Astronomy & Celestial Mechanics
the sky, computed
Concept

Inner working angle — where it appears

The smallest separation at which a high-contrast instrument can detect a companion. It is set by the coronagraph's optics and by how much of a planet's flux the reference subtraction removes, and it decides which planets a survey can look for at all.

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

Contrast against separation, which is where direct imaging lives. Planet-to-star brightness ratio against apparent separation, both logarithmic, for a system 10 parsecs away. The reflected-light curves are A_g(R_p/a)² and fall as the inverse square of the orbit; the thermal curve is the ratio of two Planck functions at 10 µm and does not, which is why every imaged planet so far is young and hot rather than merely large. The vertical lines are diffraction limits λ/D — nothing inside a telescope's own line is reachable by it at any contrast at all. An Earth at ten parsecs sits at 6.3e-10, which is 4 orders of magnitude below the faintest planet yet imaged. The four imaged planets are plotted at their measured near-infrared contrasts rather than at 10 µm, because the near infrared is the band they were found in — which is itself part of the argument, since a young planet is hot enough to be bright where its star is not.

Nine orders of magnitude, half an arcsecond apart

Photographing a planet is not a resolution problem. It is a contrast problem, and the contrast is set by an inverse square that punishes exactly the planets a telescope can most easily separate.

exoplanets · Direct imaging 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.

Adaptive opticsAlbedoAngular differential imagingAngular separationArchival dataContrastContrast curveCoronagraphDiffraction limitNon-common-path errorPrincipal component analysisReference differential imaging

All concepts