Astronomy & Celestial Mechanics
the sky, computed
Concept

Photoionisation — where it appears

The removal of an electron from an atom or ion by a photon energetic enough to free it. In a nebula, recombination after photoionisation turns the ionising photons absorbed into emission lines, so a line's luminosity counts the photons the source emitted in every direction the gas covers.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

One planet's helium line, around four kinds of star. The excess absorption at the centre of the 1083 nm helium line during transit, against the mass-loss rate, for one sub-Neptune — 26 Earth masses, 4.4 Earth radii, 0.0525 AU — losing an isothermal wind at 8,000 K, around four representative stellar spectra. Both scales logarithmic. The same outflow absorbs very differently: at 1 × 10¹⁰ g s⁻¹ the depth is 0.06%, 0.14%, 0.35%, 0.40% around an F star, a Sun-like star, an active K dwarf, an active M dwarf. Read the other way, a measured depth of 1% means 1.1 × 10¹¹ g s⁻¹ around an F star, 6.3 × 10¹⁰ g s⁻¹ around a Sun-like star, 3.0 × 10¹⁰ g s⁻¹ around an active K dwarf, 2.9 × 10¹⁰ g s⁻¹ around an active M dwarf — a factor of 4 between the extremes, from the star alone.

A helium line that weighs the star first

The metastable helium line at 1083 nanometres made the escape of a planet's atmosphere measurable from the ground. But the atoms it sees exist only in a balance between the star's extreme-ultraviolet light, which fills the level, and its mid-ultraviolet, which empties it — so the same outflow is six times deeper around an active K dwarf than around an F star, one depth allows a fifty-fold range of mass-loss rates across the wind's possible temperatures, and a rate inferred from it inherits a share of every error in a spectrum that cannot be observed.

exoplanets · Atmospheric escape 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 Almost everything is ionised, and then almost nothing is. The ionised fraction of hydrogen against distance from an O7 star in gas of 10 per cubic centimetre, from integrating photoionisation balance outward, in units of the counted radius of 14.62 parsecs. The fraction is near one until about the edge and then falls from 90% to 10% within 0.192 parsecs, 1.3% of the radius. That width is about 18 mean free paths of an ionising photon in neutral gas (0.011 pc). Nothing about the star sets it. A region with no gradual boundary is a surprising result of a smooth input, and it comes from the fact that a photon that gets as far as the neutral gas is absorbed at once.

An ionised sphere that is a count of photons

A hot star sits in a cloud of hydrogen and ionises it, out to a radius, and there the ionisation stops within a tiny fraction of the distance. That edge was predicted in 1939 from a single count: every recombination uses up one photon, so the star can hold ionised only as many atoms as its light can pay for. By the equation that describes a stellar atmosphere at the same temperature, the same gas would hold ten orders of magnitude fewer neutral atoms than it does. In a nebula the temperature is not what decides the ionisation. A budget is.

starlight · Ionisation

Named alongside it

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

RecombinationAtmospheric escapeBeamingEddington limitExtreme-ultravioletH II regionIonisation frontLine-broadeningMass loss rateMetastable heliumNeutron starsParker wind

All concepts