Astronomy & Celestial Mechanics
the sky, computed
Concept

Stellar occultation — where it appears

The passage of a solar-system body in front of a star, recorded as a light curve at high cadence. Its resolution is set by how fast the geometry changes rather than by any aperture, so tens of metres is routine and no image comes close.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A wave whose crests count out 35 kilograms per square metre of ring. Optical depth across a spiral density wave in Saturn's A ring, drawn outwards from the 5:3 inner Lindblad resonance with Mimas at 131,988 km. The wave is launched at the resonance on the left and damps away to the right. Its wavelength is not constant: it starts at about 5.6 km and has shortened to 1.13 km by the last crest drawn, because the wavenumber grows in proportion to the distance from resonance and the ring's own self-gravity is the only restoring force in the dispersion relation. That makes the pattern a chirp with exactly one unknown in it. Fitting the 24 crest positions actually drawn here — the square of each one's distance from resonance against its number, which is a straight line — returns a surface density of 35.0 kilograms per square metre against the 35 the profile was built from. The rings have been weighed this way rather than by anything touching them: the mass per unit area follows from counting bright bands in a light curve as a star sets behind the ring.

A ring weighed by the wave crossing it

Saturn's rings are a few tens of metres thick and spread over an area larger than the Earth, made of pieces nobody can resolve, and nothing has ever landed on them. Their mass per unit area is nevertheless known to a few per cent — from the rate at which the crests of a wave crowd together as it travels outwards.

gravitation · Planetary rings Two dips a side, 36.5 seconds apart, symmetric about a body 256 km across. One observer's light curve across a small body with two narrow rings, at a chord 44 km from the centre. The body itself removes the star for 11.2 seconds; the four brief dips, two either side of it, are ring crossings, at 391 km and 405 km from the centre and 7 km and 3 km wide radially. The evidence that they are rings and not two more objects is the symmetry: each pair sits at equal times before and after mid-event, to within 0.07 s here, and two independent bodies have no reason to do that. Each dip is drawn wider than the ring is thick because the chord crosses obliquely — the path length through the material goes as 1/cos, which is also why a ring is deeper near the ansae. Nothing in this light curve was looked for: Chariklo's rings turned up in 2013 in a run recorded to measure a diameter, and every ring system found since has been found the same way.

A star that blinked before it should have

In March 1977 three teams watching a star pass behind Uranus recorded it dimming five times before the planet arrived — and then, symmetrically, five times again on the way out. The symmetry is the whole argument — nothing but a set of rings concentric with the planet produces a mirror image about closest approach.

sky · Occultations A shadow whose centre is brighter than no shadow at all. The flux an observer records against their distance from the centre of the shadow, for a body of half-light radius 1180 km with an isothermal atmosphere of scale height 55 km. Away from the centre the curve is the ordinary occultation light curve — the star fading as refraction spreads its light — and near it the two limbs' contributions both carry a geometric factor of the impact parameter over the shadow position, which grows without bound on the axis. The spherical atmosphere reaches 34.79 of the unocculted flux. The ray that arrives on the axis has impact parameter 1019 km, which is 161 km — 2.9 scale heights — below the half-light level, at a pressure 19 times higher. That is the only part of an occultation that reaches there. The peak is finite only because the star is not a point: the geometric factor is softened at 3 km, which is the star's own size projected to the shadow. The second curve is the same atmosphere flattened by 2.0 per cent, which spreads the focus over 20 km and drops the peak to 19.8. A real flattened body gives a caustic rather than a broad peak — several sharp spikes, spread in two dimensions rather than one — so the width here is right, the structure is not, and the height is an upper bound.

The brightest instant of an occultation is its middle

A spherical atmosphere is a lens with a focal length of astronomical units, and an observer standing at the exact centre of the shadow is standing at its focus. The star does not disappear there — it brightens, by more than it would have been unocculted, and the ray that arrives has come from far deeper than anything else in the event.

sky · Occultations The astrometry an occultation campaign has to have. How far the shadow lands from where it was predicted, against the angular error in the positions it was predicted from, for a Centaur at 15 AU, a Kuiper belt object at 40 AU, Uranus at 19 AU. The conversion is one line — an angle times a distance — and one milliarcsecond at one astronomical unit is 0.7255 kilometres. The horizontal bands are each body's own shadow width, which is its diameter, and the crossing is the accuracy at which a campaign stops being a lottery: a Centaur needs 23.0 mas, a Kuiper belt object needs 4.1 mas, Uranus needs 3701.0 mas. Before the all-sky astrometric surveys the typical error was tens of milliarcseconds, which is thousands of kilometres at these distances, so events by small bodies were found by accident and not by appointment. The same event then measures the body's position to a few milliarcseconds or better, which improves the ephemeris that predicts the next one.

Each event pays for the prediction of the next

An occultation is predicted from two positions and lands where the arithmetic says. Recording it then measures the occulting body's position to a few milliarcseconds — better than a year of imaging — so the observation that the prediction made possible improves the ephemeris the next prediction comes from.

sky · Occultations

Named alongside it

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

Astrometric predictionOptical depthShadow pathShepherd moonAtmospheric oblatenessCatalogueCausticThe central flashDiffractionDispersion relationEphemerisThe Fresnel scale

All concepts