Astronomy & Celestial Mechanics
the sky, computed
Concept

Photometric calibration — where it appears

The transfer of a brightness scale between instruments, filters and epochs so that magnitudes measured in different places can be compared. It is uncertain at the level of about a hundredth of a magnitude, which is the same size as the whole dark-energy signal.

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

The Bouguer line, and the intercept nobody observed. Instrumental magnitude against airmass for one star of magnitude 10 outside the atmosphere, observed at 5 airmasses in 5 bands. Each slope is that band's extinction coefficient, computed from Rayleigh scattering, an aerosol term and ozone rather than assumed: U 0.493, B 0.246, V 0.126, R 0.061, I 0.027 magnitudes per airmass. Every line is fitted through its points and extended to X = 0, and the intercept there is the published magnitude — a measurement made at an airmass no observation is ever taken at, because the smallest airmass available is 1 and that is already a whole atmosphere. Two consequences follow and neither is a detail. The slope has to be re-measured every night, because the aerosol term changes with the weather and is not a property of the site. And the U-band line is 3.9 times steeper than the V-band one, so the extrapolation is 3.9 times longer in exactly the band where photons are scarcest — which is why ultraviolet photometry from the ground was always the least trustworthy part of a magnitude system.

A magnitude measured where nothing was measured

Every published brightness is an extrapolation off the end of a graph. A star is observed through one atmosphere at least, a line is fitted against airmass, and the number quoted is its intercept at zero — a place no observation is ever taken from.

starlight · Extinction w = −0.9 is 34 millimagnitudes, and one supernova scatters by 120. Above: how much the distance modulus moves when the dark energy is not a constant. Each curve is a universe with the same Ωₘ = 0.315 and a different equation of state w, drawn as a difference from w = −1 in magnitudes. At redshift a half, w = −0.9 is worth 34 millimagnitudes — the shaded band is the 0.12-magnitude intrinsic scatter of a single standardised type Ia supernova, and the signal is a fifth of it. Nothing about one object can see this; the measurement is the mean of 1500, whose error on the mean is 3.1 millimagnitudes, and even that only works because the shape of the curve in redshift is different from every systematic anybody has thought of. Below: why the supernovae are not enough on their own. Each locus is the set of (Ωₘ, w) that a measurement cannot tell apart from the fiducial model — computed, not sketched: the supernova curve is the ridge of the same sum of squares a fit would minimise over 0.02–1 in redshift, and the acoustic-scale curve is the exact set of models with the same comoving distance to last scattering, which is what fixes the angle the microwave background's first peak subtends. They cross at 36 degrees. Neither is a measurement of w and the pair is, which is why the constraint on the equation of state is a picture of two loci crossing rather than a number read off a curve — and why −1.03 ± 0.03 is a statement about how well they cross rather than about how well anything was measured.

The number that would say whether it is a constant

Whether dark energy is a cosmological constant is the question of whether w is exactly −1, and w = −0.9 changes a distance modulus by thirty-four millimagnitudes at redshift a half — a fifth of the scatter of a single supernova, along a degeneracy only the acoustic scale can cut across.

cosmology · Dark energy

Named alongside it

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

Acoustic scaleAerosolAirmassAtmospheric extinctionBouguer lineColour termCosmological constantDark energy densityDeceleration parameterDegeneracy directionEquation of stateFigure of merit

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