Astronomy & Celestial Mechanics
the sky, computed
Concept

Love numbers — where it appears

Dimensionless numbers measuring how much a body deforms under a tidal pull, and how much its gravity field changes as a result. Their values encode the body's interior — its rigidity, its central concentration, and whether it holds a liquid layer.

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

What a deformability is made of. The two factors of the tidal deformability Λ = ⅔ k₂ C⁻⁵ for a 1.4 solar-mass neutron star, each relative to its value at 12 km, on a logarithmic scale, against the star's radius. The Love number k₂ — the same number that measures a moon's response to a planet's tide — rises by a factor of 1.6 between 10 and 14 km; the inverse fifth power of the compactness rises by 5.4. Of the change in Λ across that range, 78 per cent, on a logarithmic scale, comes from the compactness: most of what a deformability measures is how large the star is for its mass. The Love number carries the rest: how centrally concentrated the matter is, which is where the equation of state enters beyond the radius.

A Love number measured at nuclear density

The number that told Cassini there was water under Titan's ice is defined the same way for a neutron star, and in the last tenth of a second before two of them merge it changes the shape of the gravitational wave they emit. What the wave measures is mostly not the Love number itself but the star's size, raised to the sixth power — which makes a faint tidal signal into one of the few direct measurements of how large matter at nuclear density lets a star be.

gravitation · Love numbers Six moons, and how long each takes to move. The time each of Saturn's six largest moons would take to move outward by its own orbital radius, a divided by its rate of change, on a logarithmic scale. Bars: a constant tidal quality factor tuned to the inner moons' measured motion, under which the time grows steeply with distance and falls with mass — 6 billion years for Enceladus, 210 billion for Titan. Dashed: Titan's measured migration, 11 centimetres a year, which is 11 billion years — 19 times faster than the constant-Q prediction and within a factor of two of the inner moons, where the constant-Q picture puts them a factor of 33 apart. Resonance locking predicts exactly that: one time scale for every locked moon, set by the planet rather than by the moon.

A migration timed by the planet and not the moon

Titan is Saturn's most distant large moon, and by the standard account of tides it should be the slowest to move — a two-hundred-billion-year journey across its own orbit. It is moving eleven centimetres a year, twenty times faster, on the same time scale as the small moons close to the planet. A quality factor cannot do that. An oscillation inside Saturn, tuned to each moon in turn and dragged along by the planet's own slow evolution, can.

gravitation · Tidal heating

Named alongside it

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

Chirp massCompactnessDynamical tideEnceladusEquation of stateGravitational wavesNeutron starsOrbital resonancePlanetary oscillationsPolytropesPost-newtonianResonance locking

All concepts