Extreme mass loss during common envelope evolution: the origin of the double low-mass white dwarf system J2102--4145

Abstract

Eclipsing close double white dwarf (WD) systems provide a unique opportunity to directly constrain hydrogen-envelope retention and test common-envelope (CE) evolution in low-mass stars, since they allow precise determinations of stellar masses and radii. We analyze J2102-4145, an eclipsing binary composed of two low-mass helium-core white dwarfs in a 2.4-hour orbit. By comparing the observed radii and effective temperatures with updated evolutionary models for CE evolution and stable Roche-lobe overflow (SRLOF), we confirm that both stars are helium-core white dwarfs. The primary, with a mass of 0.375 solar masses, is consistent with SRLOF models that retain thick hydrogen envelopes and sustain residual nuclear burning, whereas the secondary, with a mass of 0.314 solar masses, can only be reproduced by CE models in which the hydrogen envelope is almost completely removed. The inferred cooling ages (approximately 220 Myr for the secondary and between about 260 and 510 Myr for the primary, depending on the contribution of residual nuclear burning) support a formation sequence in which the primary formed first through SRLOF, followed by a CE phase that produced the compact secondary. Reconstruction of the CE energy budget yields progenitor and orbital parameters consistent with this evolutionary picture. The unusually small radius of the secondary requires an extremely thin hydrogen envelope, with a mass below about 10e-7 solar masses, well below the values predicted by standard bifurcation criteria. J2102-4145 therefore provides one of the strongest observational constraints on the hydrogen-envelope mass of post-CE low-mass white dwarfs and represents a benchmark challenge for current prescriptions of envelope ejection.

Figures (5)

• Figure 1: Internal structure of a $1.5\,M_\odot$ pre-CE RGB star at the epoch when the H-free core is $0.3202\,M_\odot$ (plotted versus the Lagrangian mass coordinate $m_r$). Shown are the H abundance by mass, $X_{\rm H}(m_r)$, and the cumulative H mass interior to $m_r$, $M_{\rm H}(<m_r)$, which increases outward. Vertical dashed lines mark the BP criteria ($X_{\rm H}=0.1$, peak nuclear energy generation, and maximum compression). The dashed green line marks $M_{\rm H}=1.0\times10^{-7}\,M_\odot$, the H content inferred for the secondary of J2102--4145 from the observed $(R, T_{\rm eff})$. The plot shows only the innermost envelope layers of the RGB progenitor, which set the residual H content.
• Figure 2: Stellar radius ($R_\odot$) versus $T_{\rm eff}$ for He-core WD sequences with different $M_{\rm H}$. Shown are CE models at $M=0.3208\,M_\odot$ ($M_{\rm H}=6.6\times10^{-6}$, $10^{-6}$, and $10^{-7}\,M_\odot$) and at $M=0.363\,M_\odot$ ($M_{\rm H}=5\times10^{-6}\,M_\odot$) althausCE, together with SRLOF tracks from 2013AA...557A..19A (blue dashed). The J2102--4145 components are shown with $1\sigma$ errors in $R$ and $T_{\rm eff}$, including the observed mass ranges of the primary ($M_1$) and secondary ($M_2$) amaral2024. The curve annotations in the plot indicate the stellar mass and H envelope mass, in the format $M$:$M_{\rm H}$ (both in $M_\odot$), for each evolutionary sequence. The primary matches an SRLOF model with $M_{\rm H}\sim3\times10^{-4}\,M_\odot$, while the secondary requires $M_{\rm H}\lesssim10^{-7}\,M_\odot$ (see text).
• Figure 3: Evolution of $T_{\rm eff}$ since the end of mass loss for selected He-core WD models. The red curve shows the CE track ($M=0.3208\,M_\odot$, $M_{\rm H}=10^{-7}\,M_\odot$) used for the secondary. Solid blue is the post-SRLOF model for the primary from 2013AA...557A..19A with residual burning $L_{\rm nuc}/L\simeq0.25$, and dashed blue is a variant computed here with increased residual burning ($L_{\rm nuc}/L\simeq0.70$) to illustrate its impact on the cooling. Colored bars indicate the cooling ages inferred at the measured $T_{\rm eff}$ of each component, with their widths obtained by propagating the observational uncertainty in $T_{\rm eff}$ along the corresponding track (at fixed $M$ and $M_{\rm H}$).
• Figure 4: Schematic diagram illustrating the proposed formation sequence of J2102--4145, including the two mass-transfer episodes. Stellar separations are not to scale.
• Figure 5: CE efficiency as a function of the residual H mass in the secondary WD. The grey band marks the range compatible with the observed radius of the secondary, $\log M_{\rm H}\le -6.5$.