The impact of stellar envelopes on the formation of merging compact-object binaries

The common envelope (CE) phase play a key role in the formation of many astrophysical systems, including merging compact-object binaries. In a tight binary system, the CE phase happens when one star overfills its Roche lobe and initiates a process of dynamically unstable mass transfer. In this scenario, the mass transfer rate increases with time, the secondary star cannot accrete all the incoming material, and the latter surrounds the entire binary. The gas surrounding the binary star is known as CE. During the CE phase, the binary system rotates at a different rate than the CE. The orbital energy decreases due to the friction between the binary system and the CE. Due to orbital energy loss, the core of the donor and the companion star spiral toward one another within the CE (spiral-in phase). The orbital semi-major axis of binary systems can shrink by orders of magnitude during the spiral-in phase. The lost fraction of orbital energy is transferred to the envelope, which heats up and expands. The CE phase can end with two different outcomes. In the first scenario, the envelope is ejected, leaving the binary system with quite small semi-major axes. In the other scenario, during the spiral-in phase, the two stars merge and become an (evolved) massive star. Self-consistent hydrodynamical simulations of CE are very complex and computationally expensive. In fast population-synthesis studies, the CE phase is simulated via the (α,λ)- formalism, where α parameterizes the fraction of orbital energy transferred to the envelope, and λ is the envelope’s binding-energy parameter. The time required for a binary system to merge is highly dependent on the α and λ parameters, so their values have a crucial impact on the interpretation of many astrophysical systems, including merging compact-object binaries. While constraining the α parameter is challenging, we can calculate the λ values and consider λ as a physical quantity instead of a parameter. In this thesis, we present new results on self-consistent calculations of the binding energy parameter for a large set of hydrogen and helium stars, using the up-todate tracks from the PARSEC stellar evolution code. We demonstrate how the definition of the core-envelope boundary, the nature of the energy sources, metallicity, stellar mass, and evolutionary stage influence the value of λ parameters. We show that the new λ values are up to one order of magnitude lower than those obtained in previous studies and we discuss the associated implication for the formation of merging compact-object binaries. We present fitting formulas for the new binding energy parameters for hydrogen and helium stars obtained in this work, and we evaluate their accuracy with respect to self-consistent data. The SEVN population-synthesis code is the ground for implementing the new bindingenergy prescriptions obtained in this thesis and for an up-to-date astrophysical interpretation of present and forthcoming gravitational-wave sources. Since the SEVN code is based on the star tracks of the PARSEC stellar evolution code, it will be self-consistent to test our new CE prescriptions and study their impact on the evolutionary pathways of binary systems. In this thesis, we focus mainly on introducing several technical improvements in the SEVN code (e.g., adaptive data loading, single and multi-node parallelization), which is the preparatory work that will be crucial to perform efficient simulations of large populations of binary stars and testing the new binding-energy prescriptions.