Observing Orbital Decay in the Ultracompact Hot Subdwarf Binary System ZTFJ213056.71+442046.5

Abstract: Ultracompact Galactic binary systems (UCBs) emit low-frequency gravitational waves (GWs). The emission of GWs is causing these systems to lose angular momentum, which is detectable by observing an orbital period decay. ZTFJ213056.71+442046.5 (ZTFJ2130) is an UCB with a period of 39.3401(1) minutes consisting of a Roche lobe-filling hot subdwarf and a white dwarf companion. We attempt to measure the orbital decay rate $\dot{P}$ caused by GW emission of ZTFJ2130 and predict the expected GW signal for LISA. High-speed photometry was conducted using the FLI Kepler KL4040FI CMOS camera, mounted to the 1.2-meter Oskar L\"uhning telescope at the Hamburg Observatory as well as the Hamamatsu ORCA-Quest 2 qCMOS camera at the 1.23-meter telescope at CAHA in Spain. ZTFJ2130 was observed on six nights between August 2024 and September 2025. The obtained lightcurves combined with previous high-cadence observations were used to conduct an O-C timing analysis. Additionally, we employed the LISA data analysis tool ldasoft to model the expected GW data. We measure a period change of $(-1.97\pm0.05)\times10^{-12}\,\mathrm{ss^{-1}}$. Assuming only GW emission, this result was used to calculate a chirp mass of $(0.408\pm0.006)\,\mathrm{M_{\odot}}$. From ldasoft we predict that LISA will be able to measure the chirp mass with an uncertainty of 5%. We measure $\dot{P}$ with an uncertainty of only 2% and show that modern (q)CMOS detectors are well suited to provide precise timing measurements, enabling the measurement of the orbital decay of UCBs with high precision with modest size telescopes. The derived orbital decay is fully consistent with predictions from spectral and lightcurve modeling. We show that future observations with LISA can potentially provide a deviation from only gravitational wave effects, e.g. due to accretion, if the effect is sufficiently large.