Mountains on neutron stars

In this case two neutron stars were orbiting each other. Relativity predicts they orbit would be unstable due to energy loss caused by gravity waves. Observation confirmed decaying orbit, we have not actually observed the gravity waves them selfs.

Gravitational waves have not been directly detected by laboratory instruments here on Earth. The LIGO and VIRGO collaborations are looking for gravitational waves by using large laser interferometers, but haven't detected any yet.

The article is referring to the first indirect detection of gravitational waves. Binary stars emit gravitational waves which carry energy away from the system. The loss of energy causes the two stars to spiral into a closer orbit until eventually they merge. Using general relativity, you can predict how the semi-major axis will change as a function of time [1]. Hulse & Taylor measured the change in semi-major axis in a binary pulsar and found that it matched the predictions of general relativity.

[1] http://adsabs.harvard.edu/abs/1964PhRv..136.1224P

Yes, there is an index of refraction for gravitational waves passing through matter. As the gravitational wave passes through, particles in the material oscillate, producing their own gravitational waves. The combined gravitational wave from the original gravitational wave plus the secondary gravitational waves is broader. The increased wavelength implies a decreased speed. An idealized equation for this index of refraction can be found in Eq. 18 here:

http://link.springer.com/article/10.1007%2FBF00891464#page-1

The paper calculates the index of refraction for the Earth and finds that n - 1 ~ 10^-17, so it's a very small effect indeed. For something much more dense and stiff, like a neutron star, it would be higher by many orders of magnitude. But without knowing the equation of state of a neutron star it's impossible to calculate n.

It's mostly due to the total mass of the star, since a more massive star has greater gravitational force at its surface, overwhelming the structural forces in the particles.

From my reading of it:

>The size of the highest mountain of order ∼ εR can be roughly estimated from the inequality (292).

>P, P˙ and I are, respectively, the pulsar’s period, period derivative and moment of inertia [in inequality (292)].

Those terms are all just multiplied together in the inequality, so changes in any of them could affect epsilon (the "dimensionless parameter characterizing deformations of the star")

Pulsar will always slow down, thanks to magnetosphere interacting with interstellar environments.