Approximately 150 low-mass white dwarfs (WDs), with masses below 0.4 Msun, have been discovered. The majority of these low-mass WDs are observed in binary systems as they cannot be formed through single-star evolution within the Hubble time. The study, led by Larissa Antunes Amaral (University of Valparaíso, Chile), presents a comprehensive analysis of the double low-mass WD eclipsing binary system J2102-4145. The investigation involved an extensive observational campaign, resulting in the acquisition of approximately 28 hours of high-speed photometric data across multiple nights using NTT/ULTRACAM, SOAR/Goodman, and SMARTS-1m telescopes. These observations have provided critical insights into the orbital characteristics of this system, including parameters such as inclination and orbital period. To disentangle the binary components of J2102-4145, the study employed the XTgrid spectral fitting method with GMOS/Gemini-South and X-Shooter data. Additionally, the PHOEBE package was used for light curve analysis on NTT/ULTRACAM high-speed time-series photometry data to constrain the properties of the binary. The analysis reveals remarkable similarities between the two components of this binary system. For the primary star, we determined T_eff,1 = 13688 (65) K, log(g₁) = 7.36 (0.01), R₁ = 0.0211 (0.0002) Rsun, and M₁ = 0.375 (0.003) Msun, while the secondary star is characterized by T_eff,2 = 12952 (53) K, log(g₂) = 7.32 (0.01), R₂ = 0.0203 (0.0002) Rsun, and M₂ = 0.310 (0.003) Msun. Furthermore, there is a notable discrepancy between T_eff and R of the less massive WD compared to evolutionary sequences for WDs from the literature, which has significant implications for our understanding of WD evolution. The article discusses a potential formation scenario for this system that might explain this discrepancy and explore its future evolution. The conclusions predict that this system will merge in about 800 Myr, evolving into a helium-rich hot subdwarf star and later into a hybrid He/CO WD.

XTgrid model for a flux-calibrated VLT/X-Shooter observation of J2102-4145:

Figure 2.: Best-fit XTgrid models to the VLT/X-Shooter observations. The orbital phase increases from bottom to top. The observations are shown with grey/black lines and the theoretical models are blue. The black observations mark the quadratures, the nearest phases to minimum and maximum radial valocity differences between the binary members.

Astroserver provided the spectroscopic analysis of the project to find the T_eff and log(g) of the binary members. By interpolating in a grid of ELM WD models we built synthetic composite spectra and adjusted the surface parameters and the flux contributions until the members reproduced the observations. Figure 1 shows the flux calibrated optical spectrum of J2102-4145, and reflects how the WDs add up to the observation. Figure 2 shows the orbital phase resolved VLT/X-Shooter observations of the system together with the best-fit models. The analysis was perfomed on two parallel threads, each working on one component of the binary. The threads updated the stellar parameters and combined their model with the other thread to evaluate the flux contribution to the composite spectrum, and these steps were iterated until convergence.

Figure 3.: Radial velocity curve of J2102-4145.

The radial velocity curves in Figure 3 were obtained by measuring the Doppler shifts of the line cores swith respect to synthetic spectra, as part of the global spectral analysis. The nearly equal semi-amplitdes (K₁ = 221 km/s, and K₂ = 185 km/s) shows the two WDs have very similar masses.

Figure 4.: Position of J2102-4145 A and B in the T_eff - log(g) diagram of ELM WDs. The blue and red edges of the ZZ Ceti instability strip are marked with dashed lines.

The position of the stars in the T_eff - log(g) diagram marks that the binary members are hotter than the blue edge of the ZZ Ceti instability strip. The majority of WDs are near log(g)=8 (cgs), and ELM WDs are below log(g)=7.5 (cgs). After about 50 million years of cooling the stars will reach the theoretical blue edge of the instability region.

Figure 5.: The future orbital evolution of the system will lead to a merger event and formation of a He-rich subdwarf star in about 800 Myr from now.

The orbital evolution of the system is currently driven by gravitational wave emission. In about 800 Myr the orbit will shrink enough for the less massive WD to fill its Roche lobe and start mass transfer onto the more massive component. The rapid stripping and accretion will result in an AM CVn type binary, which cannot avoid its fate and the stars eventually merge. The merger event results in a CO-core He-rich hot subdwarf, which is going to be massive enough to ignite He shell fusion. The star becomes once again a luminous hot object for about 100 Myr. Finally, when all fusion ceases, the star will start its last journey along the WD cooling tracks as a DB type WD.

Fits to all spectra:

• WD1 - WD2 decomposition
• WD2 - WD1 decomposition