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<p>Dear Roland,<br>
First thanks for the explanation of notions and I would check the paper of GRHydro.</p>
<p>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, <span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">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 (<span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px">0.00012701-<span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"> 0.00012605)*18*18*18*4=<span>0.0224
M. <br>
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 ?</span></span></span></span></p>
<p><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span>Thank
you.</span></span></span></span></p>
<p><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span>Best
regards,</span></span></span></span></p>
<p><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span style="font-family:Calibri,Helvetica,sans-serif,serif,EmojiFont; font-size:16px"><span>Chia-Hui</span></span></span></span></p>
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<div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>寄件者:</b> Roland Haas <rhaas@illinois.edu><br>
<b>寄件日期:</b> 2018年9月25日 上午 01:22:16<br>
<b>收件者:</b> 林家暉<br>
<b>副本:</b> Einstein Toolkit Users<br>
<b>主旨:</b> Re: [Users] mass estimation of neutron star</font>
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<div class="PlainText">Hello Chia-Hui,<br>
<br>
> Thanks for your information. However I have further questions:<br>
> 1.In your expression :\int \sqrt{\gamma} \rho W d^3x ,is the gamma Lorentz factor ? And what is W?<br>
Uhm, gamma is the determinant of the three metric, W is the Lorentz<br>
factor. The equation was for illustration only, I would definitely not<br>
take it very seriously. See eg the GRHydro paper:<br>
<a href="https://arxiv.org/pdf/1304.5544">https://arxiv.org/pdf/1304.5544</a> eq 10 for the definitions of the quantities.<br>
<br>
> 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 ?<br>
<br>
What you call "cell mass" is the "cell volume". You also have to take<br>
any symmetries into account. Eg if you used both rotation180 symmetry<br>
and z symmetry then you are only evolving 1/4 of the physical volume<br>
and thus have to multiply the number by 4. This then gives you the<br>
expected result. This multiplication is needed because (for technical<br>
reason) Carpet computes the "sum" reduction assuming a cell volume of 1.<br>
<br>
<br>
> 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.<br>
<br>
The density in rho.xy.h5 is not sufficient since it is only the<br>
quantity "rho" above so you are missing eg the Lorentz factor W and the<br>
metric determinant "gamma". Also rho.xy.h5 contains only data in the xy<br>
plane and not the full 3 volume (which would be in rho.xyz.file_*.h5).<br>
Finally you would have to manually take care of not double counting in<br>
regions where finer grid overlaps a coarser grid. It is much easier to<br>
rely on Cactus to do this for you via the "sum" scalar output.<br>
<br>
Yours,<br>
Roland<br>
<br>
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