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@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/document... see the example parfile here: https://bitbucket.org/einsteintoolkit/einsteinanalysis/raw/39b8ae09c3b55d842...).

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

-- My email is as private as my paper mail. I therefore support encrypting and signing email messages. Get my PGP key from http://pgp.mit.edu .

Dear Roland, First thanks for the explanation of notions and I would check the paper of GRHydro.

To my understanding, "sum" output multiply dxdydz is the total mass of the neutron star(s) in the simulation.Is this correct ? In my case which is gallery example, initial sum = 0.00012605 and final sum is 0.00012701 so that the mass increases from the initial binary neutron star to the final merged neutron star is (0.00012701- 0.00012605)*18*18*18*4=0.0224 M. This is somehow different to what I thought. I originally think that during the inspiral and merging . some mass would outflow due to tidal force , so the total mass of neutron star would decrease. Contrast to this, the mass gained. IS this means accretion mass is larger than the summation of outflow mass and energy radiated away by the gravitational wave ?

Thank you.

Best regards,

Chia-Hui

________________________________ 寄件者: Roland Haas rhaas@illinois.edu 寄件日期: 2018年9月25日 上午 01:22:16 收件者: 林家暉 副本: Einstein Toolkit Users 主旨: Re: [Users] mass estimation of neutron star

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

-- My email is as private as my paper mail. I therefore support encrypting and signing email messages. Get my PGP key from http://pgp.mit.edu .

Dear Roland,

Thanks for your detailed reply.

For GRHydro I have further questions:

1. It is GRMHD code so that it should be able to consider magnetic field. Is magnetic field considered in the gallery example of BNS? Because I did not see the relevant output data. 2. I would like to simulate r-process in the future, is GRHydro capable of it ? Because time scale for r-process is much larger than BNS merger, so maybe I will need other thorn ?

Best regards, Chia-Hui

________________________________ 寄件者: Roland Haas rhaas@illinois.edu 寄件日期: 2018年9月25日 下午 07:43:33 收件者: 林家暉 副本: Einstein Toolkit Users 主旨: Re: [Users] mass estimation of neutron star

Dear Chia-Hui,

To my understanding, "sum" output multiply dxdydz is the total mass of the neutron star(s) in the simulation. Is this correct ?

That is correct.

In my case which is gallery example, initial sum = 0.00012605 and final sum is 0.00012701 so that the mass increases from the initial binary neutron star to the final merged neutron star is (0.00012701- 0.00012605)*18*18*18*4=0.0224 M. This is somehow different to what I thought. I originally think that during the inspiral and merging . some mass would outflow due to tidal force , so the total mass of neutron star would decrease.

The sum is over the full domain so unless some of the tidal outflows reach the edge of the domain or are otherwise removed (eg by numerical effects inside of a black hole where we apply tricks to make the code not crash) then the total rest mass will be conserved.

The slight increase that you see may well be due to either accretion of atmosphere onto the star or due to numerical issues at mesh refinement boundaries since the default mesh refinement technique used in the Einstein Toolkit is not conservative (it uses vertex centering and no refluxing, both of which can be changed by options to the parameter file and by using the Refluxing thorn).

Contrast to this, the mass gained. IS this means accretion mass is larger than the summation of outflow mass and energy radiated away by the gravitational wave ?

Energy radiated would not show up in the balance since the rest mass is literally just the sum of baryons present which does not change as energy is radiated away.

If you are interested in the amount of matter ejected I would suggest looking at the Outflow thorn: https://www.einsteintoolkit.org/thornguide/EinsteinAnalysis/Outflow/document... which is part of the Einstein Toolkit. It measures the amount of matter that passes through spheres of constant radius. It has an example parfile (with very low resolution) in its test directory.

Yours, Roland

-- My email is as private as my paper mail. I therefore support encrypting and signing email messages. Get my PGP key from http://pgp.mit.edu .

Dear Roland,

Thanks for your reply. I would check out those works.

In addition , I would like to ask question about computation consumption. For the BNS merger (using .par file in the gallery file), it costs about 5000 core hours (48 cores for 100 hours) for the completed simulation (to iteration=15000). Is it reasonable? And is there some way to save the computational resources ?

Best regards,

Chia-Hui

________________________________ 寄件者: Roland Haas rhaas@illinois.edu 寄件日期: 2018年9月27日 上午 05:37:02 收件者: 林家暉 副本: Einstein Toolkit Users 主旨: Re: [Users] mass estimation of neutron star

Hello Chia-Hui,

1. It is GRMHD code so that it should be able to consider magnetic

field. Is magnetic field considered in the gallery example of BNS? Because I did not see the relevant output data.

I do not think there is an explicit magnetised BNS example in the gallery. There is a single magnetised star in the runs we did for the GRHydro MHD paper, for which you can find the parameter file here: https://www.einsteintoolkit.org/mp.html in the magnetized TOV parfile https://www.einsteintoolkit.org/publications/2013_MHD/par/tov/tov8m3.par

A binary could likely be set up similarly. You can also try and see if IllinoisGRMHD (part of the Einstein Toolkit) has parameter files for this situation.

2. I would like to simulate r-process in the future, is GRHydro

capable of it ? Because time scale for r-process is much larger than BNS merger, so maybe I will need other thorn ?

There is no nucleosynthesis code available in the Einstein Toolkit. For postprocessing you could have a look at Jonas Lippuner's SkyNet code: http://jonaslippuner.com/research/skynet/ which was used to postprocess data from supernova simulations using the Einstein Toolkit https://arxiv.org/abs/1712.09370

It is likely too slow (since it contains too many species) to directly use it during evolution (and there is no equation of state implemented right now that would allow for multiple species in the gas, though you may ask around in the list of someone has implemented anything they would be willing to share).

Yours, Roland

-- My email is as private as my paper mail. I therefore support encrypting and signing email messages. Get my PGP key from http://pgp.mit.edu .

Dear Roland,

Thanks for your reply.

For the previous question about r-process, I found a document(https://stellarcollapse.org/media/micra2013/moesta.pdf) saying that GRHydro could consider neutrino leakage. But I have no ideal how to implement it. Is there any suggested way to deal with neutrino leakage with GRHydro (or other thorns) ?

Thank you.

Best regards,

Chia-Hui

________________________________ 寄件者: Roland Haas rhaas@illinois.edu 寄件日期: 2018年10月2日 下午 09:11:21 收件者: 林家暉 副本: Einstein Toolkit Users 主旨: Re: [Users] mass estimation of neutron star

Hello Chia-Hui,

In addition , I would like to ask question about computation consumption. For the BNS merger (using .par file in the gallery file), it costs about 5000 core hours (48 cores for 100 hours) for the completed simulation (to iteration=15000). Is it reasonable? And is there some way to save the computational resources ?

If you want to save overall resources you could reduce the number of cores used (assuming you do not run out of memory). For example running on 32 cores will make it run slower but not by a factor of 48/32 so that the total resources (number-of-cores * hours-used) goes down.

You could also try reducing (slightly!) the resolution eg by a factor of 1.25 which would make the simulation cheaper (but also loose significantly in accuracy). Finally you could try and make the simulation domain smaller, which safes a bit but not a whole lot usually.

You can also try and see if reducing the amount of output produced makes any difference (though that is unlikely). This is the outXXX_every parameters and generally everything with an _every in its name.

Yours, Roland

-- My email is as private as my paper mail. I therefore support encrypting and signing email messages. Get my PGP key from http://pgp.mit.edu .

Dear Roland,

Thank you for your suggestion and information!

Best regards,

Chia-Hui

________________________________ 寄件者: Roland Haas rhaas@illinois.edu 寄件日期: 2018年10月5日 下午 11:49:50 收件者: 林家暉 副本: Einstein Toolkit Users 主旨: Re: [Users] mass estimation of neutron star

Hello Chia-Hui,

https://stellarcollapse.org is your best starting point. Please have a look at the page for the publications listed there on https://www.stellarcollapse.org/node/17 in particular for the leakage code:

https://sntheory.org/ottetal2013 https://stellarcollapse.org/cc3dgrmhd

and the code page for the Zelmani codes (Leakage and M1 as well as version of GRHydro):

https://stellarcollapse.org/Zelmani

where both the newest public version of the leakage and the M1 codes are available for download.

For the R-process please look at

http://sntheory.org/lippunerroberts2015

and Jonas' skynet code page:

https://bitbucket.org/jlippuner/skynet

Yours, Roland

Dear Roland,

Thanks for your reply.

For the previous question about r-process, I found a document(https://stellarcollapse.org/media/micra2013/moesta.pdf) saying that GRHydro could consider neutrino leakage. But I have no ideal how to implement it. Is there any suggested way to deal with neutrino leakage with GRHydro (or other thorns) ?

Thank you.

Best regards,

Chia-Hui

---

寄件者: Roland Haas rhaas@illinois.edu 寄件日期: 2018年10月2日 下午 09:11:21 收件者: 林家暉 副本: Einstein Toolkit Users 主旨: Re: [Users] mass estimation of neutron star

Hello Chia-Hui,

...

In addition , I would like to ask question about computation consumption. For the BNS merger (using .par file in the gallery file), it costs about 5000 core hours (48 cores for 100 hours) for the completed simulation (to iteration=15000). Is it reasonable? And is there some way to save the computational resources ?

If you want to save overall resources you could reduce the number of cores used (assuming you do not run out of memory). For example running on 32 cores will make it run slower but not by a factor of 48/32 so that the total resources (number-of-cores * hours-used) goes down.

You could also try reducing (slightly!) the resolution eg by a factor of 1.25 which would make the simulation cheaper (but also loose significantly in accuracy). Finally you could try and make the simulation domain smaller, which safes a bit but not a whole lot usually.

You can also try and see if reducing the amount of output produced makes any difference (though that is unlikely). This is the outXXX_every parameters and generally everything with an _every in its name.

Yours, Roland

-- My email is as private as my paper mail. I therefore support encrypting and signing email messages. Get my PGP key from http://pgp.mit.edu .

-- My email is as private as my paper mail. I therefore support encrypting and signing email messages. Get my PGP key from http://pgp.mit.edu .