Astronomy & Celestial Mechanics
the sky, computed
Concept

Contamination — where it appears

Light in a measurement that comes from sources other than the target, most often unresolved neighbouring stars. In transit surveys it dilutes depths and can turn an eclipsing binary in the background into an apparent planet.

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

Two objects, the same 1.055 per cent, and only one of them a planet. A planet of 0.1027 stellar radii transiting at impact parameter 0.3, and a background eclipsing binary of radius ratio 0.62 whose 38 per cent eclipse is diluted by the target's light to 1.055 per cent — the same depth to nine decimal places, because the dilution was chosen to make it so. A blend contributing 2.7 per cent of the light in the aperture can manufacture any planetary depth at all, so the depth is not evidence about what produced it. Two things in the same photometry are. The ingress occupies 20.4 per cent of the planet's transit and 80.3 per cent of the blend's, a factor of 3.9: the shape of the shoulders is set by the radius ratio of whatever is actually eclipsing, and dilution scales a curve without changing its shape. And the duration with the period gives the mean density of the star being crossed — 1.41 g/cm³ here against 0.15, a factor of 9 — so a blend usually implies a host of a completely different kind from the one the spectrum shows. Neither test needs an observation the survey did not already make, and neither of them proves a planet: they reject specific alternatives, and what is left is a probability.

A planet that is never confirmed, only validated

A background eclipsing binary diluted by the target's light reproduces a planetary transit depth exactly, and no amount of better photometry separates the two. Most known planets are therefore the output of a probability calculation rather than a detection, and the honest statement about them is a statement about a false-positive rate.

exoplanets · Transits How much too small a planet looks when a second star shares its light. The factor by which a planet's true radius exceeds the radius inferred from its transit, against the mass of an unresolved companion star in units of the Sun's, for a planet transiting a Sun-like primary and for one transiting the companion, with the radius computed in both cases from the diluted depth and the primary's radius. Logarithmic vertical axis. A planet on the primary is diluted by the companion's light alone, and the factor is √(1 + F₂/F₁), never more than √2 = 1.41, reached for an equal twin; for a companion of half a solar mass, whose 3943 K surface gives 4.5 per cent of the primary's light in a Kepler-like band, it is 1.022. A planet on the companion is diluted by the primary's much larger light and measured against the wrong star's radius, and the factor is (R₂/R₁)√(1 + F₁/F₂): 2.6 for the half-solar-mass companion and 4.3 for one of 0.3 solar masses. The two curves meet at √2 for twins. The stars are a main-sequence sketch — power-law radii, a smoothed luminosity law and blackbody spectra — good to tens of per cent in flux ratio.

The Earth-sized bin is where diluted planets land

A star with an unresolved companion shares its aperture with that companion's light, and every planet found around either star is measured too small. The error runs one way only, so the smallest radius bin receives planets from every larger one and returns none. With a companion beside three stars in ten, more than a quarter of the planets called Earth-sized are something larger.

exoplanets · Detection bias

Named alongside it

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

DilutionAdaptive opticsAstrophysical false-positiveA background eclipsing binaryBinary starsBlendCentroid shiftDetection thresholdFalse-positive probabilityFlux ratioLikelihood ratioOccurrence rate

All concepts