Astronomy & Celestial Mechanics
the sky, computed
Concept

Transit photometry — where it appears

Measuring a star's brightness repeatedly to detect the small, regular dips made when a planet crosses its disc. The dip's depth gives the planet's size relative to the star, its duration the orbit's geometry, and its period the orbital period.

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

Ten comparison stars as bright as the target cost 5 per cent in precision; ten 2 magnitudes fainter cost 23. The precision of a V = 12 target measured relative to an ensemble of comparison stars on the same 60-second frames, against the number of comparison stars, on a logarithmic precision axis, for comparisons 1 mag brighter, as bright as the target, 1 mag fainter, 2 mag fainter. A change in the atmosphere's transparency of 2.0 per cent — which would put the target's raw brightness out by 20.0 mmag — multiplies every star by the same factor and vanishes from the ratio. What is left is the target's own noise, 0.89 mmag, plus the ensemble's, which falls as the inverse square root of the number of stars in it. With comparisons as bright as the target the result is σ√(1 + 1/N): one comparison costs 41 per cent, ten cost 5. Fainter comparisons are noisier and need many more to reach the same point; brighter ones help, but the target's own noise is a floor the ensemble can only approach. Scintillation is treated as independent from star to star, which is right for stars more than a few arcseconds apart on a large telescope and makes it part of the noise that does not cancel. The figure also cannot show the defining weakness: every comparison star is assumed constant, and a variable among them injects its variability into every measurement made against the ensemble.

The comparison stars are part of the measurement

Measuring a star against others on the same frame cancels everything the atmosphere and the instrument do to all of them at once — a two per cent change in transparency vanishes completely. What does not vanish is the comparison stars' own noise, which the target inherits, and the variability of any comparison that is not constant, which the target reports as its own.

starlight · Photon noise The same data searched with a box and with a sine. The signal-to-noise ratio of the best fit at each trial period, for the light curve of the previous figure, searched two ways: with a box of three trial durations at every phase, and with a sinusoid. The box search peaks at 3.85 days with a signal-to-noise ratio of 7.3, against a true period of 3.85. The sinusoid's best peak anywhere is 3.3, at 1.59 days, and at the true period it reaches only 1.5 — no higher than the peaks the noise makes elsewhere in the search. The planet is a clear detection to one method and invisible to the other, in the same numbers.

A periodogram shaped like a shadow

A periodogram that fits sinusoids sees a transiting planet only through the fundamental harmonic of its box-shaped dip, which for a short transit is a few per cent of the signal. Folding the data at each trial period and fitting a box recovers all of it — five times the signal-to-noise for a transit two per cent of the orbit long, eighteen times for an Earth crossing the Sun. The box pays for its extra parameters in trials, and the price is about one unit of signal-to-noise.

starlight · Periodograms

Named alongside it

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

Atmospheric extinctionBox least squaresCommon mode noiseComparison starDifferential photometryFalse-alarm probabilityInverse variance weightingLight curveMatched filterPeriodogramPhoton noiseScintillation

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