Astronomy & Celestial Mechanics
the sky, computed
Concept

Zodiacal light — where it appears

Sunlight scattered off interplanetary dust, seen as a faint glow along the ecliptic. It is two orders of magnitude brighter than the extragalactic background at optical wavelengths, so every measurement of that background is a foreground subtraction rather than a photometric measurement.

Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.

Below 0.46 microns a grain is not in orbit at all. The ratio of the radiation force to the gravitational force on a dust grain, against the grain's radius, for three densities. Every line has slope exactly −1 because gravity acts on the mass and radiation on the cross-section, and the ratio of a volume to an area is a length. Two horizontal lines matter and they are different statements. At β = 1 the star does not attract the grain at all. At β = 1/2 a grain released at rest from a circular orbit is already unbound, because it keeps the speed appropriate to the full stellar mass while feeling only half of it — and since dust is made by breaking up larger bodies that were on circular orbits, the lower line is the one that applies. For rock at 2500 kilograms a cubic metre that is 0.46 microns; for ice it is 1.15, and for iron 0.15. A collisional cascade that grinds material finer runs into this floor and stops, and the material that would have been finer leaves the system on a hyperbola.

The drag that sorts a disc by size

Starlight does three different things to a dust grain depending on how big it is — blows it out of the system, drags it inward over millennia, or ignores it entirely. Which one happens is decided by a single length, and whether it happens at all is decided by how crowded the disc is.

orbits · Collisional cascade The darkness, itemised. The extragalactic background light as a spectrum: νIᵥ against wavelength, in nanowatts per square metre per steradian, with wavelength logarithmic. The total under the two humps is not read off a plot — it is the integral (c/4π)∫ε(z)(1+z)⁻¹|dt/dz|dz of the Madau–Dickinson star formation history, taking a continuously star-forming population to radiate 10¹⁰ solar luminosities per solar mass per year, and it comes to 37.5 nW m⁻² sr⁻¹. Half of it was emitted beyond z = 0.91, which is the figure's real content: the dark sky is dominated by light released when the universe was 45 per cent of its present age. The split between the two humps is an assumption rather than a result — 50 per cent of the starlight is taken to be absorbed by dust and re-radiated near 140 µm, and the shapes are lognormals of about the observed widths — but the AREA under each is the computed quantity. Measured, the two come to about 24 and 26: the calculation falls 25 per cent short, and whether the missing light is real or a residual foreground is unsettled.

The darkness has a number in it

The night sky is not black. It carries about sixty nanowatts per square metre per steradian, and that number is the sum of every photon every star has ever emitted, redshifted and added up over thirteen billion years.

cosmology · Olbers's paradox The sky's darkness, measured as an opacity. Optical depth to electron–positron pair production against gamma-ray energy, for sources at redshifts 0.03, 0.1, 0.3, 1, both axes logarithmic. A gamma ray of energy E is absorbed most readily by background photons near twice the square of the electron rest energy divided by E: at 1 TeV that is 2.37 µm and at 100 GeV it is 0.24 µm, so the energy axis is a wavelength axis for the background light, running backwards — and the background it is evaluated against is the same two-component spectrum the star formation history produced, not a flat number. Above the marked τ = 1 the universe is opaque. The depth is computed in the delta-function approximation, the cross-section replaced by 0.2 of the Thomson value over a bandwidth of order the energy, with the background's comoving density evolving as (1+z)^1.2. That is a factor-of-two calculation and the shape is what it gets right: the horizon closes from z = 0.59 at 100 GeV to z = 0.16 at 1 TeV. The measurement runs the other way. A blazar's spectrum is observed, the absorbed part is the difference between it and the spectrum the source is believed to have emitted, and that difference gives the background — in the near infrared, where no direct measurement can subtract the zodiacal light well enough to compete.

A background weighed by what it stops

The faintest light in the universe cannot be photographed from inside the Solar System, because the zodiacal foreground is a hundred times brighter. It can be weighed instead, by the bite it takes out of a blazar at a trillion electronvolts.

cosmology · Olbers's paradox 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 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.

Surface brightnessComoving distanceCoronagraphCosmological dimmingDirect imagingExozodiacal dustExtragalactic background lightHabitable zoneOptical depthStar formation historySurvey yieldAlbedo

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