Astronomy & Celestial Mechanics
the sky, computed
Concept

Ultraluminous x-ray sources — where it appears

Off-nuclear X-ray sources in galaxies that appear brighter than a stellar-mass black hole accreting at its Eddington limit could be. Some pulse, so they are neutron stars, and the question is how much of their brightness is real and how much is light beamed towards the observer.

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

A field that makes electrons transparent. The electron-scattering cross-section for photons polarised across a strong magnetic field, as a share of the free-electron value, against photon energy, for fields of 10¹², 10¹³, 10¹⁴ gauss, on logarithmic axes. Below the electron cyclotron energy — 12, 116, 1160 keV for these fields — an electron bound to the field can barely respond to a wave whose electric field is perpendicular to it, and the cross-section falls as the square of the ratio of energies. At the 10 keV of these sources' X-rays, a 10¹⁴ gauss field reduces it 13,456-fold. The Eddington limit is written with the free-electron cross-section; in such a field it is the wrong number.

A limit written for free electrons

The Eddington limit says a star cannot shine brighter than the point where its light pushes its own gas away, and the push is calculated for free electrons scattering light. In a magnetic field of a hundred trillion gauss an electron is not free. It is bound to the field, it can barely respond to light polarised across it, and the limit calculated for it is the wrong number by a factor of hundreds — which is one of two ways a neutron star can shine five hundred times brighter than it is supposed to.

stars · Eddington limit 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

Named alongside it

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

Eddington limitNeutron starsAccretion columnBeamingCorotation radiusCyclotron resonanceElectron scatteringMagnetarsMagnetospheric radiusPhotoionisationRecombination linesStellar winds

All concepts