On 8 Jun 2020, at 14:48, Ian Hinder 
<[email protected]<mailto:[email protected]>> wrote:



On 4 Jun 2020, at 16:39, Bill Gabella 
<[email protected]<mailto:[email protected]>> wrote:

** [ZE] NRPyPN we use two punctures for initial data in ETK.  Looking
for low ecc BBH intial data parameter solvers.  Wrote one based on
literature.  Option in Two Punctures that you sepcify the 8 input params
and outputs the initial data, P_t and P_r.  If close to ecc =0, as close
as Post-Newtonian allows.  ES-Good enough params or need to iterate?
ZE-Paper by Ramos-Buades et al. https://arxiv.org/abs/1810.00036 .  They
say with one iteration can drop ecc to order 1/10^3 .  RH-Good to have
the notebook in the utils folder for Two Punctures.  ZE-Tedious, but the
C version is not too hard and integrate with Two Punctures.  RH-Very low
eccentricity requires man iterations, a glitch shows that ecc energy
goes up.  Scheme gives back P_t and P_r.  PN in C does iteration zero,
but not later ones.  RH&ZE-Iteration greater than 1 is not in NRPyPN but
RH's student has been doing that.  RH-I will reach out to principals and
discuss this.  Does two orbits and sees what to update, and then
re-submits itself, and want ecc < 1e-6 .  First bit is all eccentricity
reduction.  ZE-Found typos in the original paper.  dE_GW/dt was very
different than other groups use.  RH-Recevied their Mathematica
notebook, so hopefully better than the paper.

Some links to NRPyPN, Low-eccentricity Post-Newtonian BBH initial data
parameters (for Two Punctures):
https://nbviewer.jupyter.org/github/zachetienne/nrpytutorial/blob/master/NRPyPN/NRPyPN.ipynb
https://github.com/zachetienne/nrpytutorial/tree/master/NRPyPN   (source
codes)

Hi,

I developed an infrastructure for obtaining low-eccentricity parameters for 
BBH.  It is implemented and freely-available in SimulationTools for 
Mathematica.  See 
https://bitbucket.org/simulationtools/simulationtools/src/master/EccentricityReduction.m.
  I haven't used it in a while, but can't think why it wouldn't still work.  It 
lacks documentation - if someone is interested in using it or developing it 
further, I can see if I can find some time to write up some docs.

You can use it to generate an initial guess from PN 
(QuasiCircularParametersFromPostNewtonian[{m_, q_, chi1_, chi2_, om_}]) for any 
aligned-spin case (you can probably use chi_z for precessing cases).  This will 
give you the separation, orbital angular momentum (r * py) and radial linear 
momentum (px).  You then run a simulation with these parameters for a few 
orbits, and analyse the results.  The method uses the time derivative of the 
radial separation for its eccentricity estimator. You use 
BinaryEccentricityFromSeparationDerivative, passing it the separation as a 
function of time (which you can get from ReadBinarySeparation), and a time 
window in which to measure the eccentricity.  You can get a suitable window 
from EccentricityFitWindow, which calculates it using a simple heuristic from 
the initial orbital frequency to give two orbits.  You can then use 
ReduceEccentricity with the results of 
BinaryEccentricityFromSeparationDerivative which gives you updated TwoPunctures 
parameters.

There are a number of higher level functions designed to fit this into an 
automated workflow.  I was using it with SimFactory 3, which supports the idea 
of post-simulation scripts and "termination reasons".  I had it set up so that 
when Cactus terminates during an eccentricity reduction run, it would run a 
script 
(https://bitbucket.org/simulationtools/simulationtools/src/master/Scripts/AnalyseEccentricity)
 which would call SimulationTools to estimate the next separation and radial 
momentum (I chose to keep the angular momentum L fixed, since that corresponds 
to fixed omega at 0 PN (maybe 1 PN?)).  The post-simulation script is 
https://bitbucket.org/ianhinder/simfactory3/src/master/simfactory/etc/appdb/scripts/post-simulation,
 and it has a number of heuristics for what to do in different cases.

There are a lot of parts to this system, but it used to run extremely well, and 
was fully automated, and was used to produce many production simulations, 
including the very high spin simulations used in 
https://arxiv.org/abs/1810.10585, with chi_z = 0.9 and mass ratios up to 5.

I forgot to mention the crucial part!  For those simulations, it's very 
challenging to get the eccentricity down; typically I could only get it down to 
~1e-3, but that is usually enough.  For simple cases, like equal mass, 
non-spinning, if you are at a large separation (e.g. 15 orbits), the method was 
able to iterate the eccentricity down to something like 1e-6.

--
Ian Hinder
Research Software Engineer
University of Manchester, UK

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