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Register a new userAnalytical Solutions for Radiation-Driven Winds in Massive Stars II: The $delta$-slow Regime
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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 $delta$-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.
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We present two self-consistent procedures that couple the hydrodynamics with calculations of the line-force in the frame of radiation wind theory. These procedures give us the line-force parameters, the velocity field, and the mass-loss rate. The first one is based on the so-called m-CAK theory. A full set of line-force parameters for $T_text{eff}ge 32,000$ K and surface gravities higher than 3.4 dex for two different metallicities are presented, along with their corresponding wind parameters. We find that the dependence of line-force parameters on effective temperature is enhanced by the dependence on $log g$. For the case of homogeneous winds (without clumping) comparison of self-consistent mass-loss rates shows a good agreement with empirical values. We also consider self-consistent wind solutions that are used as input in FASTWIND to calculate synthetic spectra. By comparison with the observed spectra for three stars with clumped winds, we found that varying the clumping factor the synthetic spectra rapidly converge into the neighbourhood region of the solution. Therefore, this self-consistent m-CAK procedure significantly reduces the number of free parameters needed to obtain a synthetic spectrum. The second procedure (called Lambert-procedure) provides a self-consistent solution beyond m-CAK theory, and line-acceleration is calculated by the full NLTE radiative transfer code CMFGEN. Both the mass-loss rate and the clumping factor are set as free parameters, hence their values are obtained by spectral fitting after the respective self-consistent hydrodynamics is calculated. Since performing the Lambert-procedure requires significant computational power, the analysis is made only for the star z-Puppis. The promising results gives a positive balance about the future applications for the self-consistent solutions presented on this thesis.
Massive stars present strong stellar that which are described by the radiation driven wind theory. Accurate mass-loss rates are necessary to properly describe the stellar evolution across the Hertzsprung--Russel Diagram. We present a self-consistent procedure that coupled the hydrodynamics with calculations of the line-force, giving as results the line-force parameters, the velocity field, and the mass-loss rate. Our calculations contemplate the contribution to the line-force multiplier from more than $sim 900,000$ atomic transitions, an NLTE radiation flux from the photosphere and a quasi-LTE approximation for the occupational numbers. A full set of line-force parameters for $T_text{eff}ge 32,000$ K, surface gravities higher than 3.4 dex for two different metallicities are presented, with their corresponding wind parameters (terminal velocities and mass-loss rates). The already known dependence of line-force parameters on effective temperature is enhanced by the dependence on $log g$. The terminal velocities present a stepper scaling relation with respect to the escape velocity, this might explain the scatter values observed in the hot side of the bistability jump. Moreover, a comparison of self-consistent mass-loss rates with empirical values shows a good agreement. Self-consistent wind solutions are used as input in FASTWIND to calculate synthetic spectra. We show, comparing with the observed spectra for three stars, that varying the clumping factor, the synthetic spectra rapidly converge into the neighbourhood region of the solution. It is important to stress that our self-consistent procedure significantly reduces the number of free parameters needed to obtain a synthetic spectrum.
The standard, or fast, solutions of m-CAK line-driven wind theory cannot account for slowly outflowing disks like the ones that surround Be stars. It has been previously shown that there exists another family of solutions --- the $Omega$-slow solutions --- that is characterized by much slower terminal velocities and higher mass-loss rates. We have solved the one-dimensional m-CAK hydrodynamical equation of rotating radiation-driven winds for this latter solution, starting from standard values of the line force parameters ($alpha$, $k$, and $delta$), and then systematically varying the values of $alpha$ and $k$. Terminal velocities and mass-loss rates that are in good agreement with those found in Be stars are obtained from the solutions with lower $alpha$ and higher $k$ values. Furthermore, the equatorial densities of such solutions are comparable to those that are typically assumed in ad hoc models. For very high values of $k$, we find that the wind solutions exhibit a new kind of behavior.
Hot massive stars present strong stellar winds that are driven by absorption, scattering and re-emission of photons by the ions of the atmosphere (textit{line-driven winds}). A better comprehension of this phenomenon, and a more accurate calculation of hydrodynamics and radiative acceleration is required to reduce the number of free parameters in spectral fitting, to determine accurate wind parameters such as mass-loss rates and velocity profiles. We use the non-LTE model-atmosphere code CMFGEN to numerically solve the radiative transfer equation in the stellar atmosphere and to calculate the radiative acceleration $g_text{rad}(r)$. Under the assumption that the radiative acceleration depends only on the radial coordinate, we solve analytically the equation of motion by means of the Lambert $W$-function. An iterative procedure between the solution of the radiative transfer and the equation of motion is executed in order to obtain a final self-consistent velocity field that is no longer based on any $beta$-law. We apply the Lambert-procedure to three O supergiant stars ($zeta$-Puppis, HD~165763 and $alpha$-Cam) and discuss the Lambert-solutions for the velocity profiles. It is found that, even without recalculation of the mass-loss rate, the Lambert-procedure allows the calculation of consistent velocity profiles that reduce the number of free parameters when a spectral fitting using CMFGEN is performed. Synthetic spectra calculated from our Lambert-solutions show significant differences compared to the initial $beta$-law CMFGEN models. The results indicate the importance of consistent velocity profile calculation in the CMFGEN code and its usage in a fitting procedure and interpretation of observed spectra.
We investigate the effects of stellar limb-darkening and photospheric perturbations for the onset of wind structure arising from the strong, intrinsic line-deshadowing instability (LDI) of a line-driven stellar wind. A linear perturbation analysis shows that including limb-darkening reduces the stabilizing effect of the diffuse radiation, leading to a net instability growth rate even at the wind base. Numerical radiation-hydrodynamics simulations of the non-linear evolution of this instability then show that, in comparison with previous models assuming a uniformly bright star without base perturbations, wind structure now develops much closer ($r la 1.1 R_star$) to the photosphere. This is in much better agreement with observations of O-type stars, which typically indicate the presence of strong clumping quite near the wind base.
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