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Register a new userClumping in the inner winds of hot, massive stars from hydrodynamical line-driven instability simulations
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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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This review describes the evidence for small-scale structure, `clumping, in the radiation line-driven winds of hot, massive stars. In particular, we focus on examining to what extent simulations of the strong instability inherent to line-driving can explain the multitude of observational evidence for wind clumping, as well as on how to properly account for extensive structures in density and velocity when interpreting the various wind diagnostics used to derive mass-loss rates.
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.
(Abridged) The behaviour of mass loss across bi-stability jump is a key uncertainty in models of massive stars. While an increase in mass loss is theoretically predicted, this has so far not been observationally confirmed. However, radiation-driven winds of massive stars are known to exhibit clumpy structures triggered by the line-deshadowing instability (LDI). Wind clumping affects empirical mass-loss rates inferred from density square-dependent spectral diagnostics. If clumping properties differ significantly for O and B supergiants across the bi-stability jump, this may help alleviate discrepancies between theory and observations. We investigate with analytical and numerical tools how the onset of clumpy structures behaves in the winds of O supergiants (OSG) and B supergiants (BSG) across the bi-stability jump. We derive a scaling relation for the linear growth rate of the LDI for a single optically thick line and apply it in both regimes. We run 1D time-dependent line-driven instability simulations to study the non-linear evolution of the LDI in clumpy OSG and BSG winds. Linear perturbation analysis for a single line shows that the LDI linear growth rate scales strongly with stellar effective temperature and terminal wind speed. This implies significantly lower growth rates for (cooler, slower) BSG winds than for OSG winds. This is confirmed by the non-linear simulations, which show significant differences in OSG and BSG wind structure formation, with the latter characterized by significantly weaker clumping factors and lower velocity dispersions. This suggests that lower correction factors due to clumping should be employed when deriving empirical mass-loss rates for BSGs on the cool side of the bi-stability jump. Moreover, the non-linear simulations provide a theoretical background toward explaining the general lack of observed intrinsic X-ray emission in (single) B star winds.
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 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.
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