Astronomy & Celestial Mechanics
the sky, computed
Concept

Convolution — where it appears

An operation that smears one function by another, summing shifted copies of the first weighted by the second. A population's supernova rate is its star-formation history convolved with the delay-time distribution; an image is the sky convolved with the point-spread function.

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

A gap 1 per cent deep that became 63. The distribution of planet radii, drawn three ways: the underlying distribution with a gap in it, the same distribution convolved with a 25 per cent stellar radius error, and convolved with a 5 per cent one. Every planet radius is the transit depth's square root multiplied by a stellar radius, so an error in the star is an error in the planet, and a population of planets inherits the population of stellar errors as a smearing. The gap is 1 per cent deep at the old precision and 63 at the new one, and its centre does not move — a symmetric smearing hides a feature without displacing it. That is what happened when parallaxes for a hundred thousand planet hosts arrived: no new planets were observed, and a feature that had been marginal became unambiguous.

A planet radius is a stellar radius

A transit measures a ratio and nothing else. Every planet radius ever published is that ratio multiplied by a stellar radius that came from somewhere entirely different, so a population of planets inherits the errors of a population of stars — and when the stars were measured better, a feature nobody could see became unmistakable.

exoplanets · Planet composition A power law has no timescale: half the Type Ia supernovae by 740 Myr and a tail to 13.7 Gyr. The fraction of all the Type Ia supernovae a single burst of star formation will ever produce that have exploded by a given delay, on a logarithmic time axis, for t⁻¹ from 40 Myr; t⁻¹·⁴ from 40 Myr; single delay of 1 Gyr; Gaussian, 3 ± 1 Gyr. The power law is what rates measured against host-galaxy ages and against the cosmic star-formation history both favour, and its cumulative fraction rises as the logarithm of the delay — equal numbers per decade of time. Half have exploded by the geometric mean of its limits, 740 Myr, 55 per cent by 1 Gyr, and the last are still exploding after a Hubble time. A single delay turns the whole population on at once; a Gaussian concentrates it at a characteristic age. The power law's shape has a physical reading: if white dwarfs explode when a pair of them merges by emitting gravitational waves, the merger time goes as the fourth power of their separation, and a broad distribution of separations becomes a distribution of delays with no preferred scale. What the drawing cannot say is which progenitors are involved — the measured rates constrain the shape and the normalisation, about one Ia per thousand solar masses of stars formed, and not the mechanism.

The iron clock has no single delay

The α-element knee is drawn as though Type Ia supernovae switched on a billion years after the stars that made them. Measured rates say otherwise — the delays are spread evenly over every decade from forty million years to a Hubble time, as a power law with no timescale in it — and a clock with no timescale bends where a clock with one would break.

galaxies · Chemical evolution

Named alongside it

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

Alpha enhancementAlpha kneeChemical evolutionCosmic star formation historyDelay time distributionDouble degenerateGravitational wavesMeasurement errorOccurrence rateParallaxPhotoevaporationPopulation statistics

All concepts