# Neutron Stars of unequal mass merging

Is the difference in masses between merging Neutron Stars the cause of the massive gravitational disturbances due to the unbalanced decaying orbit right before the merger?

Not exactly. Gravitational waves from binaries occur because there is a quadrupole moment of the system. That is, there is an uneven distribution of mass moving about and this causes the waves, but it is not the asymmetry between the masses that is contributing most of the moment (note that there is no dipole contribution to the radiation).

However, the intensity of the waves depends on the unevenness of the masses. The energy loss scales as $\langle E'\rangle \propto M_1^2M_2^2(M_1+M_2)$ where $M_1$ and $M_2$ the masses. Suppose $M_1=fM$ and $M_2=(1-f)M$, where $f$ measures how uneven they are. Then $\langle E'\rangle \propto f^2(1-f)^2 M^3$. That is, it is zero for $f=0,1$ (a mass being "orbited" by nothing), and maximal for $f=1/2$ (two equally sized masses). So actually it is evenly matched binaries that are most detectable.

what GR calls a quadrupole is not a true topological four-pole, but rather a rotating dipole. It is a quadrupole in 4D spacetime, but not a quadrupole in physical 3D space.

Popularizations of gravitational radiation show the phase shifts propagating in the plane of rotation of the binary pair. Correct source simulation is available at the CalTech site. Radiation is perpendicular to plane of rotation. Similarly, time symmetry requires source/detector reciprocity, optimum orientation of plane defined by interferometer arms is perpendicular to line between source and detector.

Seems curious that this is so different from say the earth's gravitational tides as driven by the moon. There optimal orientation is in the plane of rotation of earth-moon pair, not perpendicular as for gravitational radiation.

Here one might look for guidance to quantum gravity to realize there must be some sort of profound contradiction. Likely taking the quadrupole to be in spacetime rather than space has caused a sign error in the GR analysis of the antenna pattern?

as far as i know need for quadrupole was driven by attractive-only character of gravity, requires spin two which requires four poles.

important to keep in mind the difference between near and far fields. In near field the potentials as a function of separation vary differently. This becomes important in quantum gravity, one has to be able to work in the near field. To understand the antenna pattern one has to understand impedances and impedance matching. In the case of quantum gravity the relevant impedances are quantized.

• I understand they are poled, during their windown comes harmonic disturbance in gravity spcae time due to their differences in mass, i wonder if hypothetically they were the exat same mass down to the atom would the gravitational wave smooth transition instead of a wave, because if so that could have practical applications.......right. – Robert Bobo Jr. Nov 20 '17 at 13:17