[Users] mass estimation of neutron star

[林家暉]

Dear Roland,

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?

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 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.

Best regards,
Chia-Hui



________________________________
寄件者: Roland Haas <rhaas at illinois.edu>
寄件日期: 2018年9月24日 下午 10:52:36
收件者: 林家暉
副本: Einstein Toolkit Users
主旨: Re: [Users] mass estimation of neutron star

Hello Chia-Hui,

I am very sorry for the late response.

There are (at least) two notions of mass that are relevant for neutron
stars

1. the baryon mass which is the integral \int \sqrt{\gamma} \rho W d^3x
2. the ADM mass (or a similar object) which is the mass measured by an
observer far away

the former can be computed as the integral of the "dens" variable of
GRHydro for example by requesting "sum" scalar output for it:

CarpetIOScalar::outScalar_vars = "GRHydro::dens"
CarpetIOScalar::outScalar_every = 1

and then multiplying the numbers in there by the volume of a cell on
the coarsest grid (ie the product of the values of CoordBase::dx,
CoordBase::dy, and CoordBase::dz in the parameter file).

The later can be computed using the QuasiLocalMeasures thorn on a
spherical surface or using the ADMMass thorn
(https://www.einsteintoolkit.org/thornguide/EinsteinAnalysis/ADMMass/documentation.html
see the example parfile here:
https://bitbucket.org/einsteintoolkit/einsteinanalysis/raw/39b8ae09c3b55d842e19ed5e89a716d3534883d0/ADMMass/test/tov_carpet.par).

Yours,
Roland

> Dear whom it may concern,
>
> I simulated the binary neutron star merger as in gallery code(https://einsteintoolkit.org/gallery/bns/index.html). I tried to find out the mass of the merged neutron star. For test, I calculated the initial mass of each neutron star  from the file rho.xy.h5 which is the rest mass density. What I computed is about 0.9 solar mass , however it supposed to be much larger because the baryonic mass of the initial data of each neutron star is about 1.45 solar mass. I also calculated magnetic energy which corresponds to about 1e-6 solar mass  which is not a possible reason of the discrepancy. I also considered velocity which may increase mass due to the relativity but the maximum of the initial velocity is only about 0.1c which also does not raise the mass too much. What is the possible reason that the total rest mass is so much smaller than the baryonic mass ?
>
> Thank you.
>
>
> Best regards,
>
> Chia-Hui



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