I ArayaChristen, AlejandraAlejandraChristenCure, MichelMichelCureL S CidaleR O J VeneroArcos, CatalinaCatalinaArcosA C Gormaz-MatamalaM HauckeP EscárateH Clavería2025-12-072025-12-072021-04-1010.1093/mnras/stab995https://cris-uv-2.scimago.es/handle/123456789/7529<jats:title>ABSTRACT</jats:title> <jats:p>Accurate mass-loss rates and terminal velocities from massive stars winds are essential to obtain synthetic spectra from radiative transfer calculations and to determine the evolutionary path of massive stars. From a theoretical point of view, analytical expressions for the wind parameters and velocity profile would have many advantages over numerical calculations that solve the complex non-linear set of hydrodynamic equations. In a previous work, we obtained an analytical description for the fast wind regime. Now, we propose an approximate expression for the line-force in terms of new parameters and obtain a velocity profile closed-form solution (in terms of the Lambert W function) for the δ-slow regime. Using this analytical velocity profile, we were able to obtain the mass-loss rates based on the m-CAK theory. Moreover, we established a relation between this new set of line-force parameters with the known stellar and m-CAK line-force parameters. To this purpose, we calculated a grid of numerical hydrodynamical models and performed a multivariate multiple regression. The numerical and our descriptions lead to good agreement between their values.</jats:p>journal-article