Tracing the environmental history of observed galaxies via extended fast action minimization method

We present a novel application of the extended Fast Action Minimization method (eFAM) aimed at assessing the role of the environment in shaping galaxy evolution and validate our approach against the Magneticum hydrodynamical simulation. We consider the z similar or equal to 0 snapshot as our observed catalogue and use the reconstructed trajectories of galaxies to model the evolution of cosmic structures. At the statistical level, the fraction of volume occupied by voids, sheets, filaments, and clusters in the reconstructed and simulated high-redshift snapshots agree within 1 sigma. Locally, we estimate the accuracy of eFAM structures by computing their purity with respect to simulated structures, P, at the cells of a regular grid. Up to z = 1.2, clusters have 0.58 < P < 0.93, filaments vary in 0.90 < P < 0.99, sheets show 0.78 < P < 0.92, and voids have 0.90 < P < 0.92. As redshift increases, comparing reconstructed and simulated tracers becomes more difficult and the purity decreases to P similar to 0.6. We retrieve the environmental history of individual galaxies by tracing their trajectories through the cosmic web and relate their observed gas fraction, f(gas), with the time spent within different structures. For galaxies in clusters and filaments, eFAM reproduces the dependence of f(gas) on the redshift of accretion/infall as traced by the simulations with a 1.5 sigma statistical agreement (which decreases to 2.5 sigma for low-mass galaxies in filaments). These results support the application of eFAM to observational data to study the environmental dependence of galaxy properties, offering a complementary approach to that based on light-cone observations.