A global view of post-interaction white dwarf-main sequence binaries

Abstract

Common-envelope evolution (CEE) is among the most uncertain phases in binary evolution. To empirically constrain CEE, we construct a uniformly selected sample of eclipsing post--common-envelope binaries (PCEBs). Starting from an unresolved white dwarf-main-sequence (WDMS) candidate sample within 200 pc selected from the Gaia color-magnitude diagram, we identify 39 detached eclipsing WDMS binaries using ZTF light curves. The binaries contain cool M dwarfs orbiting warm white dwarfs with orbital periods ($P_{\rm orb}$) of 0.1-2 d. The sample's simple selection function allows us to model observational incompleteness and infer intrinsic properties of the PCEB population. We find an orbital-period distribution consistent with being log-uniform over 0.1-2 d, contrary to recent reports of a bimodal distribution. The companion-mass distribution peaks around $0.25~{\rm M_\odot}$ and declines steeply toward larger masses. The estimated local space density is $7.2\times10^{-5}~{\rm pc^{-3}}$, corresponding to a Galaxy-wide birth rate of 0.01 per year. Combining our results with recent Gaia-based constraints on wider WDMS binaries, we construct an empirical period distribution of post-interaction WDMS binaries spanning 0.1-1000 d. The emerging period distribution is roughly log-flat (d$N/{\rm d}\log P_{\rm orb}\propto P_{\rm orb}^0$) at $P_{\rm orb} < 2$ d and log-increasing (d$N/{\rm d}\log P_{\rm orb}\propto P_{\rm orb}^1$) at $P_{\rm orb} = 100-1000$ d. The 10-100 d regime remains poorly constrained, but a few nearby systems suggest it is also well-populated. Short-period PCEBs ($P_{\rm orb}<2$ d) with M dwarf companions are roughly 2-3 times more common than wide ($P_{\rm orb} = 100-1000$ d) WDMS binaries with FGK companions, which likely formed through stable mass transfer. These results provide direct observational constraints on CEE and an empirical benchmark for binary-population models.

Figures (12)

• Figure 1: Sample selection in the Gaia color--magnitude diagram. Black points show the full $200$ pc sample after our astrometric quality cuts and extinction corrections. The dashed lines indicate the region used to define unresolved WDMS candidates. Inside this region, we identify $N=3777$ sources (blue points) that form the parent WDMS sample, from which we identify $39$ eclipsing PCEBs (red).
• Figure 2: Periodic variables that are (bottom) and are not (top) selected in the WDMS EB sample during visual inspection. We show ZTF $r$-band (red circles) and $g$-band (blue squares) light curves for six representative systems. The top three are not selected, either because their variability is not due to a WD eclipse (latter two) or because they are eclipsing but are a cataclysmic variable (left, see text). The bottom panel shows systems that are selected as WDMS EBs, which exhibit a range of eclipse depths and durations from orbital periods of $0.1$ to $2$ days.
• Figure 3: Sensitivity of our eclipsing binary search. We show the results of our injection recovery analysis, where the top panel shows the detection probability as a function of orbital period for all sources, and the bottom panel shows the median inclination of detected eclipsing binaries (black line with $1\sigma$ shaded). At the shortest periods, the search is sensitive to a broader range of inclinations, whereas only edge-on systems are retrieved at $P_{\rm orb} \mathrel{\hbox{$\sim$} \hbox{$>$}} 1$ day. Even at the shortest periods, only $\sim30\%$ of systems are eclipsing. The drop at $P_{\rm orb} \approx 1$ day corresponds to the terrestrial alias.
• Figure 4: Completeness-corrected orbital period distribution of PCEBs. The gray histogram shows the observed period distribution of our sample. The black curve shows the bias-corrected distribution with Poisson error bars included for each bin. The orbital period distribution of WDMS PCEBs in this period range is consistent with log-uniform.
• Figure 5: Detection efficiency as a function of companion mass. The dashed curve shows the fraction of PCEBs that fall within our Gaia CMD selection region ($f_{\rm CMD}$). The dotted curve shows the probability that a PCEB inside the CMD region is eclipsing and recovered in ZTF light curves ($f_{\rm detected~|~CMD}$). The solid curve shows the total detection efficiency ($f_{\rm detected,~total}$).