Radiation pattern of a GW source

Question

Accelerated masses produce gravitational waves. A binary star system in which two stars orbit a common center of mass emits gravitational waves. The greatest power is emitted in the plane perpendicular to the stars' orbit. Therefore the following statements must be correct:

1. The radiation pattern (points of equal intensity) looks something like Eta Carinae.
2. The amplitude of the GW disappears at all points on the (local) ecliptic of the binary star.
3. Therefore, a two-dimensional representation like in Wikipedia is wrong and leads to wrong conclusions.
4. Since a GW is circularly polarized, the radiation must be right-hand circular in one half-space and left-hand circular in the other half-space.
5. Since the same amount of energy is radiated in both directions, the angular momentum of the binary system does not change.

My question: GW are usually represented as plus-polarized and cross-polarized waves. Neither text description nor images indicate circular polarization. Right or wrong?

Answer 1

Gravitational waves are tensor modes that are, in general, a mixture of two orthogonal polarisation states known as plus and cross.

By analogy with electromagnetic waves, you can refer to a wave formed from a superposition of equal amplitude plus and cross polarised waves, with 90 degree phase shift between them, as "circularly polarised".

That state of affairs is approximately what you get emitted along the axis of a binary system with a circular orbit. If the binary was instead viewed in the plane of the orbit, only one of the two polarisation states would be seen and you could then refer to that as linearly polarised, again, by analogy.

However it is only an analogy, a gravitational wave of a single polarisation causes a disturbance over the whole of the plane perpendicular to its propagation, apart from along two perpendicular lines. A linearly polarised electromagnetic wave has a field aligned along just a single axis.

Of the things you say that "must be correct", 1, 2 and 5 are not true.

(1) It looks more complicated than that.

(2) Possibly I haven't understood what you mean. The strain amplitude is about half of its peak in the orbital plane of the binary.

(3) Agreed, this is a poor visualization. Again, it is an analogy. The pictures and animations here are much better.

(4) Correct, oppositely handed circularly polarised waves travel along the orbital axis in opposite directions.

(5) Since the handedness of the polarisation flips for waves travelling along the orbital axis in opposite directions, the waves do carry away angular momentum. That is why there is an inspiral.

e.g. if you are looking at the binary from "the top" and it is orbiting clockwise, you see clockwise circularly polarised GWs. If you look at the same binary from below you see it orbiting anticlockwise and receive anti-clockwise circularly polarised GWs.