Astronomy & Celestial Mechanics
the sky, computed
Concept

Shape noise — where it appears

The scatter of galaxies' intrinsic shapes, about 0.25 per component, against which a weak-lensing shear of about one per cent has to be measured. It averages down only as the square root of the number of galaxies, which is why lensing surveys count them in millions.

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 Stretched towards the mass, sheared across it. Two rings of galaxies around the same concentration of mass. Left, galaxies physically beside it: its tidal field stretches each one along the line to the centre, so their long axes point radially and their mean tangential ellipticity is −0.30. Right, galaxies far behind it: their light is deflected past the mass and each image is sheared tangentially, with mean tangential ellipticity +0.30. The two patterns are perpendicular. A weak-lensing survey correlates the shapes of foreground and background galaxies to measure the shear, and when a foreground galaxy was aligned by the very structure that lenses the background one, their product is negative — −0.090 here — and subtracts from the signal rather than adding noise to it. What the picture exaggerates is the size: real intrinsic alignments are a per cent or two in the mean, buried under a random shape scatter of about 0.3, and are found only statistically.

The shape a galaxy was given before it was lensed

Weak lensing assumes that galaxies point in random directions, so that a coherent stretch can only have been put there by the light's journey. The tidal field that set every galaxy's spin also stretched its shape — towards the very mass that lenses the galaxies behind it — and the resulting error is not noise but a signal of the opposite sign.

cosmology · Tidal torque theory

Named alongside it

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

Cosmic shearPhotometric redshiftConvergenceCorrelation functionCritical surface densityThe cross componentExcess surface densityGalaxy biasIntrinsic alignmentLarge-scale structureLinear growthThe mass-sheet degeneracy

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