Concept

Compact binary — where it appears

A pair of neutron stars or black holes close enough for gravitational radiation to shrink the orbit within the age of the universe. How such pairs are assembled is read from the distribution of their spins rather than from any individual system.

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

$GW150914: 33 Hz to 250 Hz in 0.22 seconds. The strain of GW150914 — two black holes — through the last 0.22 seconds before merger, computed from the quadrupole sweep at the chirp mass its fit returned, 28.716 solar masses, and drawn at the luminosity distance it returned, 440 megaparsecs. Two things rise together and neither is free to rise on its own: the frequency goes from 33 Hz to 250 Hz, and the envelope — the outer curve — grows by a factor of 3.9, because the amplitude goes as f^2/3 and nothing else in it changes over so short a span. The vertical axis is in units of 10⁻²¹, so the peak here is a fractional length change of about 2.9·10⁻²¹: over the four kilometres of an interferometer arm that is 1.2·10⁻¹⁷ metres, a thousandth of the width of a proton. The chirp mass is not fitted to the amplitude at all — it comes from the spacing of these zero crossings, which is why it is the best-determined number in the whole event and why the distance, which does come from the amplitude, is the worst.$

A distance with no ladder under it

The frequency sweep of an inspiral fixes the chirp mass with no distance in it, and the amplitude then gives the luminosity distance directly, because one expression fixes both. That is a distance measured with nothing calibrated beneath it — and its error budget is one angle.

gravitation · Gravitational waves

A cycle and a radiation, racing for the same pericentre. Two integrations of the same compact triple, in units of the cycle's own timescale at the starting separation. The dashed curves are the semi-major axis and the solid ones the eccentricity. Radiation alone shrinks the orbit slowly and smoothly, reaching a tenth of its starting size after 1136 cycle times — which the closed form for a circular inspiral predicts to within a few per cent, and which is the check that the integrator is right. With the cycle running, the distant companion drives the eccentricity to 0.9104, the pericentre falls by two orders of magnitude, and the radiation — whose rate goes as the inverse seventh power of one minus the square of the eccentricity — empties the orbit in 18. That is a factor of 62, obtained without changing a single parameter of either mechanism. The two do not merely add: the cycle manufactures, at its own peak, exactly the configuration in which the radiation is most efficient, and the radiation then shrinks the orbit until the relativistic precession switches the cycle off.

A cycle that builds what the wave needs

Gravitational radiation empties an orbit at a rate that goes as the inverse seventh power of one minus the square of the eccentricity. A distant companion drives exactly that eccentricity, over and over. The two are not independent mechanisms that happen to act on the same binary — the first manufactures, at its own peak, the configuration the second is most efficient in.

orbits · Kozai–Lidov

A donor that grows as it is eaten

A white dwarf that loses mass gets bigger, so a binary in which one white dwarf feeds another runs backwards — its period lengthens as the donor shrinks. Whether the pair survives first contact at all depends less on the donor than on whether the stream finds room to form a disc, and for most pairs it does not.

stars · Mass transfer

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.

Gravitational waves Mass transfer Roche lobe overflow White dwarf Accretion disc Apsidal precession Binding energy Chandrasekhar limit Chirp mass Coalescence Common envelope Core mass

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