Reconstructing post-common envelope white dwarf-main-sequence binary histories through inverse population synthesis techniques: A case study of ZTF eclipsing binaries

Context. The evolution of binary stellar systems involves a wide range of physical processes, many of which are not yet well understood. This is particularly true for close binary systems formed of a white dwarf and a main-sequence star. For instance, characterizing certain mass transfer episodes that may lead to a common-envelope phase and its subsequent evolution is still an open problem. Fortunately, the observational capabilities of current surveys, coupled with the feasibility of population synthesis models, enable us to reconstruct the past history of these systems, shedding light on their evolution and theoretical modeling. Aims. We aim to build a general-purpose algorithm based on inverse population synthesis techniques, able to reconstruct the past history of binary systems, particularly those involving a white dwarf and a main-sequence star. This algorithm will be applied to a sample of eclipsing binaries, aiming to ascertain their progenitors and past histories. Additionally, the resulting input space parameters will be analyzed, with a specific focus on the common-envelope phase. Methods. With the help of a consolidated population synthesis code, MRBIN, we developed an algorithm able to find the progenitor parameters of a given evolved binary system. The performance of the algorithm was tested on a set of synthetic binary systems. Once validated, it was applied to a sample 30 white dwarf plus main-sequence eclipsing binaries observed by the Zwicky Transient Facility survey. Results. We determined the input space parameters of the progenitors for the 30 eclipsing binary systems to which the algorithm was applied. These parameters included the initial primary and secondary masses, the orbital separation and eccentricity, the common-envelope efficiency (alpha CE), and the age at which the system was formed. Furthermore, the analysis of the global properties revealed some important features: a mild anticorrelation between the common-envelope efficiency parameter and the secondary mass, the absence of a universal value of alpha CE along with no need for internal energy, although in the low-mass regime, the high values of alpha CE suggest a possible contribution, and an initial thermalized eccentricity distribution. Conclusions. Although a strong degeneracy among the input parameters exists in the reconstruction of post-common envelope binary systems, the high accuracy obtained for the eclipsing-binary systems analyzed here has allowed our algorithm to make a reasonable determination of the initial parameters without the need to include external constraints. The global properties found here so far, can be substantially improved when analyzing a future volume-complete sample.