Hide and Seek with Gaia. Detectability of Predicted Thin-Disc Metal-Rich RR Lyrae Binaries in Gaia DR3 and DR4

Abstract

RR Lyrae stars (RRLs) are classical tracers of old stellar populations, yet growing evidence suggests the presence of a metal-rich ([Fe/H]>-0.5), intermediate-age (2-7 Gyr) sub-population in the Milky Way disc. Binary evolution, particularly stable mass transfer, has been proposed as a viable formation channel, predicting that most metal-rich, intermediate-age (<9 Gyr) RRLs should reside in binaries with orbital periods of ~900-2000 days. However, no genuine RRL binaries have been robustly identified, including in the Gaia DR3 astrometric binary catalogues, despite Gaia being sensitive to the predicted orbital-period range. We investigate whether the lack of detections in Gaia DR3 reflects an intrinsically low binary fraction or instead arises from observational biases. We analyse a carefully selected sample of 100 Gaia DR3 RRLs designed to trace the metal-rich population with thin-disc kinematics and compare them with predictions from binary evolution models. We generate realistic Gaia observation mocks, including variability-induced astrometric biases, and assess the detectability of binaries and the posterior constraints on the hidden binary fraction using astrometric quality indicators, such as RUWE, and a robust Bayesian inference. While current uncertainties prevent a definitive rejection of a high fraction of hidden binaries, our results reveal tensions between existing binary evolution predictions and the Gaia DR3 non-detections. This suggests either the presence of unaccounted systematics in the modelling of Gaia observations or the need to revise assumptions in binary evolution models. We predict that Gaia DR4 will significantly improve the binary detectability and provide powerful new constraints on the post-interaction binary populations.

Figures (15)

• Figure 1: Expected age range of RRLs based on single star models (shaded areas as a function of metallicity and progenitor mass loss, $\Delta m$). The models are based on the solar-scaled PARSEC v1.2S stellar tracks Chen15 and are computed following the method described in Appendix C of Zhang25, from which we also take the age estimates of RRL populations inferred via a kinematic comparison with O-rich Mira variable stars (white diamonds). The red dots show the metallicity and age range (2--4 Gyr) for the RRL associated with the Trumpler 5 open cluster Mateu25. This figure shows that high mass loss is required to explain RRLs for [Fe/H]$\gtrsim-1$ and age $< 5$ Gyr.
• Figure 2: Properties of the Gaia DR3 RRL subsample used in our analysis. Left: sky distribution in Galactic coordinates with colormap showing the photometric metallicity. Right: photometric metallicity as a function of distance, with associated uncertainties shown as grey error bars and with colormap showing the Gaia DR3 RUWERUWE (see text). Distances are estimated as the inverse parallax after correcting for the global Gaia DR3 parallax zero-point offset.
• Figure 3: Comparison between model-predicted RUWERUWE ($\mathtt\texttt{RUWE}\xspace_\mathrm{model}$) and Gaia DR3 values ($\mathtt\texttt{RUWE}\xspace_\mathrm{DR3}$) for the RRLs in the analysed sample (see panel titles and Table \ref{['tab:models']}). The four left-hand panels show both the binary model (blue circles) and the single-star model (red squares); the remaining panels show the binary model only. Markers indicate the mean of 1000 realisations, with error bars corresponding to 2 times the standard deviation ($\approx95\%$ confidence interval). The thick grey line marks $\mathtt\texttt{RUWE}\xspace_\mathrm{model}=\mathtt\texttt{RUWE}\xspace_\mathrm{DR3}$, and the black dashed line indicates $\mathtt\texttt{RUWE}\xspace=1.4$.
• Figure 4: Median (lines) and 95% credible intervals (shaded regions) of the cumulative distribution function (CDF) of the Gaia DR3 detectability, $\mathcal{O}$, which defines the probability of receiving an astrometric binary detection (see Section \ref{['sec:detectability_definition']}). The left panel includes all RRLs in the analysed sample, while the right panel additionally applies a metallicity cut $\mathrm{[Fe/H]}>-0.3$. Colours and line styles correspond to the models listed in Table \ref{['tab:models']}. Posteriors are obtained by drawing $10^4$ samples per star from Equation \ref{['eq:detectability']} and sampling the photometric metallicities assuming Gaussian uncertainties.
• Figure 5: Binary-fraction posterior (Equation \ref{['eq:lkl']}) as a function of metallicity, inferred using the metallicity-dependent Gaussian Process model (Equation \ref{['eq:fbin']}). Shaded regions show 68% (green), 95% (red), and 99.5% (gray) credible intervals. Each panel corresponds to a different model, as indicated in the panel labels (see Table \ref{['tab:models']}). The black dashed line marks $f_\mathrm{bin}=0.7$, the binary fraction consistent with the binary formation model for metal-rich RRLs, assuming a conservative 30% contamination (non metal-rich RRLs in the thin disc and non-RRL contaminants; see Section \ref{['sec:sample']}).