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Population demographics of white dwarf binaries with intermediate separations: Gaia constraints on post-AGB mass transfer

Natsuko Yamaguchi, Kareem El-Badry, Sahar Shahaf

Abstract

Astrometry from the Gaia mission has revealed a large population of white dwarf (WD) + main sequence (MS) binaries with periods of $100 - 1000\,$d. These systems have separations intermediate to predictions from standard binary evolution scenarios, challenging models of binary interaction and mass transfer. Because the selection function of Gaia astrometric catalogs is complex, the underlying population demographics of WD+MS binaries remain imperfectly understood. We present a forward-model of the AU-scale WD+MS binary population probed by Gaia that begins with a realistic binary population and incorporates a full model of Gaia mock observations and astrometric model fitting, as well as cuts employed in producing the Gaia astrometric catalog and selecting WD+MS binary candidates. We model the formation of AU-scale WD+MS binaries as the result of interaction when the WD progenitor is an AGB star. We test several models for the binaries' formation, including stable mass transfer with theoretically predicted stability criteria and two different formalisms for common envelope evolution. None of these models succeed in reproducing the observed component mass distributions or the absolute number of WD+MS binaries. The data are best reproduced by a model in which post-AGB binaries remain wide only if the accretor-to-donor mass ratio exceeds $\sim 0.4$. Our model allows us to constrain the intrinsic population demographics of intermediate-separation WD+MS binaries. The inferred period distribution is close to flat, with ${\rm d}N/{\rm d}P_{\rm orb}\propto P_{\rm orb}^{0.12}$, while the WD mass distribution is sharply peaked at $0.6\,M_{\odot}$. The model implies that $\sim 0.4\%$ of solar-type stars have WD companions with periods of $100 - 1000\,$d.

Population demographics of white dwarf binaries with intermediate separations: Gaia constraints on post-AGB mass transfer

Abstract

Astrometry from the Gaia mission has revealed a large population of white dwarf (WD) + main sequence (MS) binaries with periods of d. These systems have separations intermediate to predictions from standard binary evolution scenarios, challenging models of binary interaction and mass transfer. Because the selection function of Gaia astrometric catalogs is complex, the underlying population demographics of WD+MS binaries remain imperfectly understood. We present a forward-model of the AU-scale WD+MS binary population probed by Gaia that begins with a realistic binary population and incorporates a full model of Gaia mock observations and astrometric model fitting, as well as cuts employed in producing the Gaia astrometric catalog and selecting WD+MS binary candidates. We model the formation of AU-scale WD+MS binaries as the result of interaction when the WD progenitor is an AGB star. We test several models for the binaries' formation, including stable mass transfer with theoretically predicted stability criteria and two different formalisms for common envelope evolution. None of these models succeed in reproducing the observed component mass distributions or the absolute number of WD+MS binaries. The data are best reproduced by a model in which post-AGB binaries remain wide only if the accretor-to-donor mass ratio exceeds . Our model allows us to constrain the intrinsic population demographics of intermediate-separation WD+MS binaries. The inferred period distribution is close to flat, with , while the WD mass distribution is sharply peaked at . The model implies that of solar-type stars have WD companions with periods of d.

Paper Structure

This paper contains 36 sections, 8 equations, 20 figures, 1 table.

Table of Contents

  1. Introduction
  2. Forward model of the Gaia DR3 NSS catalog
  3. Initial binary population
  4. Formation of compact objects
  5. Post-interaction separations
  6. Mock observations
  7. Triples
  8. AMRF sample of WD+MS binaries
  9. Color excess cut
  10. Color excess distribution
  11. AMRF distributions
  12. Results of E24 model
  13. Modifications to the E24 model
  14. Interaction on the RGB vs. AGB
  15. Donor mass at the onset of MT
  16. ...and 21 more sections

Figures (20)

  • Figure 1: Examples of orbits and their mock observations. In all cases, we consider a $1.0\,M_{\odot}$ luminous primary and a dark $0.6\,M_{\odot}$ secondary in a slightly eccentric ($e=0.1$) orbit. Different orbital periods and distances are considered in each panel. The ratio of semi-major axis and parallax to their respective errors are quoted on the bottom of each panel; quality cuts on these parameters determine whether each binary receives an orbital solution. The leftmost panel is most representative of a typical system in the AMRF sample and receives an orbital solution. The middle one is excluded from the NSS catalog due to having $\varpi/\sigma_{\varpi}$ that is too low, despite the orbit being fairly well constrained. The rightmost orbit gets an acceleration solution and is therefore not fit with an orbital solution.
  • Figure 2: Fraction of the simulated zero-age binary population that are in hierarchical triples as a function of the true primary mass (i.e. maximum mass of the two/three components in the system). In blue is the inputted triple fraction from Offner2023ASPC.
  • Figure 3: Distributions of the astrometric function, $f_{\rm m,ast}$, for the orbital solutions in the simulated empirical (green) and true (blue) NSS catalogs. Contributions from the different components in the simulated catalog are shown with unfilled histograms. We see that the total number of orbital solutions as well as the $f_{\rm m,ast}$ distribution of the mock and true catalog are in rough agreement with each other.
  • Figure 4: The four panels show 2D binned plots of the color excess against various stellar and orbital parameters of all sources in the non-class I catalog of Shahaf2024MNRAS.
  • Figure 5: Distribution of color excess for systems in the non-class I sample (Left) and those that end up in the final NCE sample (Right). On average, triples have larger color excess and are therefore effectively excluded from the final sample. However, we also find that more than half of true WD+MS binaries are removed in the process. The distribution for the observed non-class I sample is significantly broader than that of our model, possibly due to inaccuracy in the measured metallicities (Section \ref{['sssec:color_excess_dist']} and Appendix \ref{['ssec:appendix_CE_met_spread']}).
  • ...and 15 more figures