Astronomy & Celestial Mechanics
the sky, computed
Concept

Type ia supernovae — where it appears

The thermonuclear explosion of a white dwarf, whose peak brightness measures a mass of nickel-56 and whose light curve says which. They are standardisable rather than standard: the peak brightness correlates with the decline rate, and applying that correction is what makes them usable as distance indicators.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

A light curve that is a decay chain. Bolometric luminosity against days since explosion, for three Type Ia models synthesising 0.3 M☉, 0.6 M☉, 0.9 M☉ of ⁵⁶Ni, from Arnett's one-zone diffusion model. Nothing in the shape is fitted: the two timescales are the laboratory half-lives of ⁵⁶Ni and ⁵⁶Co, 8.8 and 111.3 days, and the rise is those decays seen through an envelope that takes 11.3, 15.5, 18.6 days to leak. Each peaks at 14, 18, 21 days, and at maximum the luminosity equals the instantaneous deposited power to within 0.6% — Arnett's rule, and the only reason a peak brightness can be read as a mass of nickel. After maximum the curves settle to nearly straight lines on this logarithmic axis, declining at 0.0360 magnitudes a day against ⁵⁶Co's own 0.0098. The difference is gamma-ray escape: the ejecta become transparent to the very photons that are supposed to be heating them, and the tail is therefore steeper than the isotope. The one thing the tail is not is a property of the star — it is a half-life, plus a column density that is falling as t⁻².

The candle that has to be standardised

A Type Ia's light is the decay of half a solar mass of nickel-56 seen through an expanding envelope. Their peak brightnesses span six-tenths of a magnitude — and it is the width of the light curve, not anything else, that says which.

stars · Supernovae A one-parameter model, and 9 times too many metal-poor stars. The metallicity distribution of long-lived stars near the Sun — the bars — against two models of how a galaxy enriches itself. The closed box is as simple as a model of a galaxy can be: gas turns into stars, stars make metals and return them, nothing enters and nothing leaves. It has exactly one parameter, the yield, and it predicts the whole curve. It gets the peak roughly right and the tail catastrophically wrong: 13.7 per cent of its stars fall below [Fe/H] = -1 against an observed 1.6 per cent, a factor of 9. This is the G-dwarf problem, and the reason it is an argument rather than a discrepancy is that the failure cannot be fixed by changing the yield: the yield sets where the peak is, and moving the peak to fix the tail moves it away from the data. What is wrong is a boundary condition. Let gas keep arriving — pristine, at roughly the rate it is being consumed — and the gas is never both abundant and metal-poor for long, so few stars form while it is. That is the second curve, with 3.2 per cent below -1, and it needed no new nucleosynthesis and no new parameter beyond the fact of accretion. The picture cannot show the thing that would settle it directly, which is the infall itself: the gas arriving on the disc now is a few solar masses a year spread over twenty kiloparsecs, and it has never been securely detected.

A histogram that says the box was not closed

The simplest model of a galaxy enriching itself has exactly one parameter and predicts the whole metallicity distribution of its surviving stars. The solar neighbourhood's disagrees, in a specific direction — and the failure is not in the nucleosynthesis but in a boundary condition.

galaxies · Chemical evolution Distance modulus against redshift, for three universes. The distance modulus μ = 5 log₁₀(D_L/10 pc) against redshift for three universes, all with H₀ = 67.36 km/s/Mpc, with 60 model supernovae drawn from the ΛCDM curve with 0.15 magnitudes of scatter. The point of the figure is how little difference there is: across two decades of redshift the three curves stay within a few tenths of a magnitude, and at z = 0.5 the accelerating and decelerating cases differ by 0.387 mag. A cosmology is not read off this plot. It is read off the residual, which is the next figure.

An expansion that was supposed to be slowing

Gravity is attractive, so an expanding universe full of matter must be decelerating, and the only question was by how much. Two teams set out to measure the deceleration and both found a quarter of a magnitude of extra faintness at redshift half — which is the wrong sign.

cosmology · Dark energy 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 evolutionStandard candleWhite dwarfAccelerating expansionArnetts ruleChandrasekhar limitClosed box modelCoincidence problemConvolutionCosmic star formation history

All concepts