The Silent Majority: The Interacting Post-Common-Envelope Binaries Underlying Cataclysmic Variables

TL;DR

This study empirically derives the intrinsic orbital-period distribution of post-common-envelope binaries (PCEBs) by cross-matching Gaia DR3 WDMS XP spectra with TESS light curves and performing a uniform periodicity search. A forward-modeling approach using injection-recovery in a PHOEBE-based framework yields a completeness-corrected distribution best described by a two-component model: a log-normal Gaussian peak near $P_{ m orb}\approx4$ h and a rising long-period tail starting around $P_{ m break}\approx13$ h, implying a dominant interacting PCEB population alongside a substantial detached PCEB reservoir. The analysis finds a PCEB fraction among WDMS binaries of $f_{ m PCEB}=29.8\pm4.5\%$, and reveals that current binary population synthesis models struggle to reproduce both the sharp short-period peak and the extended tail, hinting at varying CE efficiency or significant pre-CV contamination in the short-period regime. These results provide new empirical constraints on CE physics and reveal a substantial, largely under-classified population of pre-CVs and weakly accreting binaries that feed the CV population. The work emphasizes the importance of high-cadence, wide-field time-domain data and spectroscopic follow-up to fully map the post-CE binary landscape.

Abstract

We analyze the orbital period distribution of post-common-envelope white-dwarf-main-sequence (WDMS) binaries by cross-matching the new spectroscopic Gaia DR3 WDMS catalog with TESS light curves, and applying a uniform periodicity search and vetting pipeline. We identify 107 periodic systems, including 74 eclipsing binaries (32 new) and 33 binaries exhibiting only sinusoidal variations. Injection-recovery tests and a forward detectability model yield a completeness-corrected distribution that is well-described by a two-component function: a log-period Gaussian peaking at $P_{\rm orb} \approx 4.1 $ h with $σ\approx 1.8$ h, plus a rising component that begins near $P_{\rm orb}\approx12.9$ h. We refer to this extended component as the long-period tail. It consists exclusively of detached non-interacting post-common-envelope binaries (PCEBs) that likely emerged from the common envelope and have not yet initiated mass transfer. In contrast, the short-period Gaussian is dominated by interacting or near-contact systems (including 22 known cataclysmic variables), consistent with high Roche-lobe filling factors. From the completeness-corrected distribution we infer that $29.8\%\pm4.5\%$ of the spatially unresolved WDMSs in our parent catalog are close PCEBs. Binary population synthesis models with high common-envelope efficiencies overproduce long-period systems and fail to reproduce the sharp peak, whereas lower efficiencies ($αλ\leq 0.3$) match the peak more closely, yet still underpredict the tail. Our results hint at a large, currently under-classified reservoir of pre-cataclysmic variables and weakly accreting binaries, and provide new constraints on common-envelope physics.

Figures (17)

• Figure 1: The location on the HR diagram of all sources in the Li2024 high-confidence WDMS sample (white circles) and those with available TESS data (black circles). The Gaia 100 pc sample is shown as a gray two-dimensional histogram, for reference. WDMS candidates occupy a distinct locus between the MS and the WD sequence.
• Figure 2: Mass distributions of the WDs (solid histogram) and MS companions (dashed) in our WDMS sample. WD masses concentrate at $0.3-0.5$ M$_\odot$, while companions are mostly $0.075$-$0.6$ M$_\odot$ (late-type M dwarfs).
• Figure 3: Observed orbital period distribution for the 74 validated eclipsing WDMS binaries (CVs included). The distribution shows a clear peak near $\sim$4 h and a tail extending to a few days. Systems are color-coded by their Roche-lobe fill factor (see Appendix \ref{['sec:roche_method']}): near-contact systems with fill factor $\geq 0.9$(hatched histogram) , and detached systems with fill factor $< 0.9$(filled gray). This separation highlights the connection between orbital period and binary interaction state. We label fill-factor $\geq 0.9$ systems as interacting PCEBs which may include pre-CVs and CVs, and $<0.9$ as detached PCEBs.
• Figure 4: Mean eclipse detection probability as a function of orbital period. The black curve shows the average detection efficiency across all eclipsing systems in the sample, incorporating geometric alignment and photometric detectability. The gray-shaded region denotes the $\pm 1 \sigma$ spread in detection probability, reflecting population-level variance in system properties such as stellar radii and flux ratio. This completeness curve is used to correct the observed period distribution and recover the intrinsic distribution.
• Figure 5: Orbital period distribution of the 74 PCEBs discovered as eclipsing in TESS data (gray), the bias-corrected distribution (white) and its errors.