Calibration of Binary Population Synthesis Models Using White Dwarf Binaries from APOGEE, GALEX and Gaia

TL;DR

This study calibrates mass-transfer parameters in the COSMIC binary population synthesis framework by confronting synthetic WD+MS WD binaries with the APOGEE-Galex-Gaia catalog (AGGC). By leveraging the observed $\Delta RV_{\rm max}$ and WD/MS masses, the authors explore 20 COSMIC models spanning $\alpha$ (envelope ejection efficiency), $\beta$ (accretion efficiency), and $q_{\rm set}$ (unstable mass-transfer criteria). They find that models with $q_{\rm set}=3$ and high $\alpha$ substantially better reproduce the AGGC distributions, with $\beta$ near zero favored for matching He WDs in certain period ranges; the best overall match is model D3. The results imply that giant-branch donors are more stable and that envelope ejection may require additional energy sources or lower binding energy than traditionally assumed, guiding refinements of rapid BPS prescriptions and offering a path toward tighter constraints with forthcoming Gaia DR4 and LISA data.

Abstract

The effectiveness and stability of mass transfer in binaries system are crucial in determining its final product. Rapid binary population synthesis (BPS) codes simplify the complex physics of mass transfer by adopting parameterized prescriptions for the stability of mass transfer, accretion efficiency in stable mass transfer, and the efficiency of common-envelope ejection. We calibrate these uncertain parameters by comparing BPS models with observational data. White dwarf and main sequence binaries are an ideal population to study binary interaction, as they can be formed through stable or unstable mass transfer, or without interaction, which affect the orbital period and masses of the present-day population. The APOGEE-GALEX-Gaia catalog provides a homogeneous sample of over 500 systems with well measured radial velocities that can be used as a comparison baseline for BPS simulations of such binaries. We compare the distribution of observed maximum radial velocity variation ($ΔRV_{\rm max}$) and estimated masses to BPS models simulated with COSMIC, varying the mass transfer and common-envelope ejection efficiency, and the criteria for mass transfer stability at key evolutionary stages. The $ΔRV_{\rm max}$ comparison shows clear preference for a higher fraction of stable mass transfer during the first ascent giant branch, and for highly effective envelope ejection. For the systems with WD masses, there is a slight preference for non-conservative mass transfer. In COSMIC and similar codes, the envelope ejection efficiency and the envelope binding energy are degenerate parameters. Our result of high ejection efficiency may indicate that either additional sources of energy are required to eject the envelope, or that its binding energy is lower than traditionally assumed. Future comparisons to BPS simulations can be drawn for other datasets as they become available.

Figures (13)

• Figure 1: Overview of the white dwarf binaries in the APOGEE-Gaia-Galex catalog (AGGC). The left panel shows the full APOGEE dataset in blue and the companions of WDs in orange. The right panel shows the $\Delta RV_{\rm max}$ distribution for different cuts in the data: MS from the full APOGEE in blue, all WD binaries in the AGGC in green, and WD+MS binaries in black. The full APOGEE dataset contains 455796 targets; the MS stars in that sample number 151266. The full AGGC has 1157 candidate WD binaries, while the WD+MS systems number 588.
• Figure 2: Schematic of the possible evolutionary paths through which a binary system can go to become a WD+MS binary. The system can either not interact, or go through RLO mass transfer, which can in turn be stable or unstable, leading to a common envelope phase. The imprints of their evolution can be seen in the final masses and orbital period of the systems.
• Figure 3: Initial (top rows) and final (bottom rows) period distribution for the WD+MS binaries in models C1, C2, C3 and C4 ($\alpha = 1.0$ and fully conservative mass transfer, with different prescriptions for $q_{\rm crit}$, following Table \ref{['tab:qcflag']} -- colored histograms). The colors indicate the type of interaction the system undergoes to end up as a WD+MS binary. The numbers in the bottom rows indicate the number of systems in the final distribution according to type of interaction. The dark gray line in the top plots shows the normalized period distribution for the entire simulated population (following raghavan2010), including systems that do not end up as WD+MS binaries, but as double WDs, MS+MS binaries, mergers, and WD binaries with post-MS stars. All models are initialized with the same period distribution. The final period distribution of the WD+MS binaries are quite different between the models, indicating a stronger dependence on mass transfer stability assumptions rather than initial orbital separation.
• Figure 4: The orbital period distribution of the WD+MS binaries that went through mass transfer, either stable or unstable, in our COSMIC models. The top panel shows the variation in the period distribution due to $q_{\rm crit}$; middle panel shows the same, but due to $\alpha$, and the bottom panel, due to $\beta$. The dashed lines show the median value of the period distribution considering only the stable mass transfer systems. The dashed-dotted lines show the median period for the CEE systems. Values for the medians are shown in Table \ref{['tab:cosmicsystems']}. The largest changes in the period distribution occur when $q_{\rm crit}$ = 3, where the first ascension giant branch stars tend to have stable mass transfer. The main effect of increasing $\alpha$ is creating a post-CEE systems with larger periods, while the effect of $\beta$ is nearly negligible.
• Figure 5: The distribution of orbital periods (left panel) and $\Delta RV_{\rm max}$ (right panel) for model A3. There is an anti-correlation between period and $\Delta RV_{\rm max}$, but it is possible for short period systems to have small $\Delta RV_{\rm max}$, as $\Delta RV_{\rm max}$ has a strong dependence on the inclination, eccentricity, and the time lag between radial velocity observations. Larger $\Delta RV_{\rm max}$ are more unambiguously correlated with short period systems.