Quadrupole

The third term in a “multipole” expansion, which describes some spherical pattern as the sum of components with different angular features. This is similar to a Taylor expansion but over a sphere. The first term, called the “monopole”, is a constant that does not depend on the orientation on the sphere. The second term, called the “dipole”, splits the sphere up into two sides. One way to think about these two is as follows. Usually when you think of Newtonian gravity of a sphere, the gravitational field points equally down in all directions and does not depend on angle, and thus is a monopole. A bar magnet, with a north and south pole, has a magnetic field that is a dipole because it is broken up into two halves. The third term in the multipole expansion is the quadrupole, which breaks up the sphere into four possible parts, though there are different ways that these parts can be oriented. A gravitational wave passing by the Earth produces a quadrupolar pattern in the shifts of pulsar arrival times.