Astronomy & Celestial Mechanics
the sky, computed
Concept

Large separation — where it appears

The nearly uniform spacing in frequency between successive overtones of a star's sound waves. It is set by the time sound takes to cross the star and back, so it measures the star's mean density; with the frequency of maximum power it gives mass and radius.

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

Also named here as scaling relation, surface effect — the same set of essays touches all of them, so they are one junction rather than several.

4 per cent in one observable is 48 per cent in an age. How an error in the calibration of the large frequency separation propagates into the quantities derived from it. The two scaling relations are exact in their exponents, so a fractional error in the separation appears as twice that in the radius, four times in the mass, and — because a main-sequence lifetime falls as roughly the two-and-a-half power of the mass — ten times in an age. At the 4 per cent level, which is about what the theoretical corrections to the relation amount to for a red giant, that is 15 per cent in mass and 48 per cent in age. Nothing about the seismology is uncertain at that level; the frequencies are measured to parts in a thousand. What is uncertain is the constant of proportionality, and it is uncertain because it was calibrated on one star.

Two scaling relations calibrated on one star

Asteroseismology gives a star's mass and radius from two numbers read off its oscillation spectrum. The two relations are exact in their exponents and approximate in their constants, and the constants were fixed by requiring that the Sun come out right — so an error of a few per cent in one observable is tens of per cent in a mass and nearly a factor in an age.

stars · Asteroseismology Ridges that bend where the model's surface is wrong. An échelle diagram of a Sun-like star's oscillation frequencies — each mode's frequency against its remainder after dividing by the large separation of 135.1 µHz — for radial, dipole and quadrupole modes (red, green, blue), as a one-dimensional model predicts them (open) and as the star produces them (filled), if the model's outer layers are wrong in the way the Sun's models are. Low in the diagram the two coincide. With increasing frequency the star's modes fall behind the model's, by an amount that grows steeply and is the same for every degree, so all three ridges bend to the left together: by 19.3 µHz at 4104 µHz. The bend is the surface effect, and it is larger than the uncertainty of any measured frequency by a factor of a hundred.

A correction that grows as the fifth power of the frequency

Every model of a star gets its outermost layers wrong, because one-dimensional models cannot follow the turbulent convection that fills them. The error shows up in the star's oscillations as an offset that is nothing at low frequency and twenty microhertz at high, two hundred times a frequency's measurement error. It is corrected with a power law nobody can derive, and the correction recovers the star only when its shape happens to be right — which is why the ages of stars are fitted not to their frequencies but to ratios of differences the surface cannot reach.

stars · Asteroseismology

Named alongside it

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

Scaling relationSolar calibrationSurface effectSystematic errorAcoustic cavityAsteroseismologyBenchmark starConvectionError propagationFrequency of maximum powerRed giantStellar mass

All concepts