Illustrated Physics
physics, drawn
Concept

Thomson scattering — where it appears

The scattering of light by a free charged particle whose recoil is negligible, with a cross-section independent of the light's frequency. For an electron it is 6.65 × 10⁻²⁹ m², and it sets how opaque a hot ionised gas such as a star's interior or the early universe is to its own radiation.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

The brightest anything of a given mass can be. The Eddington luminosity against mass, with the main sequence drawn beside it. Radiation pushes outward on the electrons and gravity pulls inward on the protons, and both go as one over the distance squared — so the radius cancels out of the comparison entirely, checked here at three radii spanning four decades and coming out identical to 1e-20. What is left is a luminosity: L = 4πGMc/κ, which is 1.47 × 10³¹ watts per solar mass, or 3.8·10⁴ solar luminosities. Above it, radiation drives the outer layers away faster than gravity can hold them. The Sun is at 2.6e-5 of its own limit and in no danger; a star of 10 solar masses is at 1.2e-2; and a star of 100 is at 0.83, which is why the two lines converge at the top of the chart and why the most massive stars known are a few hundred solar masses rather than a few thousand. They do not fail to form for lack of gas; they blow away the gas that would have made them heavier, and once formed they shed mass continuously in a radiation-driven wind. The limit is the same expression for an accreting black hole, where it caps not the brightness but the rate at which mass can be taken on.

The brightness a mass cannot exceed

Light pushes outward on the electrons of a star and gravity pulls inward on its protons, and both forces fall off as one over the distance squared. The distance therefore cancels, and what is left is a limit on brightness rather than on size — 3.8 × 10⁴ times the Sun's luminosity for every solar mass, above which a body drives its own outer layers away.

astrophysics · Radiation pressure Every colour a bound electron can meet. The light-scattering cross-section of one electron bound with a resonance at 2.105 eV (589 nm) and damped only by its own radiation, in units of the Thomson cross-section, against the frequency of the light in units of the resonance, on logarithmic axes spanning nine decades of frequency and twenty-five of cross-section. Far below the resonance it rises with slope 4.001, Rayleigh's fourth power: at a hundredth of the resonance it is 1.0 × 10⁻⁸ times the Thomson value. At the resonance it spikes to 2.5 × 10¹⁵ times the Thomson value, which is 3λ²/2π = 1.66 × 10⁻¹³ m² exactly, over a width of 2.0 × 10⁻⁸ of the resonant frequency. Above it the cross-section settles to the Thomson value, 6.652 × 10⁻²⁹ m² — 1.0002 times it at a hundred times the resonance — and stays within 10 per cent of it from 4.6 times the resonant frequency, 9.8 eV, to 29 keV, 3.5 decades, until the photon energy approaches the electron's rest energy, where the Klein–Nishina factor for a free electron takes it down to 0.431 of the Thomson value at 511 keV and 0.077 at 10 MeV.

The cross-section that forgets the colour

An electron on a spring, shaken by light, scatters it — weakly and very blue below its resonance, enormously at it, and above it by exactly the same amount whatever the colour. That flat stretch is the Thomson cross-section, 6.65 × 10⁻²⁹ m², and it is why an X-ray picture of a crystal is a map of electrons and why the corona is white.

astrophysics · Radiating charge The photon a fast electron throws back. The highest energy of a laser photon scattered straight back by an electron it meets head-on, against the electron's energy, for a carbon-dioxide laser, an infrared and a green one, on logarithmic axes: dashed, 4γ² times the laser photon's energy, the double Doppler shift of a mirror moving at the electron's speed; solid, the exact edge with the electron's recoil, E·x/(1 + x) with x = 4γε/mc²; dotted, the electron's own energy, which no scattered photon reaches. A 1 GeV electron turns 1.17-eV infrared photons into gamma rays of 17.6 MeV, within 1.8 per cent of the mirror's figure. At 46.6 GeV and 2.35 eV the mirror's figure is 78.2 GeV, more than the electron has to give; the photon actually comes back with 29.2 GeV.

The photon a fast electron throws back

Shine an infrared laser at a beam of gigaelectronvolt electrons and gamma rays come back out of the collision, each carrying seventeen million times the energy of the laser photon it started as. The electron acts as a mirror moving at nearly the speed of light, and a moving mirror multiplies the energy of light by two Doppler factors. Push the electron's energy far enough and the mirror arithmetic promises photons more energetic than the electron itself — and the photon's own momentum, which the mirror ignored, steps in to stop it.

relativity · Length contraction What one scattering does to a photon's energy. The average fractional change in a photon's energy when it scatters off an electron in a gas at temperature T, against the photon's energy: (4kT − ε)/mc², for gases at 10⁶, 10⁷ and 10⁸ K. A photon below 4kT gains energy, taking it from the electrons' motion; one above loses it, as recoil, to the electrons. The crossing sits at ε = 4kT: 0.34 keV at 10⁶ K, 3.45 keV at 10⁷ K, 34.47 keV at 10⁸ K. The changes per scattering are small, a few per cent at most here, but a gas whose electrons scatter each photon many times, or that is bathed in light for long enough, is heated or cooled until the gains and losses balance over the whole spectrum.

The temperature a gas takes from the light around it

A thin, ionised gas bathed in light settles at a temperature that has nothing to do with how much light there is and everything to do with its colour. Every time a photon scatters off an electron, the two exchange a little energy: a photon softer than four times the electrons' thermal energy gains, a harder one loses by recoil. Balanced over a spectrum, the rule sets the gas at a quarter of the light's mean photon energy. That puts gas near a quasar at tens of millions of kelvin, and it caps the heating once photons approach the electron's own rest energy. For blackbody light the rule falls four per cent short, and the shortfall is the photon being a boson.

relativity · Relativistic thermodynamics

Named alongside it

The objects these essays reach for when they reach for this one.

Compton scatteringAccretionKlein nishinaBlackbodyCompton temperatureCoronaCross-sectionDoppler effectEddington limitInverse compton scatteringThe inverse-square lawLarmor formula

All concepts