# How do tidal forces change gravitational waves

If there is a binary of two neutron stars, they are going to be deformed because of the tidal forces. I suppose that it will cause a change in the movement of the stars and that will cause a change in the emitted gravitational waves.
How will that change the gravitational waves?
If we observe the gravitational waves, how can we deduct the tidal forces and so the composition of the stars?
Do the tidal effects change the frequency, the amplitude or anything else in the observations?

• The second part of your question is answered by the first. Tidal deformation does alter the GW signal, so the GW signal tells you about tidal deformation, which depends on the composition and equation of state of the stars. Apr 18 '20 at 11:29
• @RobJeffries Yes, but is there a formula for the tidal deformation?
– BOB
Apr 18 '20 at 12:02

The phase evolution of a binary during the inspiral phase can be described in the post-Newtonian (weak field) approximation as power series in the frequency $$f$$:
$$\Phi = \sum_{ij} \lambda_{i,j} f^{(i-5)/3}\log^j f,$$ where the $$\lambda_{ij}$$ encode various physical effects. Effects due to tidal deformations first show up in $$\lambda_{10,0}$$, in the form of the tidal deformation parameter $$\Lambda$$. This parameter essentially measures how easy it is to deform a neutron star, and depends on the internals of neutron star physics. (A black hole would have $$\Lambda=0$$).
In other words, the tidal interactions between the neutron stars lead to a (small) shift in the phase of the gravitational wave. This can be used to measure $$\Lambda$$ in a binary merger, which in turn tells us something about what is happening inside a neutron star.