Astronomy & Celestial Mechanics
the sky, computed
Concept

Recombination lines — where it appears

Emission lines produced as an ion captures a free electron and the electron cascades down through the levels. They are faint but depend only weakly on temperature, which makes them an abundance measure independent of the nebular thermometer.

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

The nebula's line, if the source is beamed. The luminosity of the He II 4686 Å line a surrounding nebula would emit, against the source's beaming fraction b, for sources that appear at 10⁴⁰ and 10⁴¹ erg/s to an observer in the beam, with 10% of their true output in photons able to ionise He⁺. The nebula sees the true luminosity, b times the apparent one, so its line falls in proportion to b: a source apparently at 10⁴¹ that is beamed into a hundredth of the sky lights its nebula like an unbeamed source at 10³⁹. Measured He II luminosities of nebulae round ultraluminous sources are 10³⁵ to 10³⁷ erg/s (shaded). On this conversion a source apparently at 10⁴⁰ whose nebula shows a few 10³⁶ needs no beaming at all; one apparently at 10⁴¹ with the same line is beamed into a tenth of the sky or less.

A nebula that cannot be beamed at

An X-ray source a hundred times brighter than a neutron star should be allowed to shine may be lying about its luminosity: if its light leaves through a narrow funnel pointed at the Earth, it looks as bright as a source a hundred times more powerful. A single observer cannot tell. The gas around it can. A nebula surrounding the source is lit from every direction at once and records what the source emits in all of them, and a bubble blown by its wind records the power it has put out over a million years. Each is a calorimeter no beam can fool.

stars · Eddington limit 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.

Abundance discrepancyBeamingEddington limitElectron temperatureForbidden lineH II regionMetallicityNeutron starsPhotoionisationPlanetary nebulaStellar windsSuper eddington accretion

All concepts