Astronomy & Celestial Mechanics
the sky, computed
Concept

Cooling break — where it appears

The frequency in a synchrotron spectrum above which the emitting electrons have lost much of their energy to radiation. Above it the spectrum steepens, and its position combines the field strength with the electrons' age.

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

Also named here as radio lobe — the same set of essays touches all of them, so they are one junction rather than several.

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 Spectra that age, and spectra that stop ageing. Synchrotron spectra in a 3-microgauss field, divided by the straight power law the electrons were injected with so that a spectrum with no break would be a flat line at zero, at ages of 10, 30, 100 million years. Dashed: electrons left alone, whose break falls steadily to lower frequency. Solid: the same electrons stirred throughout, gaining energy at a rate of one e-fold every 30 million years against their losses. The stirred spectra's break moves down at first and then stops, at the frequency radiated by electrons of Lorentz factor 41,763, where gain and loss balance. Read as passive spectra, the stirred ones give ages of 8.5, 18.9, 28.8 million years: the last is 3.5 times younger than the electrons are.

A lobe that reads the time since it was stirred

If a radio lobe's electrons are re-energised in place by the turbulence around them, the break in their spectrum stops falling and its spectral age stops growing, settling at the time the stirring takes to double their energy a few times over. The spectrum's shape does not betray it: a stirred lobe fits an unstirred one exactly. What betrays it is a map that stops ageing with distance, and a bill for energy that grows exponentially with the time the stirring lasts.

starlight · Synchrotron radiation

Named alongside it

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

Radio lobeSynchrotron radiationBrightness temperatureElectron energy distributionEquipartitionFermi accelerationInverse Compton scatteringMinimum-energy fieldNon-thermal emissionParticle accelerationPolarisationPower law

All concepts