Multi-band light curve analysis of the 40.5-minute period eclipsing double-degenerate binary SDSS J082239.54$+$304857.19

TL;DR

This study presents detailed multi-band light curve analysis of the eclipsing double-degenerate binary SDSS J082239.54+304857.19, measuring its orbital parameters, component sizes, and secondary temperature, and discusses prospects for detecting gravitational wave-induced orbital decay.

Contribution

It provides the first precise measurements of the system's orbital period, component radii, and secondary temperature using multi-band high-speed photometry, and forecasts future gravitational wave detection.

Findings

System's orbital period precisely measured.

Component radii and inclination determined.

Secondary star's temperature estimated at 5200 K.

Abstract

We present the Apache Point Observatory BG40 broadband and simultaneous Gemini $r$-band and $i$-band high-speed follow-up photometry observations and analysis of the 40.5 minute period eclipsing detached double-degenerate binary SDSS J082239.54$+$304857.19. Our APO data spans over 318 days and includes 13 primary eclipses, from which we precisely measure the system's orbital period and improve the time of mid-eclipse measurement. We fit the light curves for each filter individually and show that this system contains a low-mass DA white dwarf with radius $R_A=0.031\pm0.006~{\rm R_\odot}$ and a $R_B=0.013\pm0.005~{\rm R_\odot}$ companion at an inclination of $i=87.7\pm0.2^\circ$. We use the best-fitting eclipsing light curve model to estimate the temperature of the secondary star as $T_{\rm eff}=5200\pm100~{\rm K}$. Finally, while we do not record significant offsets to the expected time of mid-eclipse caused by the emission of gravitational waves with our 1-year baseline, we show that a $3\sigma$ significant measurement of the orbital decay due to gravitational waves will be possible in 2023, at which point the eclipse will occur about $8$ seconds earlier than expected.