Constraints on the Evolution of Massive Stars through Spectral Analysis. I. The WC5 Star HD 165763

Using a significantly revised non-LTE radiative transfer code that allows for the effects of line blanketing by He, C, O, Si, and Fe, we have performed a detailed analysis of the Galactic Wolf-Rayet (W-R) star HD 165763 (WR 111, WC5). Standard W-R models consistently overestimate the strength of the electron scattering wings, especially on strong lines, so we have considered models where the wind is both homogeneous and clumped. The deduced stellar parameters for HD 165763 are as follows:L=2.0×10⁵ L_solar ,R_*=1.8 R_solar ,Ṁ=1.5×10^-5 M_solar yr^-1 ,V_∞=2300 km s^-1 ,N(C)/N(He)=0.4 ,X(C)=0.462 ,N(O)/N(He)=0.1 ,X(O)=0.154 . The above results are for a clumped model in which the volume filling factor of the clumps is assumed to be 0.1 and implies (assumes) a distance of 1.55 kpc for HD 165763. Similar results are obtained for homogeneous models except that the deduced mass loss is larger, approximately 5.0×10^-5 M_solar yr^-1. The clumped model gives consistently better agreement with the line profiles, particularly the red wings, confirming the scenario that W-R winds are clumped. Because of the severe blending in WC stars and the simplicity of our approach, it is not feasible to deduce the actual filling factor or mass-loss rate. The quantity that can be determined from line strengths using our models is Ṁ/f^1/2. Using the evolutionary models of Maeder and Meynet, we find that the stellar abundances and parameters are consistent with a star of initial mass 60 M_solar and that has a present mass 10 M_solar.

The stellar parameters deduced for HD 165763 are significantly different from earlier analyses. The deduced luminosity is a factor of 2 larger, and a smaller core radius is found. The smaller radius is in better agreement with expectations from stellar evolution calculations. Both of these changes can be attributed to the effects of line blanketing. The deduced C/He abundance is similar to earlier calculations, and the O/He abundance had not previously been determined.

The observed iron spectrum, principally due to Fe V and Fe VI, is well reproduced using a solar iron mass fraction, although a variation of at least a factor of 2 about this value cannot be precluded. In particular, the models naturally produce the Fe V emission feature centered on 1470 Å and the complex Fe emission/absorption spectrum at shorter wavelengths. Also, Fe strongly modifies the line strengths and profile shapes shortward of 1800 Å and must be taken into account if we are to successfully model this region.

The reddening toward HD 165763 does not follow the mean Galactic extinction law. We determine the reddening law toward HD 165763 by comparing our model continuum levels to observations. In order to simultaneously match the UV, optical, and particularly the infrared fluxes, we used the parameterized reddening law of Cardelli, Clayton, and Mathis with E_B-V=0.3 and R=4.5, where R=A_V/E_B-V.

Based on both observational and theoretical suggestions we have considered models in which the wind is still accelerating at large radii. In particular, we discuss models in which the velocity law can be characterized by β=1 for r<10R_* but that undergo a substantial velocity increase (~600 km s^-1) beyond 10R_*. These models appear to give slightly better fits to the line profiles, but the improvements are small, and it is difficult to gauge whether observational data require such a velocity law.

We cannot yet determine whether the winds of W-R stars are driven by radiation pressure, because we neglect many higher levels of iron in our model ions, and we do not include important elements such as cobalt and nickel. However, the ``wind problem'' in W-R stars is less severe than previously assumed if clumping occurs. For our clumped model, the single scattering limit is only exceeded by a factor of 10 compared to 3 times this value for a homogeneous wind. Clumping appears to be the key to explaining the apparent high mass-loss rates determined for W-R stars and is extremely important in understanding how or even whether W-R winds are driven by radiation pressure. A reduction in W-R mass-loss rates has important implications for stellar evolution calculations.