A Falsifiable Timing Test for the Double-White-Dwarf Model of Long-Period Transients

Abstract: Long-period transients (LPTs) are a newly identified class of radio sources with burst recurrence times from minutes to hours, and their diversity suggests multiple physical origins. CHIME/ILT J1634+44, with a short period of 841 s, a long-period modulation of 4206 s, and a significant negative period derivative, strongly suggests a binary origin. For such a short-period source, Roche-lobe constraints strongly favor an ultra-compact companion, motivating a double-white-dwarf (WD--WD) interpretation. In this Letter, we show that the WD--WD channel makes a sharp timing prediction: if the burst period is the orbital clock and the long-period modulation is a spin-orbit beat, then the modulation period is not a free timescale. Instead it must evolve jointly with the orbital clock and the spin clock through gravitational-wave losses, magnetic dissipation, and tidal interaction. For CHIME/ILT J1634+44-like parameters, we find that the beat clock drift $|\dot P_b|\sim 10^{-10} \text{ s s}^{-1}$, implying an observed-minus-calculated drift of tens of seconds in one year. Joint measurements of the burst period, modulation period, and their derivatives provide a minimal and falsifiable timing test of an ultra-compact binary origin.