Astronomy & Celestial Mechanics
the sky, computed
Series

Direct imaging — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 1 · exoplanets
  2. 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.

    part 2 · exoplanets

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