Astronomy & Celestial Mechanics
the sky, computed
Concept

Principal component analysis — where it appears

A decomposition of a set of observations into the orthogonal patterns that account for most of their variance. It is used to build spectral templates and to model a speckle field, and projecting data onto a few components removes some of whatever signal they contain.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A planet that subtracts 73 per cent of itself at the inner working angle. The fraction of a planet's flux that survives an angular differential imaging subtraction, against its separation from the star in resolution elements, for a sequence covering 25 degrees of field rotation. The reference image is built from the target's own frames, so a planet that has not moved far between them is present in the reference and is removed along with the speckles. How far it moves is the arc length, which is proportional to the separation — so the self-subtraction is severe close in and negligible far out, and the half-throughput point is at 2.1 resolution elements here. The consequence for any contrast curve is that it is a statement about an algorithm as well as about an instrument: the depth reached has to be measured by injecting fake planets into the data and recovering them, because no calculation predicts what fraction of a real one survives.

A star subtracted using the star

Imaging a planet means removing a halo of scattered starlight a hundred million times brighter than the planet, and no model of that halo is good enough to subtract. So it is built from the star's own exposures — and since the planet is in those exposures too, it subtracts part of itself.

exoplanets · Direct imaging A 5 per cent continuum error, and an optical depth wrong by 1.1. The mean transmitted flux of the Lyman-alpha forest against redshift, with a 5 per cent uncertainty in the quasar continuum drawn as a band. The continuum is not observed: at these redshifts every part of the spectrum blueward of the emission line is absorbed, so the level has to be extrapolated from the red side across a region where the quasar's own spectrum has structure. A fractional error in that level is a fractional error in the flux, and since the optical depth is minus the logarithm of the flux, the resulting error in the optical depth is the fractional error divided by the flux — which grows without bound as the forest goes black. At z = 2 it is 0.06; at z = 6.2 it is 1.1. That is why measurements of when reionisation ended are quoted as limits rather than values above about redshift six.

A forest with no continuum left

Measuring how much neutral hydrogen sits between here and a distant quasar means measuring the fraction of its light that survives, which means knowing how much light there was. At high redshift nothing survives at the wavelengths that would show it, so the level is extrapolated across the region being measured — and the optical depth is the logarithm of a number divided by a guess.

cosmology · Reionisation Two references, failing in opposite places. The faintest companion each technique can detect, against separation in resolution elements, in units of the speckle noise a perfectly matched reference would leave. Angular differential imaging builds its reference from the target's own exposures, so the reference matches the instrument's state exactly and the residual speckle is small — and the companion is in every frame of it, so close in the companion subtracts most of itself and the achievable contrast collapses. Reference-star differential imaging builds the reference from archival exposures of other stars. The companion is in none of them, so the throughput is one at every separation and the curve is flat; what is lost is the match, because two stars observed at different times through different air with a differently flexed telescope have different speckles. The two cross, and where they cross depends on how large the library is: 1.1 resolution elements at 20 frames, 1.4 resolution elements at 200 frames, 1.8 resolution elements at 2000 frames. A library of thousands of archival exposures is therefore worth building, and the thing it buys is the inner working angle rather than the depth.

A reference built from other stars

Subtracting a star's halo using the star's own exposures removes part of the planet with it. Building the reference from a library of archival exposures of other stars removes none of the planet and matches the halo worse — so the two techniques fail in opposite places, and which one wins at a given separation depends on how many exposures somebody has kept.

exoplanets · Direct imaging

Named alongside it

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

Angular differential imagingContrast curveSelf subtractionSpeckle noiseThroughputArchival dataContinuum placementDetection limitThe Gunn–Peterson troughInjection recoveryInner working angleThe Lyman-α forest

All concepts