Astronomy & Celestial Mechanics
the sky, computed
Concept

Reliability — where it appears

The fraction of candidate detections at a given signal strength that are real rather than false alarms. It is measured by running a search on data in which no real signal can exist, and it falls steeply near the detection threshold.

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

Four defensible boxes, and a factor of 2.9 between the answers. Above: the occurrence surface in starlight received against planet radius, with four published definitions of "an Earth-size planet in the habitable zone" drawn on it as rectangles. The surface is a stated parameterisation — two lognormal populations at 1.3 and 2.4 Earth radii, with the radius valley at 1.9 between them, normalised so that the whole of it comes to 0.5 planets per star between one and four Earth radii inside a hundred days. Integrating it over the four boxes gives 17%, 8%, 6%, 10% — a factor of 2.9 between the conservative zone and a broad definition, before any error bar is attached to any of them. The dashed curve is what a transit survey can actually see: at one year around a Sun-like star the smallest detectable planet is 1.6 Earth radii, so the lower-left corner of every box contains no detections at all and the rate there is an extrapolation of a fitted surface rather than a count of anything. Below: the same integral with only one corner moved. Holding the flux range fixed and sliding the radius bound from 1.5 to 1.75 Earth radii — a quarter of an Earth radius, well inside the uncertainty of a measured planetary radius — changes the answer by 43 per cent, which is larger than every error bar quoted with any of these numbers. The published values of η⊕ span two per cent to sixty; roughly a factor of 2.9 of that is definition, and the rest is how far each author was willing to extrapolate past the dashed line.

The part of a rate that is a definition

Published values for the frequency of Earth-size planets in habitable zones span two per cent to sixty. The spread is not measurement error — it is where the box was drawn, on a surface that is steepest exactly at the corner every author has to choose, and outside the last detection.

exoplanets · Occurrence rates The chance that a candidate is a planet, against how strong its signal is. The reliability of a transit candidate — the fraction of candidates at a given detection statistic that are planets rather than false alarms — against the multiple-event statistic, the combined signal-to-noise of all its transits, for orbital periods of 10, 100, 350 days. Below the 7.1 threshold nothing is a candidate. At a statistic of 9 the reliability is 100 per cent, 80 per cent, 23 per cent; at 12 it is 100 per cent, 95 per cent, 44 per cent. The true planets and the false alarms are modelled, not fitted: the planets as a falling power law above the survey's completeness curve, the false alarms as an exponential tail above the threshold that grows longer and taller with period, because a long-period signal is two or three transits and two or three transits average away little of the non-Gaussian noise that makes false alarms. At short periods a candidate near threshold is nearly always real; at a year, a candidate near threshold is usually not.

At a year, most candidates are noise

A transit survey's threshold is set so that Gaussian noise yields less than one false planet in the whole catalogue. The noise is not Gaussian, and at year-long periods the candidates just above the threshold are more often artefacts than planets — so the rate of Earth analogues is partly a measurement of the noise.

exoplanets · Occurrence rates

Named alongside it

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

Detection thresholdEta earthOccurrence rateVettingCompletenessDefinitional uncertaintyExtrapolationFalse-alarmFalse-positiveHabitable zoneLook elsewhere effectSurvey completeness

All concepts