Astronomy & Celestial Mechanics
the sky, computed
Exoplanets

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.

Assumes Magnitudes and Stellar colour.

17 min read 9 figures Light is the only messengerScales that defeat intuition

The instinctive objection to photographing a planet around another star is that the two would be too close together to separate. That objection is wrong, and being wrong about it in a specific way is the beginning of understanding the problem.

Jupiter seen from ten parsecs is half an arcsecond from the Sun — five times the parallax of a star at that distance, and parallaxes at the milliarcsecond level have been routine for thirty years. Half an arcsecond is an enormous angle by the standards of modern astronomy: an 8-metre telescope working at 1.6 µm has a diffraction limit of 0.05 arcseconds, ten times finer. The separation is not the difficulty.

The difficulty is that the planet is 10−910^{-9} of the star.

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.
Fig. 1 Contrast against apparent separation for a system ten parsecs away. Reflected-light curves fall as the inverse square of the orbital distance, so the further out a planet is — the easier to resolve — the fainter it becomes. The thermal curve does not, which is why every planet imaged so far has been detected by its own heat rather than by reflected starlight. The vertical lines are diffraction limits: nothing inside a telescope’s own line is available to it at any contrast whatever.

Two ways for a planet to be bright, and both are hopeless in the visible

Reflected light. A planet intercepts the fraction (Rp/2a)2(R_p/2a)^2 of its star’s output and sends back a fraction AgA_g of it. So the contrast at full phase is

Cref=Ag(Rpa)2.C_{\text{ref}} = A_g\left(\frac{R_p}{a}\right)^2.

For Jupiter that is 0.5×(7.1×104/7.8×108)2≈4×10−90.5 \times (7.1\times10^4 / 7.8\times10^8)^2 \approx 4\times10^{-9}. For the Earth it is around 10−1010^{-10}. Both numbers are set by a ratio of a radius to an orbit, and the orbit is four orders of magnitude larger, so the square is where the nine orders of magnitude come from. There is no configuration that avoids it: bringing the planet closer raises the contrast and lowers the separation in exactly compensating measure.

Thermal emission. A planet also radiates. In the mid-infrared, where a 300 K body peaks and a 5,800 K star is far down its Rayleigh–Jeans tail, the ratio is very much better: the Earth against the Sun at 10 µm is about 10−710^{-7}, a hundred times more favourable than in reflection. And for a young planet the argument is far stronger still. A giant planet forms hot and cools over hundreds of millions of years, so at an age of 10–50 Myr it can be at 1,000–1,500 K, radiating like a very small star. Its contrast against its host in the near infrared is then 10−410^{-4} to 10−610^{-6} — a million times more accessible than the same object cold.

This is the whole selection. Every directly imaged planet is young, massive, far from its star, and observed in the infrared. That combination is not a statement about where planets are; it is the shape of the accessible region.

The inner working angle

The other constraint is a hard wall rather than a slope. No coronagraph suppresses starlight arbitrarily close to the star: diffraction sets a limit near λ/D\lambda/D, and practical designs work from about 11–3 λ/D3\,\lambda/D outward.

For an 8 m telescope at 1.6 µm that is roughly 0.05 arcseconds, or 0.5 AU at ten parsecs. For JWST at 10 µm, λ/D\lambda/D is 0.39 arcseconds — nearly 4 AU at the same distance, which puts the habitable zone of every star firmly inside the wall. For the 39 m Extremely Large Telescope at 10 µm it is 0.065 arcseconds.

Contrast against separation, which is where direct imaging lives. Planet-to-star brightness ratio against apparent separation, both logarithmic, for a system 5 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 3.8 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 3.8 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.
Fig. 2 The same construction for a system five parsecs away observed at 3.8 µm. Halving the distance doubles every apparent separation and moves the diffraction walls to the left relative to the planets, which is why the nearest stars are worth a disproportionate amount of telescope time. The contrast requirement does not improve at all — it is intrinsic to the planet — but the geometry does.

Distance therefore enters twice, and in opposite directions. A nearer system has larger apparent separations, so more of it lies outside the wall. But its planets are no brighter relative to their star, since contrast is a property of the system rather than of the observer. Direct imaging is thus a game played almost exclusively on the few dozen nearest young stars.

Contrast against separation, which is where direct imaging lives. Planet-to-star brightness ratio against apparent separation, both logarithmic, for a system 5 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.
Fig. 3 The same contrast curves for a system five parsecs away rather than ten. Nothing about the planets has changed — the reflected and thermal ratios are properties of the orbit and the temperature — and every curve slides right, because the same physical separation subtends twice the angle. Halving the distance halves the inner working angle problem, which is why the target lists for direct imaging are lists of the nearest stars and not of the brightest.

What the starlight has to be doing instead

Reaching 10−610^{-6}, let alone 10−910^{-9}, is not a matter of collecting more photons. The obstacle is the star’s own light scattered into the place the planet is.

Three things are done about it, and all three are necessary.

Adaptive optics. Atmospheric turbulence smears a stellar image over about an arcsecond, which is 20 times the diffraction limit and would bury any planet. A deformable mirror driven at a kilohertz by a wavefront sensor restores something near the diffraction limit. Extreme adaptive-optics systems use thousands of actuators and reach Strehl ratios above 90 per cent in the near infrared.

A coronagraph. A mask, or a phase-shifting element, removes the on-axis starlight while passing the off-axis planet. Modern designs are subtle — vortex charge, apodised pupils, shaped pupils — and each trades inner working angle against throughput and against how much of the field is usable.

Differential imaging. What remains after the first two is a field of speckles, quasi-static and indistinguishable from planets in a single frame. The trick is that speckles are instrumental and the planet is on the sky: with the telescope’s field rotating relative to its optics through the night, the speckles stay fixed with respect to the instrument while the planet moves. Subtracting a model of the fixed pattern removes the speckles and leaves the planet. The technique is called angular differential imaging, and it is what took ground-based contrast from 10−410^{-4} to 10−610^{-6} without any change of aperture.

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 0.55 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 0.55 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.
Fig. 4 The same planet in the visible, which is where the problem is worst. In reflected light the contrast is the albedo times the square of the planet’s radius over its orbital distance, and for an Earth analogue at one astronomical unit that is 10−1010^{-10} — ten billion to one, at a separation of a tenth of an arcsecond. The thermal infrared is easier by four orders of magnitude because the planet emits there rather than reflecting, and harder by a factor of twenty in angular resolution because the wavelength is longer. Every direct-imaging instrument ever built is a choice between those two, and the choice is different for a young giant than for an old rocky world.
Contrast against separation, which is where direct imaging lives. Planet-to-star brightness ratio against apparent separation, both logarithmic, for a system 40 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.
Fig. 5 And at forty parsecs, which is where most known planetary systems are. The curves slide left by a factor of four and the whole reflected-light branch disappears inside the inner working angle of both apertures drawn. The reason direct imaging has found tens of planets and transits have found thousands is on this plot: transits do not care how far away the star is, and imaging cares about almost nothing else.

A photograph is a spectrum waiting to happen

The reason to spend a decade of instrument development on an image, when a transit gives more precise parameters for a hundredth of the effort, is what can be done once the planet’s light is separated from the star’s.

An imaged planet’s light is its own. It can be dispersed, and the resulting spectrum belongs to the planet alone — no subtraction, no differencing, no assumption that the star was constant between two observations. That is a qualitatively better position than transmission spectroscopy, where the planetary signal is a few hundred parts per million riding on a stellar spectrum and every systematic in the instrument has to be removed to a level below it.

What has come out of those spectra is worth the trouble. Methane and water in the atmospheres of the HR 8799 planets; carbon monoxide in β Pictoris b, with the line positions Doppler-shifted enough to measure the planet’s rotation period at 8 hours; clouds of silicate dust in objects too cool for the material to stay vaporised. The same absorption features stellar spectroscopy has read for a century, read from a body a hundred million times fainter than the thing next to it.

The carbon-to-oxygen ratio measured that way is the current best hope of saying where a planet formed. Different distances from a star freeze out different ices, so the gas a planet accretes has a composition that depends on which side of which snow line it grew — and a spectrum, unlike a mass or a radius, records that.

What was actually measured

2M1207 b, 2004. The first image of a planetary-mass companion: about 5 Jupiter masses at 40 AU from a brown dwarf, in a young association 53 parsecs away. The contrast was only about 100 to 1, because the primary is itself a brown dwarf — which is a reminder that “direct imaging” is a statement about contrast, and a faint primary is worth as much as a bright planet.

HR 8799, 2008. Four planets around one A star, at 16, 27, 43 and 68 AU, imaged from the ground and subsequently watched moving along their orbits over a decade and a half. It is the only multi-planet system that has been seen rather than inferred, and the orbital motion of the four is a dynamical problem in its own right, since the system is only stable in particular resonant configurations.

β Pictoris b, 2009. A planet inside a debris disc that had been imaged twenty years earlier, in a system where the disc’s warp had already been interpreted as evidence of a massive planet. It is one of the few cases where a prediction from indirect evidence was confirmed by a photograph.

51 Eridani b, 2015. Discovered by the Gemini Planet Imager at a contrast of about 2×10−62\times10^{-6} and a separation of 0.45 arcseconds, with methane in its spectrum and an estimated temperature near 700 K. It is one of the coldest and least massive imaged planets, and its spectrum is the strongest evidence that these objects form by core accretion rather than by direct fragmentation.

And the surveys that found nothing. The value of a null result here is unusually high, because the sensitivity is computable. Large surveys of hundreds of young stars — GPIES, SHINE — found giant planets around a few per cent of them, which implies that wide-orbit giants are rare: of order 1–10 per cent of stars host a planet above 5 Jupiter masses between 10 and 100 AU. That number is a genuine measurement of the outer solar systems of other stars, and it came mostly from non-detections.

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 4 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 4 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.
Fig. 6 The same system with the thermal curve computed at four microns rather than ten. The contrast is worse — a planet’s thermal emission peaks in the mid-infrared and the star’s does not — and the diffraction limit is better, by the same factor of the wavelength. The two effects pull in opposite directions and neither is small, which is the whole of why an imaging instrument’s band is a design decision rather than a preference, and why the answer differs for a young self-luminous planet and an old one.

Where the picture stops

An image is not a mass. Photometry gives a luminosity; a mass follows only through a cooling model, and cooling models depend on how much entropy the planet retained at formation. The “hot start” and “cold start” families differ by a factor of several in the inferred mass for the same observed brightness at young ages. Where an imaged planet also has a dynamical mass — from astrometry of the host star, as Gaia now supplies for a few, or from the star’s reflex velocity over a long baseline — the models can be tested, and the early tests have been uncomfortable.

Young and massive is not representative. The imaged sample is drawn from an age range of tens of millions of years and a mass range above about 2 Jupiter masses. Nothing about it constrains the population of ordinary planets around ordinary stars.

A companion is not necessarily a planet. At the top of the mass range the objects blur into brown dwarfs, and the formation route matters more than the mass: an object that formed like a star, by fragmentation, is arguably not a planet at 8 Jupiter masses, and one that formed in a disc arguably is at 20.

The host stars are chosen, not sampled. Imaging surveys target young stars, and young stars are found in nearby moving groups, which are a handful of specific places with a particular history. A statement about how often stars have wide giant planets is really a statement about a few hundred stars aged 10–200 Myr in the solar neighbourhood, and whether those stand for stars in general is assumed rather than established. That the most massive stars live and die fastest also cuts the sample: a 2-solar-mass star is only young for a short while, so the youngest targets are systematically the most massive ones.

And one point is not an orbit. A single epoch gives a projected separation. Establishing that the object is bound at all requires showing it shares the star’s proper motion, which takes a second epoch a year or two later; establishing the orbit takes a decade or more, and even then only a fraction of an arc is covered.

And the speckles are not quite static. Angular differential imaging assumes the instrumental pattern is fixed while the sky rotates. It is fixed only to the extent that the telescope’s optics are, and thermal flexure over a night moves it slowly — so the subtraction leaves residuals that look exactly like faint companions, and the false-positive rate at the detection threshold is not small. Recovering the same source at a second epoch, in a position consistent with orbital motion rather than with the instrument, is the only real confirmation.

Contrast against separation, which is where direct imaging lives. Planet-to-star brightness ratio against apparent separation, both logarithmic, for a system 20 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 2.7e-10, which is 5 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.
Fig. 7 And what doubling the distance does. The contrast is unchanged — it is a property of the planet and its star, not of how far away the pair is — but the angular separation halves, so a system at twenty parsecs asks for twice the aperture at the same wavelength to place the planet outside the diffraction core. That is why the target lists for direct imaging are lists of nearby stars rather than of promising ones, and why the technique’s reach grows with telescope diameter rather than with integration time.

That near-absence of overlap is the practical difficulty of the whole field. A planet characterised by one method is rarely accessible to another, so the census is a set of populations measured by different instruments with different biases, stitched together by argument.

The generalisation

Suppressing a bright thing to see a faint thing next to it is one of the oldest problems in observational astronomy, and every solution has been reused.

The solar corona is a million times fainter than the disc and was visible only during eclipses until Bernard Lyot built the first coronagraph in 1930 — the same instrument, solving the same problem, ninety years before it was pointed at another star. The companions of bright stars have been separated by occulting bars and apodised masks since long before adaptive optics. Speckle interferometry, invented to beat atmospheric blurring, gave the first resolved images of stellar surfaces.

The structural similarity to the transit method is worth stating too, because they are opposite solutions to one problem. A transit does not suppress the starlight; it uses the star as a backlight and measures a change. Direct imaging suppresses the starlight and measures a presence. The first is a differential measurement and reaches parts per million; the second is an absolute one and reaches parts per million only with heroic instrumentation. That is a general rule about measurement, not a fact about planets. There is one further approach that belongs neither to the coronagraphs nor to the differencing, and it is worth a section because it removes the wall rather than working outside 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 1.8e-10, which is 5 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.
Fig. 8 The reflected-light branch for a dark planet — a geometric albedo of 0.1 rather than 0.35, which is roughly the difference between a hazy world and a cloudy one. The curve drops by a factor of three and a half at every separation, and the thermal branch does not move. An albedo is a property nobody knows in advance, so the reflected-light contrast a mission must reach is uncertain by the same factor before a single photon is collected, and missions are sized against the pessimistic end.

Cancelling the star instead of blocking it

Every technique above suppresses the starlight by putting something opaque or phase-shifting in the beam of a single telescope, and the inner working angle that results is set by that telescope’s own diffraction. There is an alternative in which the suppression is done by interference between separate apertures, and its inner working angle is set by the distance between them instead.

Combine the light from two telescopes with a half-wave phase shift imposed on one path. A source exactly on the axis arrives at the two apertures in phase, acquires the shift, and cancels. A source slightly off axis arrives with a path difference, and if that difference is a quarter of a wavelength times the appropriate geometry it does not cancel at all — it constructively interferes.

The result is a transmission pattern with a null on the star and a bright fringe at an angular offset of about half the wavelength divided by the baseline. Since the baseline can be far larger than either aperture, that offset can be far smaller than either telescope’s diffraction limit.

The technique is nulling interferometry, and it is the only proposal that reaches inside the diffraction limit of the telescopes doing the observing. It was demonstrated on the ground at mid-infrared wavelengths, where it was used not to find planets but to measure the dust in other systems — the exozodiacal light, which is itself a limiting background for any future imaging of an Earth analogue.

Two difficulties have kept it from delivering planets. The null has to be maintained: a path-length error of a few nanometres fills it in, and holding two telescopes to that tolerance through an atmosphere is the whole problem. And the transmission pattern has fringes rather than a clean field, so the planet’s position is not read off directly — it is recovered by rotating the baseline and modulating the signal, which is a reconstruction rather than a photograph.

A photograph and a null are two answers to the same problem and they fail differently: one is limited by how well the light can be blocked, the other by how well two paths can be held equal.

A last practical point that the contrast curves do not carry. Every one of them is a requirement, and what an instrument delivers is a contrast that degrades towards the star — a curve of its own, measured on the sky rather than computed. The two are compared at each separation, and a detection is a point where the delivered curve sits below the required one. The figures in this essay are half of a comparison, and the other half is an instrument’s own performance, which is why a contrast curve published with a null result is a more useful document than a detection.

One more reading covers the wavelength at which the ground-based instruments actually work.

Contrast against separation, which is where direct imaging lives. Planet-to-star brightness ratio against apparent separation, both logarithmic, for a system 30 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 1.6 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 1.6 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.
Fig. 9 Contrast against separation at 1.6 microns for a system thirty parsecs away. The diffraction limit is much tighter than in the mid-infrared and the planet is far fainter relative to its star, so the near infrared buys angular resolution and pays for it in contrast — which is the trade every direct-imaging instrument is designed around.

Where this goes next

The contrast an instrument must reach to photograph an Earth around a Sun-like star is 10−1010^{-10}, and the technologies required — starshades flown tens of thousands of kilometres from the telescope, or coronagraphs stabilised at the picometre level — are the design drivers of the next generation of space observatories. Whether the problem is soluble at all is not in doubt; whether it is soluble at a price anyone will pay is the actual question.

Later rungs on this anchor: coronagraph designs and their trade-offs. Adaptive optics and the Strehl ratio. Angular and spectral differential imaging. The hot-start and cold-start cooling tracks. Debris discs as signposts. Orbital fitting from arcs. Spectroscopy of imaged planets. Starshades. Interferometric nulling. And the contrast required for an Earth, which is the number that decides what the next fifty years of the field look like.

Where this goes next

Blackbody curves at 3000, 5800, 10000 K. Thermal emission against wavelength, each curve scaled to its own peak so the shift can be seen on one plot. The peak moves to shorter wavelengths as the temperature rises, which is why colour is a thermometer. Colour is a thermometer, and it reads across the galaxy A star's colour gives its surface temperature, from two brightness measurements and no other information. It is the cheapest useful measurement in astronomy. The magnitude scale, plotted. The logarithm of the received light against magnitude from -27 to 32, with the vertical scale left unlabelled because only its slope matters. The relation is a straight line of slope −0.4, which is what makes five magnitudes exactly a hundredfold — and the numbers run backwards, so brighter is smaller. 9 landmarks are marked, from the Sun to the deepest exposures, spanning a factor of 1.2·10²³ in received light. A scale that runs backwards, multiplies, and works Brighter stars have smaller magnitudes, and five steps is a factor of a hundred. A scale invented by eye in the second century BC turned out to be logarithmic, because eyes are. What each method can see. Planet mass against orbital distance, both logarithmic, with the detection threshold of each method drawn as the boundary it actually is. Radial velocity at 1 m/s needs mass rising as √a; astrometry at 20 µas needs it falling as 1/a, which is the only method that gets easier further out; a 100 ppm transit is a threshold on radius and so a horizontal line at about 1.4 Earth masses, cut off at 1.21 AU by the need for three transits in 4 years; direct imaging begins outside the diffraction limit, 0.6 AU at 10 parsecs for a 39 m aperture at 10 µm. The solar system is drawn on top: for two decades every one of its planets except Jupiter lay outside every region, which is the whole of what the early census was measuring. Every survey draws a different sky The first exoplanets found were enormous and impossibly close to their stars. That was not a discovery about planets. It was a measurement of what a 10 m/s spectrograph watching for three years is able to see.

What this makes readable

Essays that name this one as a prerequisite.

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The 8 of 10 essays linking to this one that name the most of the same objects.

The objects this essay names

Each one links to every other essay that touches it.

Adaptive opticsAlbedoAngular separationContrastCoronagraphDiffraction limitInner working angleStarlight suppressionThermal emissionYoung planet