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

Abstract: Binary stars consisting of a white dwarf and a main sequence star (WDMS) are valuable for studying key astrophysical questions. However, observational biases strongly affect the known population, particularly unresolved systems where the main sequence star outshines the white dwarf. This work aims to comprehensively simulate the population of unresolved WDMS binaries within 100 pc of the Sun and to compare the outcome with the currently most complete volume-limited sample available from Gaia data. We employ 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. Selection criteria matching those of Gaia observations are applied to generate synthetic populations comparable to the observed WDMS sample. The synthetic data accurately populate the expected regions in the Gaia color-magnitude 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 WDMS.