Astronomy & Celestial Mechanics
the sky, computed
Concept

Intrinsic alignment — where it appears

The tendency of galaxies to point their shapes along the tidal field they formed in, which mimics a weak-lensing shear. It is a contaminant of lensing surveys and a measurement of the tidal field in its own right, and it separates from lensing by its redshift dependence.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

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 A spin that prefers the axis in the middle. Where the spin of a tidally torqued patch points, measured against the three principal axes of the tidal field acting on it: the distribution of the absolute cosine between the spin and each axis, from 20,000 patches with random shapes in one field of principal values −0.75, 0.09, 0.66. Principal values are those of the second derivative of the potential, so a positive one compresses. An isotropic spin would give three flat lines at one. The spin avoids the most compressive and the most stretching axes and prefers the intermediate one, because the torque about each axis is proportional to the difference of the field's principal values about the other two, and the intermediate axis is the one whose two neighbours differ most: squared, those weights are 0.11, 0.66, 0.24 of the total. Fitted as Lee and Pen's alignment parameter, the directions give a = 0.617. The preference is real and it is weak — the densest bin is 3.37 times the isotropic value — which is the whole difficulty of using spins to map a field.

A spin that remembers the field and not its sign

Tidal torque theory says where a galaxy's spin should point, not only how large it should be. It points along the middle axis of the tidal field, it is exactly perpendicular to an ideal filament, and it is an even function of the field — so a map of spins can find the directions of the cosmic web and can never say which of them is collapsing.

cosmology · Tidal torque theory 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 A conversion read galaxy by galaxy, with or without an alignment. The mean ellipticity of disc galaxies along a tidal template, in bins of each galaxy's own spin estimator — the quantity whose population average is the Lee–Pen alignment — for 60,000 discs a fifth as thick as they are wide, in three samples: spins set by the torque (net alignment 0.36), 85% of them randomised (0.054), and all of them random (0.002). The points trace the same curve through the origin in every sample — not quite straight, flattening at both ends, because a disc's shape saturates when its spin lies in the sky's plane — and a straight line fitted through each sample (dashed) has slope 0.279, 0.290, 0.292. That slope is the projection factor, what a disc's shape shows of its spin, and it does not care whether the population is aligned. A sample with no alignment at all measures the conversion as well as one with a strong one; only the population's mean, where all its galaxies pile up, moves.

A conversion measured without an alignment

The factor that turns a disc galaxy's spin alignment into the shape alignment a lensing survey fits looked like something only a sample with a detected alignment could test. It is not. It is a relation each galaxy obeys on its own, so it can be read off a few hundred discs with velocity maps whether or not their spins point anywhere in particular — and what is left for the hard measurement to test is only whether a disc's shape is anything more than its projected spin.

cosmology · Tidal torque theory

Named alongside it

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

Spin alignmentTidal tensorTidal torque theoryCosmic shearShape noiseEllipticityInclinationIntegral-field spectroscopyLarge-scale structurePhotometric redshiftAngular momentumCorrelation function

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