Illustrated Physics
physics, drawn
Concept

Brightness temperature — where it appears

The temperature a blackbody would need to emit the observed intensity at a given frequency. For thermal sources it equals the physical temperature; for lasers, masers, electroluminescence or nonthermal radio sources it can be vastly higher, which is how such emission is recognised.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

The same source, seen coming and seen going. The observed flux of a moving source, relative to the same source at rest, against the angle between its motion and the line of sight, on a logarithmic scale, at β = 0.5, β = 0.9, β = 0.99. The curves span 8.1e+1, 1.3e+5, 1.6e+9 between the approaching and receding directions, which is ((1+β)/(1−β))⁴ exactly. The fourth power comes from the one quantity every observer agrees about: the specific intensity divided by the cube of the frequency. Three powers of the Doppler factor come from that invariance and the fourth from integrating over frequency. Two consequences are worth reading off. A source seen side-on is fainter than the same source at rest, by γ⁴ — a factor of 2.5e+3 at the fastest speed drawn. And half the light arrives inside a cone of 60.0°, 25.8°, 8.1°, which for a fast source is one over γ.

The brightness that is not the same for everyone

A moving source is not merely shifted in colour. Its light is concentrated forwards, so the same lamp is enormously brighter seen coming than seen going — by the fourth power of one number, which for a jet at ninety-nine per cent of light speed is a factor of a thousand million. The reason is that only one combination of intensity and frequency is the same for every observer, and everything else follows from it.

relativity · Doppler The light of a diode at room temperature is as bright as a surface thousands of kelvin hot. How many photons occupy each mode of the light, on a logarithmic scale, against photon energy. The lowest curve is the thermal glow of a 1.42 eV semiconductor at 300 K with no voltage across it. The solid curve above it is the same device with 1.3 V across it, emitting only above its gap. The dashed curve is a blackbody at 2571 K, the temperature whose light has the same occupation as the diode's at 1.472 eV, just above the gap. They cross there and nowhere else: the diode's occupation falls a factor e every 25.9 meV, as its lattice's temperature requires, and the blackbody's every 222 meV. No single temperature describes the diode's light. At each photon energy it has a brightness temperature, and that temperature is 300 K multiplied by ε/(ε − qV).

The glow that carries a voltage

Thermal radiation has no chemical potential, because walls make and destroy photons freely. A light-emitting diode is a body that glows at room temperature with a voltage written into its light — Planck's law with the voltage as the photons' chemical potential — which is why its light can be as bright as a surface thousands of kelvin hot, why at low voltage it can put out more light than the power it draws and cool itself doing so, and why a reverse voltage makes a surface look colder than it is.

thermodynamics · Chemical potential Each wavelength sees from a different height. The weighting functions of 7 infrared channels in a carbon-dioxide band — how much each height contributes to the radiance a satellite measures in that channel — for absorption strengths chosen so that the peaks sit at 3, 8, 14, 20, 27, 35, 43 km. Each is scaled to its own maximum. A channel's peak is where the carbon dioxide above that height amounts to one optical depth: deeper, its emission is absorbed on the way out; higher, there is too little gas to emit. Each function is about 17 km wide at half its peak, the same for every channel, because the absorber's density falls with one scale height, 7 km. The dotted curve is the temperature profile of the standard atmosphere, on its own scale from 180 to 300 K, whose cold tropopause and warm stratosphere the channels between them straddle.

The spectrum that is a thermometer at every height

A satellite looking down at the Earth in the infrared sees, at each wavelength, the glow of whatever layer of air that wavelength escapes from. In the wings of carbon dioxide's great absorption band the air is transparent and the satellite sees the ground; towards the band's centre the gas grows opaque and each wavelength escapes from higher up. A single spectrum is therefore a stack of thermometers at different heights, and weather forecasts are built on reading it. What cannot be read from it is anything much thinner than the ten to twenty kilometres of air each of those thermometers averages over.

quantum · Blackbody

Named alongside it

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

AberrationBand gapBlackbodyBlackbody radiationChemical potentialCosmic microwave backgroundDetailed balanceDipole anisotropyDoppler factorFluxHeat pumpInverse problem

All concepts