A Simple method to set up low eccentricity initial data for moving puncture simulations

TL;DR

This paper presents a straightforward method for setting low eccentricity initial data in moving puncture simulations, introducing new eccentricity measures and an iterative approach to optimize initial parameters.

Contribution

It introduces parameter-free eccentricity measures and a simple iterative method to achieve low eccentricity initial data in puncture simulations.

Findings

New eccentricity measures that do not require free parameters.

A practical iterative procedure to refine initial momentum parameters.

Comparison showing coordinate differences between ADMTT and puncture data.

Abstract

We introduce two new eccentricity measures to analyze numerical simulations. Unlike earlier definitions these eccentricity measures do not involve any free parameters which makes them easy to use. We show how relatively inexpensive grid setups can be used to estimate the eccentricity during the early inspiral phase. Furthermore, we compare standard puncture data and post-Newtonian data in ADMTT gauge. We find that both use different coordinates. Thus low eccentricity initial momentum parameters for a certain separation measured in ADMTT coordinates are hard to use in puncture data, because it is not known how the separation in puncture coordinates is related to the separation in ADMTT coordinates. As a remedy we provide a simple approach which allows us to iterate the momentum parameters until our numerical simulations result in acceptably low eccentricities.