Mass-Orbital Period Distribution of Massive White Dwarfs Formed Through Stable Mass Transfer

White dwarfs (WDs) in binaries can form through either the stable mass-transfer process or common envelope evolution (CEE). Compared to CEE, the stable mass-transfer process can lead to a distinct mass-orbital period ($M_{\mathrm{WD}}-P_{\mathrm{orb}}$) relation. Thus, this relation of WDs contains the information about the evolution channels. We can study the relation in WD binary systems to determine whether their progenitors undergo a CEE. We use the stellar evolution code MESA as our primary computational tool and adopt the quasi-adiabatic criterion to ensure that our models satisfy the conditions for stable mass transfer. Our study considers different mass-transfer schemes, varying metallicities, and the relation for both low-mass and intermediate-mass progenitors. Previous studies have focused on the relation for low-mass progenitors, which cannot explain some long-period, high-mass WD binaries. Our results show that the relations for intermediate-mass progenitors whose cores remain non-degenerate prior to central helium burning can account for the formation channels of long-period and massive WD binaries.