ISOSCELES Project: II. Modelling galactic B-type stars for fast and $\delta-$slow wind regimes
Radiation-driven winds in B-type stars play a key role in their evolution, yet their hydrodynamical structure remains uncertain, particularly in evolved objects. While the classical fast solution of the modified CAK theory is widely adopted, it does not always reproduce the optical wind diagnostics of B-type giants and supergiants. We investigate the applicability of the classical fast and $\delta$-slow hydrodynamical solutions to B-type stellar winds through a homogeneous spectroscopic analysis based on optical diagnostics. We analysed 50 Galactic B-type stars spanning luminosity classes I to V using mid- and high-resolution optical spectra from the IACOB, ESO-UVES, and CASLEO datasets. Synthetic spectra were taken from the ISOSCELES grid, which combines hydrodynamical wind models computed with Hydwind and NLTE radiative transfer with Fastwind. Stellar and wind parameters were derived through a multi-line $\chi^2$ fitting procedure using hydrogen, helium, and silicon lines. We find evidence for different preferred hydrodynamical regimes across luminosity classes. Most supergiants ($\sim$96%) and giants ($\sim$88%) are better reproduced by $\delta$-slow models, characterised by higher ionisation parameters, slower terminal velocities ($v_\infty \lesssim 300$,km,s$^{-1}$, and denser outflows. In contrast, most dwarfs and subgiants ($\sim$88%) are more consistent with the classical fast solution, showing higher $v_\infty$ and lower $\dot{M}$. These trends suggest a dichotomy between luminosity classes. Our results indicate that the $\delta$-slow solution provides a viable framework for modelling the optical spectra of evolved B-type stars, whereas fast solutions remain adequate for less evolved objects. The ISOSCELES grid provides a physically motivated basis for interpreting optical wind diagnostics and motivates future multi-wavelength studies of B-type stellar winds.