Astronomy & Celestial Mechanics
the sky, computed
Concept

Instrumental polarisation — where it appears

Polarisation that a telescope and its instruments add to light passing through them, from oblique reflections and coated surfaces. It must be measured and removed before a source's own polarisation can be read, often to a part in a million.

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

An instrument 1.4 times as polarised as the sky it is measuring. The Stokes plane, with the two linear polarisation parameters as axes. The tight cluster near the centre is a set of stars known to be unpolarised, observed through the same instrument: they should sit at the origin and do not, and their mean is the instrumental polarisation — 0.77 per cent here, which is 1.4 times the real polarisation of the field. The other cluster is the field stars, whose measured values are the sum of their own polarisation and the same instrumental offset. Subtracting one mean from the other recovers 0.59 per cent at the right angle. Two things make this worth doing carefully. The offset is a vector, so leaving it in rotates the measured position angle as well as changing its magnitude — by 31 degrees here — and a calibration that only fixes the scale does not touch that. And the offset depends on where the telescope was pointing, because the reflection angles do, so the standards have to be observed at the same place in the sky and at the same instrument rotation.

An instrument more polarised than the sky

Every oblique reflection polarises. A telescope is a stack of oblique reflections, so it adds a fraction of a per cent of polarisation to everything it looks at — which for most astronomical sources is more than they have themselves, and which is a vector rather than a scale error, so it rotates the answer as well as changing its size.

starlight · Polarimetry The polarised light HD 189733 b can send. The polarised part of HD 189733 b's reflected light, as a fraction of its star's light in parts per million, against orbital phase from one transit to the next, for an orbit of radius 0.0314 AU, a planet of 1.138 Jupiter radii and an inclination of 85.7°. A planet's reflected light is its geometric albedo times (R/a)² — here 3·10⁻⁴ — times a phase function, and the polarised part is that times the degree of polarisation, which for a scattering atmosphere peaks near quadrature where the planet is half lit. With an albedo of 0.4 and a peak polarisation of 0.5 the signal reaches 24 ppm (solid). The ceiling (dashed) gives the planet the largest albedo a scattering atmosphere can have, 0.75, and perfect polarisation: 91 ppm. An amplitude of 100 ppm (dotted), the order of the signal claimed in 2008, would need the planet to reflect and polarise more light than falls on it.

A polarisation capped by the light the planet catches

Light scattered by a planet's atmosphere is polarised, most strongly when the planet is half lit, and the polarisation angle turns as the planet orbits — so a planet's polarised light would weigh its atmosphere and draw its orbit on the sky without a transit. In 2008 it was reported for a hot Jupiter at a part in ten thousand of its star's light. That amplitude is more than the planet can send: no atmosphere reflects more than three-quarters of the light that falls on it or polarises more than all of it, and the light that falls on it is set by its size and its distance. The photons for a real detection are cheap; what limits it is a polarimeter stable to a part in a million.

sky · Apparent motion

Named alongside it

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

Stokes parametersCalibrationCrosstalkDepolarisationGeometric albedoHot jupiterModulationMueller matrixOrbital inclinationPhase anglePhase curvePolarimetric standard

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