Interactive · gravitational-wave modes
The angular building blocks of every gravitational-wave signal. A binary's radiation is a sum of these ₋₂Yℓm modes — the shapes below are the angular pattern of "the (2,2) mode" or "the (3,3) mode", drawn as a radius-deformed sphere.
The radius is deformed by the chosen field — colored by sign for Re and Im, by magnitude for |Y| and |Y|² — so ℓ − max(|m|, 2) gives the number of nodal circles in latitude — the spin weight sets a floor, which is why ₋₂Yℓm is not the scalar ℓ − |m| rule — and the Re and Im views show 2|m| azimuthal lobes, separated by 2|m| nodal meridians. |Y| and |Y|² are axisymmetric at every m, so those lobes vanish in both — they differ only in how sharply the latitude profile is peaked, |Y|² exaggerating the contrast between lobe and node. At m = 0 the mode is axisymmetric in every view, and Im vanishes identically. Each mode is normalized to its own peak, so shapes are comparable but amplitudes are not: the (2,2) mode dominates most black-hole mergers, and higher modes carry the finer structure that models like BOB aim to capture.
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