Hello all,

for a (somewhat recent, likely not the first nor the latest) study of how well this particular way of measuring spin of a neutron star works, you may want to consult sections III.C (in particular figure 9) of https://arxiv.org/abs/1508.06986 which deals with both initial data construction and evolution (though not in the context of the Einstein Toolkit). The method used is the one Erik suggested.

Yours, Roland

Beyhan

The QuasiLocalMeasures thorn can examine not only horizons, but also other 2-surfaces. You can set up a surface that is large and which encloses both the remnant and surrounding matter, but which is still inside the emitted gravitational wave train. QuasiLocalMeasures can then calculate the angular momentum contained inside that sphere.

As Zach mentioned, the details of setting up a parameter file to do so are difficult to explain over email. The example parameter file "Cactus/par/qc0-mclachlan.par" contains such a setup; surface #3 ("horizon" #4, although this surface is of course not a horizon) is a sphere with areal radius R=50 where such quantities are calculated.

-erik

On Wed, Mar 4, 2020 at 11:22 AM Beyhan Karakaş beyhannkarakas@gmail.com wrote:

...

Dear to whom it may concern,

I am interested in determining the spin of the remnant which are resulted from binary neutron star (initially are in irrotational configuration) merger . How could the method to determine the final spin differ (if it does) in case of remnant is a black hole or a neutron star. For the former case, I suppose QuasiLocalMeasures parameter "begin_qlm_calculations_after" along with AHFinderDirect parameter "find_after_individual" should be set to the time/iteration that the black hole formed. If this is not the case, please clarify how could it be determined? In addition, is there a way to find the evolution of the spin and orbital eccentricity of the binary?

Best regards,

Beyhan. _______________________________________________ Users mailing list Users@einsteintoolkit.org http://lists.einsteintoolkit.org/mailman/listinfo/users

On 5 Mar 2020, at 15:42, Erik Schnetter <schnetter@gmail.commailto:schnetter@gmail.com> wrote:

Beyhan

The QuasiLocalMeasures thorn can examine not only horizons, but also other 2-surfaces. You can set up a surface that is large and which encloses both the remnant and surrounding matter, but which is still inside the emitted gravitational wave train. QuasiLocalMeasures can then calculate the angular momentum contained inside that sphere.

I'm not familiar with the method as applied to neutron stars, but for a black hole system, I would probably try to do this by computing the "ADM angular momentum" of the spacetime, as well as the "Bondi angular momentum loss", their difference being the "remaining" angular momentum in the system. I think this is fairly rigorous when done with masses, but I put the quotes around the angular momenta as I don't think these quantities are on as firm a footing.

In practice, one *should* be able to compute the "ADM angular momentum" on the initial data slice by evaluating the formula on a set of finite-radius spheres using QuasiLocalMeasures, similar to what Erik mentioned, and then extrapolating to spatial infinity. I don't know if there are reasons why this won't work for neutron star initial data. The "Bondi angular momentum loss" could be calculated by measuring the angular momentum flux in the emitted gravitational waves. This is technically very challenging to get accurate. You need quite a lot of resolution, and wave extraction far enough out that you can cleanly extrapolate it to future null infinity. There are also severe complications due to junk radiation.

So this approach is quite hard to implement.

-- Ian Hinder Research Software Engineer University of Manchester, UK