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.

中文翻译：

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大质量恒星中辐射驱动风的分析解决方案 – II。δ-慢状态

来自大质量恒星风的准确质量损失率和终端速度对于从辐射传输计算中获得合成光谱和确定大质量恒星的演化路径至关重要。从理论的角度来看，风参数和速度剖面的解析表达式比求解复杂的非线性流体动力学方程组的数值计算具有许多优势。在之前的工作中，我们获得了快风状态的分析描述。现在，我们根据新参数提出线力的近似表达式，并获得 δ-慢状态的速度分布闭合形式解（根据 Lambert W 函数）。使用这种分析速度曲线，我们能够获得基于 m-CAK 理论的质量损失率。而且，我们在这组新的线力参数与已知的恒星和 m-CAK 线力参数之间建立了关系。为此，我们计算了数值流体动力学模型网格并进行了多元多元回归。数值和我们的描述导致它们的值之间的良好一致性。