Astronomy & Celestial Mechanics
the sky, computed
Concept

Electron temperature — where it appears

The temperature of the free electrons in an ionised gas, which sets how often collisions excite its ions. It is measured from ratios of lines from levels at different heights, and abundances from collisional lines depend on it exponentially.

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

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

Whether an excited ion radiates depends only on what reaches it first. The rate per second at which an oxygen ion in the state that gives the 5007 Å line loses its energy, by radiating and by collision, against electron density, both logarithmic. Radiating takes about 51 seconds whatever the surroundings. Collisions speed up with density and cross at 6.8e+5 per cubic centimetre. The air at the Earth's surface, 2.7×10¹⁹ molecules per cubic centimetre, has a collision rate about 4×10¹³ times the radiative one, so the ion loses its energy without radiating. A nebula at 10⁴ per cubic centimetre is sixty times below the crossing. The line has a tiny transition probability; the atom was never forbidden to make it, and it requires only the emptiness in which there is time.

An element that was only empty space

In 1864 William Huggins turned a spectroscope on a planetary nebula and saw a bright green line that matched nothing on Earth. It was given a name, nebulium, and it was treated as a new element for sixty years, until the periodic table had no room left for it. In 1927 Ira Bowen showed it was ordinary oxygen, emitting by a route that collisions close long before any laboratory vacuum could reach it. The line was never forbidden. It simply needs about a minute of being left alone, and nothing on Earth gets that.

starlight · Spectra How much fluctuation a factor of two needs. The abundance discrepancy factor — oxygen from the recombination line over oxygen from the forbidden lines, each computed at the [O III] temperature — against the temperature fluctuation t², for nebulae with mean temperatures of 6,000, 8,000, 10,000 K. A discrepancy of 2, typical of H II regions, needs t² = 0.047, 0.081 and 0.117 respectively — temperature variations of 34% rms at 10,000 K. Photoionisation models of a smooth nebula give t² of 0.003–0.02 (shaded), which produces a discrepancy of at most 1.19 at 10,000 K.

Two counts of the same oxygen, and the gas each one sees

A glowing nebula's oxygen can be counted from its bright forbidden lines or from its faint recombination lines, and in nearly every nebula where both are measured the second count is the larger — by a factor of two in star-forming regions and by more than a hundred in a few planetary nebulae. One explanation says the temperature varies through the gas and the forbidden lines are fooled; the other says a little cold, oxygen-rich gas is hiding inside and the recombination lines are reporting on it. The two explanations disagree about which count to believe.

starlight · Spectra

Named alongside it

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

Forbidden linePlanetary nebulaAbundance discrepancyCollisional excitationCritical densityH II regionMetallicityMetastable stateNebuliumRecombination lines

All concepts