Line-driven Radiative Winds in B-Supergiants: Bridging the Gap between Fast and Slow m-CAK Solutions

TL;DR

This study uses time-dependent hydrodynamic simulations to demonstrate that the previously reported forbidden regions in B-supergiant wind models are artifacts, showing instead a continuous solution space with complex transitional structures.

Contribution

The paper provides the first systematic time-dependent analysis of m-CAK wind solutions across the full parameter space, confirming the continuity of solutions and resolving the existence of forbidden regions.

Findings

Stable solutions exist across the entire parameter space.

Transitions between fast and slow regimes are smooth but structurally complex.

Mass-loss rates vary smoothly without artificial jumps.

Abstract

The modified Castor, Abbott, and Klein (m-CAK) theory predicts different wind regimes based on the line force parameter for changes in ionization ($\delta$) and the rotation parameter ($\Omega$). Stationary hydrodynamic studies have reported ''forbidden regions'' or gaps in this parameter space where no steady-state solution exists, suggesting physical instabilities. We investigate the stability of wind solutions within these gaps for B-supergiants to determine if they correspond to physical instabilities or numerical artifacts. We perform 1D time-dependent hydrodynamic simulations, systematically exploring the full $(\Omega, \delta)$ space for three B-supergiant models ($T_{\rm eff}=15-25$ kK), adopting a fixed density boundary condition. Our simulations reveal stable stationary solutions continuously across the entire parameter space, effectively filling the reported gaps. The transition from fast to slow regimes is smooth but structurally complex. Within the gap, the velocity profile develops a distinct ''kink'' or extended plateau in the supersonic flow, allowing the wind to reach a stable state. The mass-loss rate ($\dot{M}$) varies smoothly without artificial jumps. We find that the $\dot{M}$ gradient depends on the radiative driving strength ($k$): while $\dot{M}$ increases with $\delta$ for standard driving ($k \approx 0.32$), it decreases for the weak-driving regime ($k = 0.1$), consistent with stationary predictions. Moreover, in this regime, the final solution depends on the initial flow acceleration, confirming multiple hydrodynamic solutions. We conclude the m-CAK solution space is continuous; reported forbidden regions are artifacts of stationary methods. Time-dependent simulations effectively bridge the regimes, suggesting these transitions correspond to metastable states.