Astronomy & Celestial Mechanics
the sky, computed
Concept

Core mass — where it appears

The mass of the region at the centre of a star where nuclear burning or degeneracy sets the structure. It is not observable directly and it decides the star's luminosity, its lifetime and what it becomes.

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

A furnace with the thermostat taken out. Left, the two pressures in a red giant's helium core at 10⁶ g/cm³. The ideal-gas pressure rises with temperature, as the whole regulation of a star depends on it doing; the degenerate electron pressure is a horizontal line, because the exclusion principle does not know the temperature. At the ignition point near 10⁸ K the degenerate term is 5.1 times the gas term, so a temperature rise there raises the total pressure by almost nothing and the core does not expand. Right, what that costs. Both curves start at the same temperature with the same triple-alpha rate, whose logarithmic slope is 41 — the famous T⁴⁰, differentiated here rather than quoted. The regulated core settles; the degenerate one, with nowhere to put the extra energy, goes vertical. The flash reaches 10¹⁰ solar luminosities for a few seconds and not one photon of it is seen: every erg goes into lifting the degeneracy, and the star's visible response is to become fainter and settle on the horizontal branch.

The explosion that never reaches the surface

When helium ignites in a degenerate core the thermostat every other burning stage runs on is disconnected. The runaway reaches ten billion solar luminosities for a few seconds, and the star's visible response is to get fainter.

stars · Stellar evolution A free parameter worth 42 per cent of an age. The main-sequence lifetime of a star against its mass, for four values of the convective overshoot parameter. A convective core has a boundary where buoyancy vanishes, and a rising blob arriving there still has momentum, so it penetrates into the stable region above and mixes fresh hydrogen into the core. How far it penetrates is not computed — it is a parameter, quoted in pressure scale heights, and the values in current use range from zero to about a third. A larger core is a larger fuel supply, so the lifetime rises and the turn-off at a given age is more massive. Across the plausible range the lifetime of a two-solar-mass star changes by 42 per cent, and an age read off a cluster's turn-off changes by the same amount. That is larger than the quoted uncertainty on almost every cluster age in the literature.

A convective boundary with no theory to fix it

A convective core has an edge where buoyancy vanishes. A blob arriving there still has momentum, so it carries on, mixing fresh hydrogen into the core and extending the star's life. How far it carries on is a fitted parameter, and across its plausible range every stellar age changes by nearly half.

stars · Stellar evolution 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

Named alongside it

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

Binding energyCommon envelopeCompact binaryConvectionConvective overshootDegeneracy pressureEclipsing binaryElectron degeneracyFree parameterGravitational wavesHelium flashHorizontal branch

All concepts