A population synthesis study of the Gaia 100 pc unresolved white dwarf-main-sequence binary population

Context. Binaries consisting of a white dwarf and a main-sequence star (WDMSs) are excellent tools for studying a wide variety of open problems in modern astronomy. However, due to selection effects, the currently known WDMS population is severely affected by observational biases. This is particularly the case for unresolved systems in which the main-sequence companions usually outshine the white dwarf components. Aims. This work aims to comprehensively simulate the population of unresolved WDMSs within 100 pc of the Sun and to compare the outcome with the currently most complete volume-limited sample available from Gaia data. By doing so, we seek to refine our understanding of WDMS formation and evolution and to test the theoretical models against the observed data. Methods. We employed a population synthesis code, MRBIN, extensively developed by our group and based on Monte Carlo techniques, which uses a standard binary stellar evolutionary code adapted to cover a wide range of stars across all ages, masses, and metallicities. Different physical processes such as mass transfer, common-envelope evolution, and tidal interactions are considered. Selection criteria matching those of Gaia observations were applied to generate synthetic populations comparable to the observed WDMS sample. Results. Our analysis provides overall fractions of single main-sequence stars, white dwarfs, and resolved and unresolved WDMS ratios in excellent agreement with observed values. The synthetic data accurately populate the expected regions in the Gaia colormagnitude diagram. However, simulations predict a lower number of extremely low-mass white dwarfs, suggesting potential issues in observed mass derivations. Additionally, our analysis constrains the common-envelope efficiency to 0.1-0.4, consistent with previous findings, and estimates a total completeness of about 25% for the observed sample, confirming the strong observational limitations for unresolved WDMSs. Conclusions. This work provides understanding into WDMS evolution and highlights limitations in observational detectability, underscoring the importance of fine-tuning parameters in binary evolution models for improving population synthesis studies.