[Users] mass estimation of neutron star

[Roland Haas]

Hello Chia-Hui,

> Thanks for your information. However I have further questions:
> 1.In your expression :\int \sqrt{\gamma} \rho W d^3x ,is the gamma Lorentz factor ? And what is W?
Uhm, gamma is the determinant of the three metric, W is the Lorentz
factor. The equation was for illustration only, I would definitely not
take it very seriously. See eg the GRHydro paper:
https://arxiv.org/pdf/1304.5544 eq 10 for the definitions of the quantities.

> 2. For baryon mass case.What does the cell mass( "sum"*dx*dy*dz ) mean? In my case of binary neutron star, dx=dy=dz=18 and initial sum = 0.000126, so the cell mass=0.735 which is still much less than the initial mass of each neutron star(1.45 Ms).What is the physical meaning of the cell mass ?

What you call "cell mass" is the "cell volume". You also have to take
any symmetries into account. Eg if you used both rotation180 symmetry
and z symmetry then you are only evolving 1/4 of the physical volume
and thus have to multiply the number by 4. This then gives you the
expected result. This multiplication is needed because (for technical
reason) Carpet computes the "sum" reduction assuming a cell volume of 1.


> What I want to get is the mass lost during merge, which is 2*initial neutron star mass - final merged neutron star mass (for the equal mass binary). My first thought is integrating the density in rho.xy.h5 and assume spherical symmetry to calculate each mass.

The density in rho.xy.h5 is not sufficient since it is only the
quantity "rho" above so you are missing eg the Lorentz factor W and the
metric determinant "gamma". Also rho.xy.h5 contains only data in the xy
plane and not the full 3 volume (which would be in rho.xyz.file_*.h5).
Finally you would have to manually take care of not double counting in
regions where finer grid overlaps a coarser grid. It is much easier to
rely on Cactus to do this for you via the "sum" scalar output.

Yours,
Roland

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