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Astron. Astrophys. 350, 1007-1017 (1999)

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4. Stellar analysis

Unblanketed non-LTE spectroscopic analyses of WR124 by Hamann et al. (1993) and Crowther et al. (1995a) revealed [FORMULA]30-34kK, [FORMULA][FORMULA]5.3-5.4, [FORMULA][FORMULA][FORMULA][FORMULA] yr-1, and [FORMULA][FORMULA]700 km s-1. The latter study included hydrogen, helium, carbon and nitrogen, deriving H/He[FORMULA]0.6 by number. Hamann & Koesterke (1998a) assumed this hydrogen content, and derived equivalent stellar parameters based on an analysis of the nitrogen spectrum. In contrast, Esteban et al. (1993) used properties of M1-67 to conclude that [FORMULA][FORMULA]30kK, although a suitable unblanketed model was not found from the grid of Schmutz et al. (1992). The best agreement was obtained with the only line blanketed models available at that time, namely those for the WN9 star R84=Brey 18 ([FORMULA]=28.5kK) from Schmutz et al. (1991). A spectral comparison of WN8 and WN9 stars is presented by Crowther & Smith (1997).

4.1. Analysis technique

Our approach follows that of Crowther et al. (1995a), such that diagnostic optical lines of He I ([FORMULA]5876), He II ([FORMULA]4686) and H I (H[FORMULA]+He II [FORMULA]4859) are chosen to derive the stellar temperature, mass-loss rate, luminosity and hydrogen content. In the absence of high resolution UV observations, a wind velocity of 710 km s-1 is obtained from optical He I P Cygni line profiles. A [FORMULA]=1 velocity law is adopted, since this reproduces the optical, near-IR and mid-IR spectra of a similar WN8 star, WR147 (Morris et al. 1999).

4.2. Results

In Fig. 2, we compare spectroscopic observations of WR124 with the synthetic spectrum obtained from CMFGEN , allowing for both line blanketing and clumping. The level of agreement between optical observations and theory in Fig. 2 is excellent, except that the He I absorption components are often predicted to be too strong.

[FIGURE] Fig. 2. Comparison between the rectified optical (INT) and near-IR (UKIRT) spectrum of WR124 (solid lines) with the synthetic spectrum produced by CMFGEN , accounting for line blanketing and clumping.

We also include comparisons with H and K band UKIRT observations of WR124 in Fig. 2. Again, excellent agreement is reached. Note that UKIRT observations of He II 3.09 µm are also well reproduced. The case of He I 2.058 µm deserves special comment. Crowther et al. (1995a) discussed the difficulties in predicting emission at He I 2.058 µm for the WN8 star HD 86161, in that the predicted emission was far too weak. The strength of 2.058 µm (and He I [FORMULA]5016) is very sensitive to the optical depth of the He I [FORMULA]584 transition. Crowther et al. (1995a) attributed this failure to the neglect of line blanketing in the extreme-UV. Our results support this claim for the case of WR124, the predicted 2.058 µm emission now is in excellent agreement with observation.

Crowther et al. (1995a) obtained a similar level of consistency in their study, based on an identical optical data set, except that electron scattering wings were strongly overestimated because of their assumption of homogeneity (their Fig. 10). Allowing for clumping takes away this discrepancy, such that electron scattering wings are well reproduced with an assumed volume filling factor of f=10%, with a corresponding decrease in the required mass-loss rate by a factor of [FORMULA]3. As discussed by Hillier & Miller (1999) and Hamann & Koesterke (1998b), a unique determination of the filling factor is not possible, such that an uncertainty of [FORMULA]50% remains on the precise mass-loss rate.

The stellar parameters for this model are compared with those from the unblanketed, homogeneous analysis of Crowther et al. (1995a) in Table 3. We find that the inclusion of line blanketing has only a minor effect on the derived parameters for WNL stars. Nevertheless, also considering the effects of clumping on the mass-loss rate, the wind performance factor, [FORMULA], is reduced from 10 to [FORMULA]2!


Table 3. A comparison of stellar parameters obtained for WR124 using CMFGEN (unblanketed and blanketed) and ISA -wind (blanketed). The unblanketed results are taken from Crowther et al. (1995b), based on identical observations. In all cases, a standard velocity law with [FORMULA]=1 is assumed.

Turning to ISA -wind, we present a contour plot for the dependence of our diagnostic He I-II lines on temperature and mass-loss for WR124. We prefer to use a comparison in terms of peak intensity rather than line equivalent width since the former approach was followed for CMFGEN . Our figure allows us to quantify uncertainties in parameters, namely [FORMULA]1000 K in temperature and [FORMULA]0.1 dex in mass-loss rate. Since these represent formal uncertainties with ISA -wind, how do the derived stellar parameters compare with results from CMFGEN ? Table 3 reveals that good agreement is obtained between the two codes in derived stellar parameters, including the hydrogen content. This comparison demonstrates the validity of the Sobolev approximation for WR analyses, and represents an important result from the present study.

In Fig. 3, we compare identical optical observations of WR124 with the synthetic spectrum obtained from the ISA- wind contour plot, allowing for line blanketing. The quality of line fits is comparable to CMFGEN , except that (i) the region around [FORMULA]4100 is more severely underestimated, due to the neglect of Si IV [FORMULA]4088-4116, (ii) He I [FORMULA]5015 is too weak; (iii) He II [FORMULA]4200, [FORMULA]4542 and [FORMULA]5412 are in better agreement than CMFGEN . In the near-IR, He I 2.058 µm emission is predicted to be somewhat too strong, as is He I 2.112 µm emission, with Br[FORMULA] too weak.

[FIGURE] Fig. 3. Comparison between the rectified optical (INT) spectrum of WR124 (solid lines) with the synthetic spectrum produced by ISA -wind, accounting for line blanketing. Spectral comparisons in the red and near-IR are comparable to CMFGEN , except for those lines discusssed in the text.

[FIGURE] Fig. 4. Contour lines of equal rectified line peak intensity for He I [FORMULA]5876 (4.3, solid) and He II [FORMULA]4686 (3.55, dashed), in the stellar [FORMULA]-log [FORMULA] plane. The thick contours represent the observed values, while the thin contours show the [FORMULA]10% error margin. The rhomboids mark the parameters for which models were calculated.

4.3. Comparison of ionizing flux distributions

Our three solutions indicate very similar stellar properties for WR124 and are equally successful at reproducing its optical spectrum. How do the Lyman ionizing flux distributions of these models compare?

The unblanketed CMFGEN ionizing energy distribution is shown in Fig. 5. It is relatively flat, with a small jump beyond the He I edge at 1.81 Ryd (24.6 eV or 504 Å), and a non-negligible flux up to 3.2 Ryd (286 Å). Fig. 5 reveals that the blanketed CMFGEN distribution is much softer than the unblanketed solution, showing a large deficit for energies [FORMULA]1.3Ryd (i.e. [FORMULA]700 Å), such that a very low flux is emitted at energies beyond the He I edge. In addition, this distribution shows a moderate excess between the Lyman edge and 1.25 Ryd relative to the unblanketed case, which explains why its bolometric luminosity is essentially identical.

[FIGURE] Fig. 5. (upper panel:) Comparison between the Lyman ionizing distribution of unblanketed CMFGEN (dotted lines) and blanketed CMFGEN (solid lines) for WR124, revealing large differences; (Lower panel) as above, except for unblanketed CMFGEN (dotted lines) and blanketed ISA -wind (solid lines). Note that these diagrams are designed to emphasise the extreme UV spectral region, important for the nebular ionization, and not the overall energy distribution.

ISA- wind shows an intermediate energy distribution, with a depression around 1.7 Ryd (540 Å), but a relatively hard flux beyond the He I edge, up to energies of 2.9 Ryd (310 Å). Possible explanations for the differences in ionizing fluxes between the two blanketed cases are discussed in Sect. 5.4.

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© European Southern Observatory (ESO) 1999

Online publication: October 14, 1999