Constraining the Occurrence of ZLK-Induced White Dwarf Pollution with Dissipative Precession

TL;DR

This work quantifies the prevalence of ZLK-induced pollution of white dwarfs in WD/MS binaries by incorporating dissipative precession during the protoplanetary-disk phase. Using a large Gaia-based sample (~4400 binaries) and a semi-analytic dissipative-precession framework, the authors derive alignment fractions and ZLK-timescale constraints, finding that dissipative precession can align up to ~$0.3$ of close systems, while ZLK timescales limit pollution in wider binaries. When combining these factors, they estimate that roughly $50$–$70\%$ of WD/MS binaries possess conditions conducive to ZLK-driven pollution, with the maximum likelihood depending on whether polluting bodies originate from inner ($a_p=10$ au) or outer ($a_p=100$ au) regions. However, the present-day observed pollution rates remain low, implying ZLK-driven events likely contribute only a minority of WD pollution compared with planetesimal-driven processes. The findings inform the interpretation of WD pollution sources and the architectures of exoplanetary systems in binaries.

Abstract

Von Zeipel-Lidov-Kozai (ZLK) oscillations, induced by bound, perturbative companions to white dwarfs, have been suggested as a dynamical mechanism that may contribute to white dwarf pollution. To trigger ZLK oscillations, however, a 3-body system must reach a sufficiently large mutual inclination between orbits. The occurrence of these high-mutual-inclination configurations can be curtailed by dissipative precession at the protoplanetary disk stage, which pushes exoplanet-hosting close binary systems toward preferential orbit-orbit alignment. In this work, we constrain the fraction of white dwarfs with binary companions that can undergo ZLK-driven pollution given the effects of dissipative precession. To accrete pollution via ZLK oscillations, a white dwarf binary system must be sufficiently inclined and the characteristic timescale of the oscillations must be sufficiently short to perturb material within the white dwarf's cooling age. Considering a sample of 4400 known white dwarf/main sequence binaries, we find that $50-70\%$ have favorable parameters for ZLK pollution, depending on the orbital separation of the polluting body. While the conditions for oscillations are favorable, the tendency for ZLK to result in massive but more infrequent polluters likely restricts the rates of ZLK-induced pollution among the observed population. In general, dissipative precession is a limiting factor in pollution rates for more closely separated binaries (initial separations $<500-800$~au), while ZLK timescale constraints are most limiting for wider binaries.

Figures (7)

• Figure 1: Panel a: Masses for the WD component of each binary pair, under the assumptions of pure H, pure He, and mixed H/He atmospheres GentileFusillo2021. Initial-final mass models typically do not extend lower than $0.5 \mathrm{M_\odot}$ (the vertical line); we therefore include only WDs where at least one of the atmospheric solutions includes a mass $\geq 0.5 \mathrm{M_\odot}$. Panel b: Distribution of initial (progenitor) masses for the WD components of the binaries, obtained by applying the initial-final mass relation from Cunningham2024 to the WD masses in Panel a. Panel c: Distribution of the ratios of initial masses for the WD components relative to the masses of their MS companions. This corresponds to the mass ratio of the binary pairs when both components were on the main sequence (before formation of the WD). The companion masses are obtained through isochrone fitting (see Section \ref{['methods:initialconditiona']}). Panel d: Distribution of the initial semi-major axes of the WD/MS binary pairs when both components were on the main sequence. The choice of pure H, pure He, or mixed H/He mass model affects both the progenitor mass of the WD and the initial semi-major axis via Eq. \ref{['equation:aMS']}. The sample of WDs in the mixed H/He scenario is much smaller than those of the pure H and He cases, as GentileFusillo2021 reports mixed H/He results for a narrower range of effective temperatures ($\gtrsim6500$ K) compared to the pure H and He cases ($\gtrsim4000$ K).
• Figure 2: Distributions of final mutual inclinations $\theta_{\rm db}(t = t_\mathrm{life})$ for the simulated systems at the end of disk dissipation. Results are binned by color according to the initial separation between the WD progenitor and MS companion. The gray shaded region indicates where ZLK oscillations are prevented by mutual inclinations of $\theta_\mathrm{db}(t = t_\mathrm{life}) <= 39.2^\circ$ corresponding to $\cos[ \theta_\mathrm{db}(t = t_\mathrm{life})] \geq 0.775$.
• Figure 3: Fraction of systems that will not undergo ZLK oscillations due to alignment generated by binary-driven dissipative precession $f_\mathrm{aligned} \equiv f[\theta_\mathrm{db}(t=t_\mathrm{life}) < 39.2^\circ]$, as a function of initial binary separation $a_\mathrm{b, prog}$ obtained via Eq. \ref{['equation:aMS']}. From top to bottom, the four panels separate the samples according to the disk lifetime, WD progenitor mass, MS companion mass, and disk outer truncation radius.
• Figure 4: Cumulative distribution of initial semi-major axes, determined from WD progenitor masses, for the 40 pc sub-sample of binaries (solid lines), compared to analogous results for our full sample drawn from Gaia (dashed lines). We show results for pure H, He, and mixed H/He atmosphere cases for both the full sample and 40 pc sub-sample, as well as results using the "corrected" masses from O'Brien2024 for the 40 pc sub-sample.
• Figure 5: Distribution of calculated ZLK timescales (Eq. \ref{['eq:kozaitime']}) for the WD/MS binaries in the full sample (small points) and 40 pc sub-sample (large points), colored by the systems' randomly selected eccentricity values. For clarity we show only the values calculated using the H, with corrected WD masses for the full sample and 40 pc sub-sample, respectively. The top panel shows the fraction of systems with $T_{\rm ZLK}<T_{\rm cool}$ in each bin of initial semi-major axis, for a polluting body at 10 au (purple) and 100 au (teal).