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Optically thick wind models of WNE stars: the dependence of mass-loss rate on metallicity

Optically thick wind models of WNE stars: the dependence of mass-loss rate on metallicity. Tiit Nugis Tatu Observatory, Estonia. What is optically thick wind ?. Optically thick wind is defined as a wind with the sonic point located at large optical depth for continuum.

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Optically thick wind models of WNE stars: the dependence of mass-loss rate on metallicity

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  1. Optically thick wind models of WNE stars: the dependence of mass-loss rate on metallicity Tiit Nugis Tatu Observatory, Estonia

  2. What is optically thick wind ? • Optically thick wind is defined as a wind with the sonic point located at large optical depth for continuum. • WR-star winds are optically thick winds. Outer parts of their winds are optically thin for continuum and here the matter flow is driven by the same mechanism as in the winds of OB stars (CAK-mechanism: radiation pressure in spectral lines, amplified by Doppler shifts).

  3. Optically thick wind models • The calculation of optically thick wind models consists of three steps: • (1) - sonic point analysis, • (2) – outward integration starting from the sonic point for finding the proper optical depth, • (3) – the inward integration for matching the solution to evolutionary, hydrostatic stellar interior models.

  4. Mass-loss rate formula for optically thick winds • From the outward integration of wind formulae, we will get the mass-loss rate formula for optically thick winds (Nugis & Lamers 2002):

  5. Momentum equation

  6. Opacity (radiation pressure force) near the sonic point The opacity at the sonic point of WNE stars must be equal to about 4πGM/L • OPAL opacity ? • CAK-type forces (very large velocity gradients are needed) ?

  7. The OPAL peak opacity at the sonic point of WNE-star winds as a function of the mass • T(peak) is about 150000 K

  8. Wind model for the CAK-force • The opacity at the sonic point and above is assumed to be given by the Gayley (1995) formula • For the standard star (WN5 component in the binary system V444 Cyg) with the fixed mass-loss rate and mass we will get that α0.45, dv/dr(Rs)  0.02 1/s and Rs Rhc  0.9Rsun. • This solution is in conflict with some important observed data: model-predicted radius of the layer where electron scattering optical depth is unity is very small (about 2.5–3 times smaller as compared to the observed radius!).

  9. Convection near the sonic point • For optically thick winds we have that near their sonic points : dT/dr(rad)  -T/r • The adiabatic temperature gradient is: dT/dr(ad)  -T/3 (2/r + dv/dr/v) • If dv/dr is small then the wind becomes convectively unstable!

  10. The infuence of convective instability • Convection makes L(rad) smaller and helps to form the sonic points for the most massive WNE stars • Turbulent pressure and the enhancement of the opacity due to moving convective cells helps to form the sonic points for WNE stars with small mass

  11. Optically thick wind models with the sonic point located in the convectively unstable region • Standard star (WR139): opacity is accounted for by the modified Gayley formula and the parameter α is found to be about 0.35 • The radius of the layer τ(el)=1 is comparable to the observed value

  12. The dependence of mass-loss rate of WNE stars on Z • Opticially thick wind models predict strong dependence of the mass-loss rate on the initial metallicity. The power of that dependence is somewhat depending on the mass of the star. In the range of masses 5–10 Msun this power is 1.5 –2 and in the range of masses 10–30 Msun the power index is 1.2–1.5 • What is the observed dependence (poster PD1of Nugis, Annuk and Hirv: strong dependence on Z!)

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