Can LIGO distinguish rotating and non rotating black hole collisions?

Question

I am assuming two rotating black holes create gravitational waves as they collide.

Answer 1

Yes it can - well, to some extent. If you look at any of the merging black hole discovery papers you will see that they try and put constraints on the dimensionless spin parameter and orientations of the spins of the black holes, both before and after the merger. There is also a test for the likelihood of spinning versus non-spinning black holes.

Here is an example from Abbott et al. 2020 concerning the analysis of GW190521, a very massive black hole merger. The table reproduced below gives the magnitude of the spin parameters (the "spin magnitude") of the black holes both before an after merger. Subsequent analysis in the paper looks at how those spins might be oriented compared with the orbital plane of the binary. Notice that the error bars on the spin parameters before merger are large and the evidence that the black holes are spinning is quite weak - this is parameterised with the Bayes factor, which is the ratio of likelihoods for models with and without spin. In this case, a Bayes factor of about 8.3 is substantial but not decisive evidence that the spinning model is favoured. However, after the collision the spin parameter of the merged black hole is much better defined.

It is actually quite difficult to get good constraints on the individual spins of black holes before the merger. The signal instead chiefly depends on something called the dimensionless effective spin parameter of the system ($\chi_{\rm eff}$ in the table above), which ranges from -1 if the black hole spins are anti-aligned with the orbital angular momentum to +1 if they are aligned (e.g. Vitale et al. 2017).