Astronomy & Celestial Mechanics
the sky, computed
Concept

Planet formation — where it appears

The assembly of planets from the dust and gas of a disc around a young star, from grains to pebbles to planetesimals to planets. Its products keep a record of where and when they formed in their compositions, masses and orbits.

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

How long an event lasts, against the mass that causes it. Einstein crossing time against lens mass, on logarithmic axes, for a lens at 6.5 kpc in front of a source at 8 moving at 6 milliarcseconds a year — a typical bulge geometry. The slope is a half, exactly, because θ_E goes as the square root of the mass and t_E is θ_E divided by a proper motion: an M dwarf gives 21 days, a Jupiter gives 22 hours, a Neptune gives 4 hours, an Earth gives 1 hours. Nothing else about the event changes with the mass. The peak magnification is set by the impact parameter alone, so a free-floating Earth passing close enough produces exactly the light curve a star would, at exactly the same height, and lasts 1.2 hours instead of a month. That is the entire difficulty of detecting them: the events are ordinary and brief, so what decides whether they are found is the survey's cadence rather than its sensitivity. The dashed line is where the source becomes larger than the Einstein ring — 1.5e-4 solar masses for a 6-microarcsecond source — and below it every event is finite-source-dominated, which flattens the peak and, in the same stroke, measures θ_E.

An event of a few hours and no host

The Einstein crossing time is the square root of the lens mass and nothing else changes, so a free-floating Earth produces exactly the light curve a star does, at exactly the same height, and is over in ninety minutes. What decides whether it is found is cadence rather than sensitivity.

exoplanets · Microlensing The radius a rocky planet would have, by core fraction: at 5 M⊕ an Earth-like and a Mercury-like planet differ by 8%. Radius against mass for rocky planets of one to eight Earth masses, from Zeng and collaborators' interior models, for core mass fractions of 0, 0.33, 0.5, 0.7, 1 — from a planet with no iron core to one that is all iron. The shaded band is the range of core fractions planets would have if they kept their host stars' iron, magnesium and silicon in the stars' own proportions, for stars whose iron-to-magnesium ratio is within 0.15 dex of the Sun's: 0.26 to 0.41. The Earth, at 0.325, sits in it. At five Earth masses an Earth-like planet and one with a core fraction of 0.7, like Mercury, differ in radius by 8 per cent — a difference that transit and radial-velocity measurements can now resolve.

More iron than the star could give

A rocky planet is made of what its star was made of, minus the gases: iron, magnesium and silicon in the star's proportions, which for the Sun predict an iron core of a third of the planet's mass — and the Earth's core is 32.5 per cent. A handful of small exoplanets are so dense that their cores must hold seven-tenths of their mass, more iron than any star known to host planets could have supplied. Either something removed most of their rock after they formed, or the rock and the metal were separated before they did.

exoplanets · Planet composition

Named alongside it

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

Angular einstein radiusCore mass fractionEinstein radiusFinite-source effectFree-floating planetGiant impactLight curveMass radius relationMicrolensingOccurrence ratePlanet compositionProper motion

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