Astronomy & Celestial Mechanics
the sky, computed
Concept

Shear — where it appears

Motion in which neighbouring layers slide past one another at different speeds, as in a disc whose inner parts orbit faster than its outer. Shear stretches clumps into trailing arcs, sets the tilt of ring wakes and spiral arms, and limits how large a self-gravitating clump can grow.

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

A coherent one-per-cent distortion, invisible on every galaxy in the picture. 150 background galaxies behind a lens of Einstein radius 14″, each drawn at its own ellipticity: an intrinsic shape with a dispersion of 0.3 per component, plus the reduced shear the lens adds. The strongest shear on any galaxy here is 0.035, one part in 8 of the intrinsic scatter, so no object in this field is measurably distorted and the tangential alignment cannot be seen by eye at all. Averaged over these 150, the mean tangential ellipticity is 0.0088 ± 0.0245 against the 0.0130 the lens model predicts — consistent with the lens and equally consistent with nothing, because 150 galaxies buy a precision of 0.024 and the signal is 0.013. Detecting it at five sigma takes about 13,275 of them, which is not a picture anybody can draw. The cross component — every shape rotated by 45°, which gravitational lensing cannot produce — averages −0.0016 ± 0.0245, consistent with nothing, and that null is what separates a mass from a badly figured optic. The signal is not in any galaxy. It is in the sum, and the whole design of a lensing survey follows from that.

A one-per-cent distortion, and a million galaxies to see it

A galaxy's own shape is unknown and scatters with a dispersion of about 0.3, so a coherent one-per-cent shear is thirty times smaller than the noise on any single measurement. Nothing is ever measured about one object; the estimator is an average, and the whole design of a survey follows from 0.3 over the square root of N.

galaxies · Weak lensing One patch of ring, many optical depths. The normal optical depth an observer infers from the starlight transmitted through one patch of the A ring, treating it as a uniform sheet, against the direction of the sight line projected onto the ring plane — measured round from the radial direction — for sight lines 12°, 30°, 60° above the plane. The ring is the slab-and-gap model of the wakes: slabs 33 m wide and 8 m tall every 60 m, tilted 22° from the orbital direction, gaps of optical depth 0.12. The minima are where the sight line runs along the slabs, twice per circle; the maxima where it runs across them, where at low elevation the slabs' shadows close the gaps altogether (curves cut off at 3). At 12° the inferred value runs from 0.29 to opaque; at 60° from 0.81 to 0.97. The dashed line is the same particles spread into a uniform layer, 1.43: every observer along the slabs sees less ring than is there.

A ring that is thinner from one side

Saturn's A ring is not a sheet of particles but a field of tilted slabs, each a few dozen metres across, pulled together by the ring's own gravity and sheared apart again within an orbit. Starlight passing through it threads the gaps or meets the slabs depending on its direction, so one patch of ring has a different optical depth for every observer — and a uniform model of it hides most of the particles it contains.

gravitation · Planetary rings

Named alongside it

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

ConvergenceCosmic shearCritical surface densityThe cross componentExcess surface densityGravitational instabilityHill sphereThe mass-sheet degeneracyOptical depthPhotometric redshiftPlanetary ringsThe point-spread function

All concepts