The first phase of mass transfer in low-mass binaries: neither stable nor a common envelope

TL;DR

This study addresses how the first mass-transfer phase shapes the formation of double helium white dwarf binaries. It uses the core mass–radius relation to reconstruct progenitor evolution and performs forward modelling for three channels—stable mass transfer, double common envelope with $oldsymbol{\alpha\lambda}$, and angular-momentum balance with $oldsymbol{\gamma}$—to predict the WD-mass distribution, testing against a sample of observed systems via ConTEST. The results show stable MT and double CE are generally inconsistent with the data, while the $oldsymbol{\gamma}$-prescription with $oldsymbol{\gamma} \approx 1.5$–$1.75$ provides the best match, though not perfectly, and several systems exhibit eccentric post-transfer orbits that standard channels do not readily explain. These findings challenge canonical formation channels for the first MT phase and have implications for population studies of double WDs and related transients, underscoring the need for more detailed modelling and broader metallicity coverage.

Abstract

The masses of the white dwarfs in a binary carry information about previous mass-transfer phases. The core mass -- radius relation of low-mass giants gives the size of the progenitor of a helium white dwarf at the moment it last filled its Roche lobe. Previously, we used this information for a few observed systems to propose a new mass-transfer type, based on an angular momentum balance. Our aim is to investigate if stable mass transfer instead of the angular momentum prescription is consistent with the observed double helium white dwarf masses. We reconstruct the progenitor evolution of observed double helium white dwarfs using the core mass -- radius relation and evaluate if the periods at the start of the second phases of mass transfer are consistent with the outcome of stable mass transfer. More generally, we calculate the mass distribution of double helium white dwarfs for three different progenitors scenarios: double common envelope (with parameter $αλ$), angular momentum prescription (with parameter $γ$) and stable mass transfer. We find that the observed systems are generally not consistent with stable mass transfer. Stable mass transfer leads to a tight correlation between the two white dwarf masses in a binary that is not consistent with the observed mass distribution. Double common envelope evolution is a particularly poor fit to the observations. The angular momentum prescription can populate the observed mass distribution, but not perfectly. We conclude that the first phase of mass transfer initiated on the red giant branch in low-mass systems does not generally proceed as stable mass transfer nor as common envelope, and thus is poorly understood. This may be related to the fact that for many observed binaries that have finished the first phase of mass transfer the orbit is eccentric, which is an unexpected outcome of mass transfer.

Figures (10)

• Figure 1: In orange: Reconstructed periods ($P_m$) as function of $M_{WD2}$. The top line shows $M_2 =1$$M_\odot$ and solar metallicity, and the bottom line shows $M_2 =2$$M_\odot$ and intermediate metallicity. The vertical orange bar indicates the possible values of $P_m$ for WD0455-295.(source id 6) based on the mass of the youngest WD ($M_\mathrm{WD2} = 0.4$$M_\odot$). The dashed blue line shows expected periods after stable mass transfer as function of $M_{WD1}$. The position of WD0455-295 is indicated by the vertical blue bar at the position of its mass of the first formed WD ($M_\mathrm{WD1} = 0.44$$M_\odot$). The two periods are not consistent, as shown by the dotted horizontal line at $P_{m, stable}$ .
• Figure 2: Reconstructed intermediate period based on reconstructing the second phase of mass transfer (y-axis) versus expected intermediate period based on the assumption that the first phase of mass transfer was stable (x-axis). The diamond shapes indicate the possible values for the observed systems for different assumptions. Lowering the metallicity lowers both periods, while increasing $M_2$ lowers only the values on the y-axis. Top right of each diamond thus is for solar metallicity and $M_2 = 1$$M_\odot$ and bottom left is for intermediate metallicity and $M_2 = 2$$M_\odot$. The shading indicates that, very broadly, the upper parts are more likely scenarios (see text). If all systems were formed through stable mass transfer, all shapes should intersect with the diagonal. Systems 1, 16, and 17 have identical masses and thus fall on top of each other.
• Figure 3: Predicted mass distribution based on different assumptions for the first phase of mass transfer. In dark blue, we show the predicted masses in the case that the first phase of mass transfer was stable. The orange area underneath covers the range for stable mass transfer as found by 2024ApJ...977...24Z. The results for the case where the first phase of mass transfer was a common envelope with $\alpha \lambda = 2$ is shown in light salmon on the far left, and those for the case where the first phase was described by the angular momentum balance with $\gamma = 1.6$ are shown in green. The data points and their uncertainties are plotted in black, with the labels indicating the ID of the source in Table \ref{['tab:observations']}. The four data points for which the order of formation is not completely clear are plotted in blue and connected with dotted lines with the masses reversed (see text). Systems 1, 16, and 17 have identical masses and thus fall on top of each other.
• Figure 4: Kernel density estimate of reconstructed $\gamma$ values for each of the systems in Table \ref{['tab:observations']} for a set of different values of initial masses and metallicity as well as different WD masses following the uncertainties in the derived masses. The KDE combines values for specific progenitor masses and bracket the range of possible $\gamma$ values for the range of progenitor masses and the uncertainties in the WD masses.
• Figure 5: Same as Fig \ref{['fig:M1m2']}, but with the masses of the sdB + WD binaries overplotted.