Astronomy & Celestial Mechanics
the sky, computed
Concept

Red giant — where it appears

A star that has exhausted hydrogen in its core and expanded, becoming large, cool and luminous. Its convective envelope, its oscillations and its brightness make it the workhorse tracer for distances, abundances and ages in distant populations.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A hundredfold expansion is a four-order slowdown. Equatorial rotation speed against radius for three stars leaving the main sequence at 2, 10, 100 km/s, on the single assumption that nothing exerts a torque. Both axes are logarithmic. The specific angular momentum is held fixed along each track and checked at four radii rather than assumed, so the speed falls as the reciprocal of the radius and then faster, as the moment of inertia coefficient slides from 0.073 on the main sequence to 0.02 in a centrally condensed giant envelope. A star at 100 km/s crosses the 8 km/s line — the usual boundary for calling a giant a rapid rotator — at 45.6 solar radii, and everything larger is slower. That is why the observed giants are almost all under two kilometres a second, and why the one or two per cent that are not cannot be explained by anything the star did on its own: the angular momentum has to have been delivered, by a swallowed companion or a merger. The figure assumes no mass loss, which for the largest radii drawn is the weakest of its assumptions.

A surface that slowed because the star grew

A star leaving the main sequence expands by a factor of a hundred. Conserve its angular momentum and its equator slows by four orders of magnitude, which is why every red giant is a slow rotator. One or two per cent are not, and a giant turning at fifty kilometres a second has to have been given the angular momentum by something else.

stars · Stellar evolution 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 Orbital energy spent against the envelope it has to lift. The orbital energy a 0.6 M☉ companion releases by spiralling in from the onset of a common envelope down to a final separation, against that separation (curve), and the binding energy of the 0.85 M☉ envelope of a 1.2 M☉ giant with a 0.35 M☉ core, divided by the efficiency, for αλ of 0.25, 0.5, 1 (horizontal lines). Energies are in units of GM☉²/R☉. The giant fills its lobe at a separation of 118 R☉, and the companion releases nothing net until the orbit has shrunk below 34 R☉, because the envelope's mass leaves with the envelope; from there it falls until the energy released pays for the envelope, so each crossing is a final orbit — 1.29, 2.48, 4.63 R☉. The released energy grows only as one over the separation, so halving the efficiency halves the final orbit: a factor of four in αλ is a factor of four in the outcome, and there is no measurement of αλ that does not run through outcomes like these.

The least known number in binary evolution

When a giant swallows its companion, the companion spirals inward until the orbital energy it has released is enough to throw the envelope off. The final orbit is set by one product of two unknowns, it moves in proportion to that product, and the merger time of the white dwarfs it leaves moves as its fourth power.

stars · Mass transfer The end of the red giant branch, found as an edge. The luminosity function of a synthetic galaxy halo — the number of red giants against apparent magnitude in the I band, smoothed — and its derivative, which is what the edge detector computes, searched over the magnitudes brighter than the branch's crowded lower part, as every application of the method does. 1582 stars are drawn: red giants rising in number towards fainter magnitudes as ten to the 0.3 times the magnitude, ending at the tip at magnitude 24, with a sixth as many asymptotic giants thinning out above it, all measured with errors of 0.08 magnitudes. The derivative peaks sharply where the counts jump, here at 24.09 — 0.09 from the true tip. The red giant branch ends where helium ignites in a degenerate core of almost fixed mass, so the tip's absolute magnitude is close to −4.05 for old, metal-poor stars, and the edge's apparent magnitude is a distance.

An edge that needs no pulsation

The local measurement of the expansion rate rests on a calibration step, and for decades that step was the Cepheid variables. The tip of the red giant branch replaces it with an edge — the brightness at which old stars ignite helium, nearly the same in every galaxy — found by counting stars rather than modelling them. It gives a slightly lower expansion rate, and whether the difference is a flaw in one calibration or in both is the local half of the Hubble tension.

cosmology · Hubble constant

Named alongside it

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

Angular momentumAsteroseismologyBenchmark starBinding energyCepheid variableCommon envelopeCompact binaryConvective envelopeCore envelope couplingCore massDegeneracy pressureError propagation

All concepts