Radiation-driven stellar winds at the fast–slow transition: New hydrodynamic solutions

¹ Departamento de espectroscopía, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque S/N, BF1900FWA La Plata, Buenos Aires, Argentina
² Instituto de Astrofísica de La Plata, CCT La Plata, CONICET-UNLP, Paseo del Bosque S/N, BF1900FWA La Plata, Buenos Aires, Argentina
³ Centro Multidisciplinario de Física, Vicerrectoría de Investigación, Universidad Mayor, 8580745 Santiago, Chile
⁴ Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111, Casilla 5030, Valparaíso, Chile

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 January 2026
Accepted: 16 April 2026

Abstract

Context. Radiation-driven winds of massive stars can be described within the modified Castor-Abbott-Klein theory, which parametrises the radiation force through three key quantities: α, δ, and k. Different combinations of these parameters, together with rotation, result in three types of stationary solutions, namely fast (or classical), δ-slow, and Ω-slow solutions.

Aims. The primary objective of this work is to model radiation-driven winds inside the gap region between the fast and δ-slow regimes, where stationary solutions have proven elusive. We computed synthetic line profiles of H I, He I, and Si IV to illustrate the morphology of different wind regimes.

Methods. We employed the time-dependent hydrodynamic code ZEUS-3D, capable of obtaining stationary solutions by progressing through an initial solution. Then, we computed the line profiles solving the transfer equation for an expanding atmosphere, assuming spherical symmetry in the comoving frame, under non-local thermodynamic equilibrium conditions.

Results. We find new stationary solutions in the gap region, alongside their corresponding line profiles for a typical B supergiant star model. In this model, the new solutions are stable, and some present a kink in the velocity profile at a fixed distance from the star, depending on the δ value. Perturbations in the wind ionisation may trigger transitions between different hydrodynamic regimes and offer a plausible explanation for structured and variable winds. A systematic investigation of these effects will be the subject of future work. Furthermore, we investigated the resulting line profiles from different hydrodynamic solutions and compared them with those predicted by a velocity profile given by a β-law using the same global wind parameters.