Astronomy & Celestial Mechanics
the sky, computed
Concept

Coronagraph — where it appears

An instrument that blocks a star's light inside a telescope so that faint companions beside it can be imaged. Its performance is a contrast reached at each separation, and residual starlight scattered around the mask sets how faint a planet it can find.

Named by 4 essays across 2 fields — 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 What shares a resolution element with an Earth twin. Light collected in one resolution element around an Earth-like planet in the habitable zone of a Sun-like star, against the system's distance, both on logarithmic scales, for a 6 metre telescope at visible wavelengths, in units of the planet's own light at 10 parsecs. The planet and the leaked starlight both dim as the square of distance. The exozodiacal dust, at 3 times the Solar System's level, and the Solar System's own zodiacal light do not dim at all: each is a surface brightness, and a resolution element at a greater distance simply contains more dust. The exozodi equals the planet at 9.1 parsecs and is 11 times it at 30.

Dust that does not dim with distance

An Earth-like planet around a nearby star is seen against the glow of the dust in its own system, and the two behave differently with distance. The planet is a point, and it fades as the square of how far away it is. The dust is a surface, and a surface does not fade at all — a more distant system packs more dust into each resolution element in exactly the proportion its light is diluted. So the dust around a star, not the telescope's contrast, sets how far away an Earth can be found, and how many stars a search can reach.

exoplanets · Direct imaging A shadow 77 mm across at 144.3 m: an occulter 1.42 m wide and a 50 mm aperture inside its umbra. Side view of an eclipse made by two spacecraft, distances along the axis in metres and widths across it in metres, the vertical scale magnified about fifty times. Sunlight arrives from the left. The occulting disc, 1.42 m across, casts an umbra — the cone from which none of the Sun's disc is visible — which narrows because the Sun is not a point: its edges converge at a rate set by the Sun's angular radius, 959.6 arcseconds, and would meet 153 m behind the disc. At 144.3 m, where the coronagraph sits, the umbra is 77 mm across and the aperture 50 mm; the penumbra, from which part of the Sun is visible, extends to 2.76 m. From the aperture the occulter's edge hides the Sun out to 1.058 solar radii, so the corona is visible from just beyond the limb.

An eclipse held in place to a millimetre

A total eclipse of the Sun works because the Moon's disc happens to match the Sun's almost exactly, and it lasts a few minutes. Two spacecraft flying 144 metres apart can make one that lasts six hours: a disc 1.4 metres across, with a coronagraph sitting in its shadow. The geometry that sets the shadow's size also sets the price. At that separation the umbra is 77 millimetres across around a 50-millimetre aperture, so the formation has to hold itself in line with the Sun to a centimetre — and to two millimetres in January, when the Sun is at its largest.

sky · Phases and eclipses Where a ten-micron zodi comes from. How much each logarithmic interval of radius contributes to the ten-micron glow of a Sun-like star's exozodiacal dust, for blackbody grains in the Solar System's radial profile, seen face-on from 10 pc: with no instrument (dashed) and through a 14.4 m nulling interferometer whose fringes suppress the light near the star (solid, with the averaged transmission dotted). Without the null the glow is concentrated far inside the habitable zone at 1 AU (marked), because the grains' emission at ten microns rises steeply with their temperature: half of it comes from inside 0.34 AU. The null removes the innermost part and pushes the sensitivity outward, but half the nulled signal still comes from inside 0.69 AU, peaking at 0.74. A zodi level measured this way is a measurement of the dust between a few tenths of an AU and the habitable zone, extrapolated to the habitable zone with the Sun's profile.

A zodi measured in heat and needed in light

The dust around nearby stars that will limit the search for Earth-like planets in reflected light has been measured — but in its own glow at ten microns, by an interferometer whose fringes hide the dust nearest the star. Converting that measurement into the visible brightness at the habitable zone needs the dust's radial profile and its grains' albedo and temperature, none of which was measured. The same ten-micron zodi can mean a quarter or ten times the visible dust a coronagraph will see.

exoplanets · Direct imaging

Named alongside it

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

AlbedoDirect imagingExozodiacal dustHabitable zoneSurface brightnessSurvey yieldZodiacal lightAdaptive opticsAngular diameterAngular separationBlackbodyContrast

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