Physical explanation for the coincidence of source and migration periods

Determine the physical mechanism, if any, that could explain why the source-function truncation period P_cut and the migration period P_mig are approximately equal in Solution 2 of the hot-Jupiter population model.

Background

Solution 2 fits the observed hot-Jupiter period distribution when the source-function truncation period and the characteristic migration period both lie near 3–4 days. The paper characterizes this coincidence as a finely tuned condition rather than a result explained by the model.

The authors explicitly state that they lack a physical explanation for this coincidence, leaving unresolved whether it reflects an underlying formation or tidal-migration mechanism or is merely a parameter-level degeneracy.

References

Solution 2 requires $P_\mathrm{mig}\approx P_\mathrm{cut}$, a coincidence for which we do not have a physical explanation, making this solution appear finely-tuned.

— Constraining Tidal Migration with the Hot Jupiter Population  (2609.10850 - Ma et al., 9 Sep 2026) in Section 4.2, “Data Fitting”