properties using the equations of general relativity. This type of work is called numerical relativity.
• Gravitational waves have what is called quadrupolar nature – this means that when a gravitational wave passes through a circle, one axis stretches while the other shrinks.
• The amount of stretching and shrinking ($\Delta L$) is proportional to the amplitude, or strain ($h$) , of the wave as well as the size of that region of spacetime ($L$) according to this equation: $$\Delta L = h * L$$
• Over a distance of 1m this would result in spacetime stretching by 10-21m, roughly 1 million times smaller than the width of an atomic nucleus.
• This posed a problem for detecting gravitational waves, since any spacetime stretching would be extremely small.

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