Astronomy & Celestial Mechanics
the sky, computed
Concept

Cosmic shear — where it appears

The coherent one-per-cent distortion of distant galaxy shapes by the gravity of everything between them and the observer. It is measured by averaging a million shapes so that the intrinsic ellipticities cancel, and its amplitude constrains how much matter there is and how clumped it is.

Named by 6 essays across 3 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 Two bands 2.1 standard deviations apart, and neither is a point. The plane of the matter density against the amplitude of matter fluctuations, with the constraints from a weak-lensing survey and from the microwave background drawn as bands. Lensing measures the shear produced by structure along the line of sight, and that shear depends on how much matter there is and on how clumpy it is in a fixed combination — more matter arranged less clumpily gives the same signal. The locus is a power law of exponent one half, and the combination it fixes is written S₈. The two bands are separated by 2.1 standard deviations, and whatever that separation is, it is a statement about the growth of structure between recombination and now rather than about either measurement's precision. Neither band alone determines either quantity, which is why the disagreement is quoted in the combination rather than in the parameters.

Two parameters that lensing measures as one

A weak-lensing survey measures how much the shapes of distant galaxies are distorted by the matter in front of them, and that distortion depends on how much matter there is and on how clumpily it is arranged. The two enter as a product. What the survey determines is one number, and the disagreement between surveys and the microwave background is stated in that number because neither measures either quantity alone.

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 The matter power spectrum with galaxies' feedback taken out. The ratio of the matter power spectrum with baryonic feedback to the spectrum without it, against wavenumber in h per megaparsec on a logarithmic scale, for three strengths of feedback that span the range the large hydrodynamic simulations disagree over. Gas blown out of haloes by supernovae and active nuclei removes mass from scales below a few megaparsecs, so the ratio falls below one from about 0.5 h per megaparsec and is deepest near 4 h per megaparsec, at 9, 17 and 26 per cent; at still smaller scales gas that has cooled into galaxy centres adds mass back. The marks show the wavenumber that dominates a lensing measurement at multipoles 100, 1000, 5000, taken where the lensing kernel for sources at redshift 1 peaks: 0.09, 0.87, 4.35 h per megaparsec. The shape is a parametric stand-in placed where simulations put the effect, not a simulation.

A measurement of dark matter that needs a model of galaxies

Weak lensing weighs all the matter, dark and ordinary, by how it bends light. But the ordinary matter does not sit where gravity alone would put it — galaxies' supernovae and black holes blow a large part of it out of their haloes — and the scales where that happens are the scales that carry most of a lensing survey's statistical power. Ignored, it reads as a less clumpy universe, in the direction of the disagreement lensing has with the microwave background.

galaxies · Weak lensing The fraction of a spin alignment a disc can show. The ratio of a disc population's shape alignment — its mean ellipticity along the projected tidal template — to the Lee–Pen alignment of its spins, against the discs' thickness as a fraction of their diameter, each point from 30,000 discs in a field of shape 0.2. The thinnest disc drawn, 0.05 of its diameter, passes 0.204 per unit of spin alignment; a disc a fifth as thick, typical of a spiral's stellar disc, 0.171; a body as thick as it is wide passes nothing, because a sphere has no shape to align. The ratio is the conversion between what a spin survey measures and what a lensing survey fits, and it is small for two reasons that multiply: a spin alignment is a weak preference among directions, and a disc shows its direction only in proportion to how far it is tipped towards edge-on.

An alignment a disc shows only when it is tipped

A disc galaxy's outline on the sky is its spin seen in projection, so the torque alignment of spins has to appear in shapes too. It does, multiplied by a factor near a sixth and carried almost entirely by the discs seen close to edge-on — which is how a lensing survey can fit the term and find nothing while a survey of spins finds it.

cosmology · Tidal torque theory How small an outlier fraction the mean redshift can bear. The shift in a tomographic bin's mean redshift, f·Δz, against the outlier fraction f, for outliers displaced by Δz = 0.5, 1.5, 2.5, both logarithmic. The dashed line is the requirement for a bin at z = 0.8, 0.0036. Outliers half a unit of redshift away must be fewer than 0.72% of the bin; outliers two and a half units away, fewer than 0.14% — or known to that precision, since a known fraction can be corrected. The best photometric redshifts reach outlier fractions of a few per cent, ten to a hundred times above these lines.

A mean that a few per cent of strays can drag

A lensing survey sorts its galaxies into slices of redshift by their colours, and what its cosmology needs from each slice is a single number, the mean redshift, to two parts in a thousand. A few per cent of the galaxies in a slice are catastrophic outliers — young galaxies at redshift three mistaken for old ones at one — and each moves the mean by its full error. Three per cent of strays two redshift units away move it twenty times more than the survey can tolerate, and finding them needs spectra of exactly the galaxies whose spectra fail.

starlight · Magnitudes

Named alongside it

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

Photometric redshiftIntrinsic alignmentShape noiseSigma 8Systematic errorWeak lensingSpin alignmentTidal tensorTidal torque theoryAGN feedbackBaryonic feedbackCatastrophic outliers

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