On 1 Feb 2012, at 05:02, Eloisa Bentivegna wrote:

On Feb 1, 2012, at 3:12 AM, Jose Fiestas Iquira wrote:

...

Dear all, I am using WeylScal for BH binary coalescence, and I am obtaining 'weylscal4::psi4r...' and 'weylscal4::psi4i ...' files, with which I could plot the wave against distance/time. Could somebody advise me how to get the energy emission due to grav. waves from the WeylScal output? I would like to construct a plot: GW Energy vs. distance/time.

Hi Jose,

there's a couple of things to keep in mind:

1. In broad terms, there is no notion of gravitational-wave energy density; one can at best associate a mass with the whole spatial hypersurface, but not state how much of this is in gravitational waves or where it is localized;
2. Under reasonable assumptions, the radiated power at infinity can be expressed in terms of the Weyl scalars. You'd probably best start learning about this is in one of the numerical-relativity textbooks: either section 8.9 of http://books.google.de/books?id=4hDvRvVJeEIC&dq=alcubierre&hl=de&sa=X&ei=GBopT--LC87ItAbI-b3FAQ&ved=0CDIQ6AEwAA or section 9.4 of http://books.google.de/books?id=dxU1OEinvRUC&dq=baumgarte&hl=de&source=gbs_navlinks_s (notice that this is still a function of time only -- no localization);

Hi Jose,

Once you have an understanding of the theory, you could also read section II.A in http://arXiv.org/abs/arXiv:0804.4184 which describes how this is usually done for NR calculations from the spherical harmonic modes. To compute the strain derivative you will probably want to use the method of http://arXiv.org/abs/arXiv:1006.1632. Before using any results of calculations such as this to draw physical conclusions, you also need to make sure that you have accurate enough simulation data. At a minimum, you should perform the simulation at different grid spacings and compare your final answer computed from each to get an idea of the effect. It is also important to extrapolate the results to infinite radius as discussed in the first reference above, because the energy flux is only defined asymptotically, and the results could be very different at different extraction radii.

Jose

I think that comparing waveforms is one of the best ways of doing so -- comparing the metric or horizon data or any strong field properties doesn't make much sense.

I believe it was pointed out that converting Psi4 to strain is a complex task. The other way around (converting strain to Psi4) should be straightforward.

Several readers on this list have extensive experience in handling and converting ET waveforms. Maybe someone is interested in a collaboration?

-erik

On Mon, Feb 6, 2012 at 9:19 PM, Jose Fiestas Iquira jafiestas@lbl.gov wrote:

Thanks. I checked the literature, and looked at the irreducible mass, given by AHFinderDirect, which is growing in time, with respect to the initial mass (ADM mass). By substracting I obtain an estimate (upper limit I guess) ob the radiated energy during coalescence.

As mentioned I am seeking for a method to test/validate ETK tools together with N-body using Post Newtonian approximations. I am using binary coalescence.

My N-body code (up to 3.5 PN terms), can calculate strain amplitudes vs. frequency, My first idea was to validate this results by creating the same plot using ETK. Would you recommend a more direct way to do such a comparison?

Thanks, Jose

On Wed, Feb 1, 2012 at 3:02 AM, Eloisa Bentivegna bentivegna@cct.lsu.edu wrote:

...

On Feb 1, 2012, at 3:12 AM, Jose Fiestas Iquira wrote:

...

Dear all, I am using WeylScal for BH binary coalescence, and I am obtaining 'weylscal4::psi4r...' and 'weylscal4::psi4i ...' files, with which I could plot the wave against distance/time. Could somebody advise me how to get the energy emission due to grav. waves from the WeylScal output? I would like to construct a plot: GW Energy vs. distance/time.

Hi Jose,

there's a couple of things to keep in mind:

1. In broad terms, there is no notion of gravitational-wave energy

density; one can at best associate a mass with the whole spatial hypersurface, but not state how much of this is in gravitational waves or where it is localized; 2) Under reasonable assumptions, the radiated power at infinity can be expressed in terms of the Weyl scalars. You'd probably best start learning about this is in one of the numerical-relativity textbooks: either section 8.9 of http://books.google.de/books?id=4hDvRvVJeEIC&dq=alcubierre&hl=de&sa=X&ei=GBopT--LC87ItAbI-b3FAQ&ved=0CDIQ6AEwAA or section 9.4 of http://books.google.de/books?id=dxU1OEinvRUC&dq=baumgarte&hl=de&source=gbs_navlinks_s (notice that this is still a function of time only -- no localization); 3) If you're just interested in how much energy leaves the system during the merger, you may be better off subtracting the final horizon mass (given by AHFinderDirect) from the ADM mass (given by TwoPunctures).

Let me know if this isn't clear enough! Eloisa

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