Verify the origin of the shortfall in the Earth-to-Neptune microlensing timescale ratio

Determine whether the shortfall of the Earth-to-Neptune peak Einstein-timescale ratio relative to the expected square-root mass scaling is a numerical artifact caused by the fixed 90-point logarithmic timescale grid, using a finer grid.

Background

The microlensing pipeline predicts peak Einstein timescales for Earth-like, Neptune-like, and Jupiter-like mass bins. Although the Neptune-to-Jupiter ratio is consistent with the expected scaling, the Earth-to-Neptune ratio is smaller than the value implied by the approximately tenfold mass increase and the relation RE∝MR_E\propto\sqrt{M}. The paper attributes this discrepancy provisionally to the finite resolution of the fixed 90-point logarithmic timescale grid, but the explanation has not been quantitatively tested. A finer grid is therefore needed to establish whether the discrepancy is numerical or physical.

References

We note that the Earth-to-Neptune step in $t_{E,\mathrm{peak}$ ($1.9\times$) falls short of the $\sim\sqrt{10}\approx3.2\times$ expected from $R_E\propto\sqrt{M}$ over the corresponding $\sim10\times$ mass step, while the Neptune-to-Jupiter step ($3.06\times$) matches this scaling well; given the identical, grid-resolution origin of the CB/PL degeneracy discussed next, we attribute this shortfall to the same fixed 90-point logarithmic $t_E$ grid rather than to a genuine departure from $R_E\propto\sqrt{M}$, but we have not verified this quantitatively and flag it as a check worth performing with a finer grid.

— The Galactic Dynamics of Free-Floating Planets: From Ejection Kicks to Microlensing  (2609.21027 - Sayed et al., 17 Sep 2026) in Section 5, subsection “Pipeline Output at the Adopted Geometry”