Astronomy & Celestial Mechanics
the sky, computed
Concept

Brightness temperature — where it appears

The temperature a blackbody would need in order to produce the observed intensity at a given frequency. It is a way of quoting a brightness rather than a claim about the source, and it exceeds any thermal value for coherent or non-thermal emission.

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

Three slopes: 2.5, −0.75 and −1.25, and only the middle one is about the electrons. A radio source's spectrum across five decades of frequency, computed for an electron population with index p = 2.5 in a uniform field. Nothing in this curve is a temperature, because a power law has no scale and therefore nothing a thermometer could read. The straight section between the two bends has slope −0.75, measured here off the drawn curve, and the electron index follows from it and from nothing else: α = (p − 1)/2, so a flux ratio between two frequencies is a measurement of the energy distribution of particles in a place no detector will ever visit. The two bends are the other two measurements. Below 80 MHz the source is opaque to its own radiation and rises as ν^2.5 — a slope fixed at 5/2 by the geometry alone, whatever the electrons are doing — and the frequency at which that happens gives an angular size for a source nothing has resolved, because the turnover is where the brightness temperature meets the electrons' own. Above 12 GHz the spectrum steepens by 0.50: the electrons that radiate at high frequency lose their energy fastest, so the top of the distribution has already emptied, and the frequency of the break is a clock. What no part of this curve gives is the magnetic field. Only the field and the particle density together enter the emission, and every field strength ever quoted for a radio source comes from assuming the two share the energy equally.

A spectrum with no temperature in it

Every spectrum in this collection so far has been a thermometer. A radio lobe's is a power law, and a power law has no scale — so there is nothing for a thermometer to read, and what the shape carries instead is the energy distribution of the particles that made it.

starlight · Synchrotron radiation One whole orbit. The system's total brightness through one orbit: the transit at phase 0, the slow rise and fall of the planet's illuminated hemisphere between, and the secondary eclipse at phase 0.5 where the planet's own light is removed. The transit is 1.05%; the secondary eclipse is 1800 ppm, about 6 times shallower.

The planet is seen when it disappears

Half an orbit after the transit the planet passes behind its star, and the light that vanishes is the planet's own. Subtracting two brightnesses taken hours apart isolates a body nothing has ever resolved.

exoplanets · Exoplanet atmospheres

Named alongside it

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

AlbedoCooling breakDay night contrastElectron energy distributionEmission spectrumEquipartitionHeat redistributionHot spot offsetMinimum-energy fieldNon-thermal emissionOccultationPhase curve

All concepts