Verify numerical force-resolution convergence

Establish the numerical convergence of the fiducial $h=0.01$ kpc finite-difference force evaluation by carrying out the planned integrations at $h=0.005$, $0.01$, $0.02$, and $0.04$ kpc and comparing the resulting velocity-dispersion and disk-departure diagnostics.

Background

The Galactic acceleration is computed with a centered finite-difference approximation using a fiducial spatial step of h=0.01h=0.01 kpc. The paper specifies a convergence test using four force-resolution values and the same initial particle realization, comparing final radial and vertical velocity dispersions and the disk-departure fraction through a maximum fractional variation. However, the test has been designed but not yet executed, so the reliability of the fiducial force-resolution choice remains unresolved.

References

We report this methodology in full so that the test is straightforward for us, or an independent party, to carry out and check against the fiducial results; until it is run, the numerical convergence of the fiducial $h=0.01$~kpc choice should be regarded as plausible (Sec.~\ref{sec:acceleration}) but not verified, and Table~\ref{tab:appendix_integration} lists $h$ among the fiducial parameters without an accompanying $\delta_{\rm max}$ value.

— The Galactic Dynamics of Free-Floating Planets: From Ejection Kicks to Microlensing  (2609.21027 - Sayed et al., 17 Sep 2026) in Appendix, Section “Numerical Integration and Force Evaluation” (Appendix A.7)