Astron. Astrophys. 333, 956-969 (1998)

2. Determination of spectral index

2.1. IR and radio observations

Table 1 summarises IR ( m) and radio fluxes for Galactic WR stars that are probable or definite thermal radio emitters. Leitherer et al. (1997) have recently compiled a list of 9 non-thermal emitters, which are mostly WR + O binaries. In two cases (WR 146, WR 147) thermal WR winds and non-thermal colliding winds have been resolved at radio frequencies, and so are included here (Dougherty et al. 1996; Williams et al. 1997). At quiescence (minimum), the radio emission from WR 140 appears to be thermal.

Table 1. Observed IR and radio fluxes (in mJy) of Galactic WR stars (ordered by subtype), where extrapolated 12µm values are given in parenthesis (see text). Spectral classifications are from Smith et al. (1996) for WN stars and Smith et al. (1990) for WC stars. In addition to the radio data presented below, there have been detections for WR 134 and WR 11 at 21 cm and 36 cm respectively (WR 134: -Hogg 1989; WR 11: -Jones 1985)

For those WR stars not observed at mid-IR wavelengths or contaminated by dust emission at that range, we have extrapolated near-IR or visible fluxes to 12µm (shown in parenthesis), assuming their spectral index is identical to the dust-free stars of similar subclasses. Near-IR photometry was taken from Hackwell et al. (1974), Cohen et al. (1975), Williams & Antonopoulou (1981), Pitault et al. (1983), Williams et al. (1987) and Crowther et al. (1995b). Line contributions in the near-IR bands were estimated from Pitault et al. (1983). The IR emission from WR 140 and WR 137 appear to be uncontaminated by dust emission during quiescence (minimum).

2.2. Distances and interstellar reddenings

Before we can obtain mass-loss rate estimates for our programme WR stars it is necessary to obtain distances, and interstellar reddening estimates to transform observed continuum fluxes into de-reddened fluxes.

Interstellar reddenings, , are given in Table 2. Our assumed reddening is taken from the mean of (i) literature values obtained by nulling the 2200 interstellar feature (Morris et al. 1993, Crowther 1993, Vacca & Torres-Dodgen 1990, Ford & Stickland 1988, Garmany et al. 1984, Underhill 1983, Nussbaumer et al. 1982, Hamann & Schwarz 1992, Eaton et al. 1985 and Stickland et al. 1984), and (ii) intrinsic colours, taken from Nugis & Niedzielski (1995) for single WR stars and from companion-corrected intrinsic colours for binary WR stars. The relationship between and monochromatic colour excess is adopted from Schmutz & Vacca (1991): (). Turner (1982) derived a slightly different relationship: . In order to correct intrinsic colours for binarity, we adopted =-0.35 for O stars and -0.30 for B companions (the latter value is also used for the companions classified as "abs") following Massey (1984). For several stars we deviated from the above technique:

Table 2. Physical parameters of WR stars with detected thermal radio-emission. Monochromatic magnitudes, , were generally taken from Torres-Dodgen & Massey (1988) or from Massey (1984). For those stars without monochromatic magnitudes, we corrected synthetic magnitudes by -0.04 mag (Schmutz & Vacca 1991) for WN stars, or -0.06 mag for WC stars (our estimate). is the fraction of the total flux emitted by the WR component in the v-band. The method of distance estimate is given in parenthesis: (a) - member of an association/cluster, (IS) - IS line study, () - fixed absolute visual magnitude, () - fixed radius, (par) - parallax measurement. The asymptotic valence electrons correspond to the normal (n) clumped wind case ( =1 for all our sample). For the higher ionization zones we assume , , for WN stars and , for WC stars

• WR 25 lies in a region of peculiar UV interstellar extinction (Crowther et al. 1995a), for which we obtained by demanding identical and ratios to WR 24 which has an identical spectral type.
• For WR 147 we determined from relative to normal WN8 stars and that obtained by Stickland et al. (1984).
• Since no reliable estimate of exists for WR 144 we have obtained its reddening assuming an identical intrinsic colour to WR 111 (WC5).

Distances, as presented in Table 2, have been derived using various techniques. For those stars which are not thought to be members of an open cluster or association, we generally used the mean absolute visual magnitudes for the respective WR (or O) spectral subtype. For most WN subtypes we obtained absolute visual magnitudes from members of clusters/associations, while we follow van der Hucht et al. (1988) for WC stars. For WR 6 and WR 124 we adopt distances obtained from their interstellar line spectra (Howarth & Schmutz 1995; Crawford & Barlow 1991). Distances to open clusters or associations are taken from Lundström & Stenholm (1984) and van der Hucht et al. (1988). For WR 78, WR 79 and WR 133 we use improved distances from Smith et al. (1994). Other exceptions are:

• WR 11 (WC8+O9 III) - Schaerer et al. (1997) reported the HIPPARCOS parallax measurements for this binary and derived a significantly smaller distance (0.26 0.04 kpc) than previously assumed (0.45 kpc).
• WR 47 (WN6+O5 V) - this star is normally assumed to be a member of the open cluster Ho 15 with a distance of 3.80 kpc. However, with this distance we obtain that , which is far from the mean of -5.43 for O5 V stars (Vacca et al. 1996). Smith et al. (1994) obtained a mass for the WN6 component which is much lower than that obtained from the orbital study of Moffat et al. (1990) - instead of . An improved consistency is obtained using a revised distance of 4.30 kpc, obtained by requiring identical differences in absolute visual magnitudes relative to mean values for their spectral types.
• WR 139 (WN5+O6 V) - both components are unusually bright ( and ) on the assumption that it is a member of the open cluster Be 86 ( kpc, Nugis 1996). A revised distance was estimated from the radius of the O component obtained by St-Louis et al. (1993). With =8.5 1 , , =0.65 and using =43 560 K and BC=-4.06 (Vacca et al. 1996), we find a distance of d =1.13 0.15 kpc.

For binaries, we have determined the fraction of the total light emitted by the WR component in the v-band () using the strength of (helium, nitrogen/carbon) WR emission () and OB absorption () lines relative to single stars and absolute visual magnitudes of the components. Smith et al. (1996) derived a relationship between (He II ) and FWHM(He II ) allowing estimates to be made of the fractional continuum brightness of WN components in binaries. For WC binaries we compared emission lines of 5806, 5696, 5590, 5470, 5411 relative to single Galactic stars.

2.3. Stellar abundances and wind velocities

Determinations of mass-loss rates from radio observations require knowledge about wind velocities and chemistries. In general, wind velocities are taken from UV P Cygni resonance lines (Prinja et al. 1990, Rochowicz & Niedzielski 1995), or near-IR He I P Cygni profiles (Eenens & Williams 1994) and are listed in Table 2 (see footnotes for exceptions).

For chemical compositions we consider the three most abundant elements in atmospheres under consideration; H, He and N for WN stars and He, C, O for WC stars. The contribution of other elements does not affect mean molecular weights. Hydrogen-to-helium ratios presented for WN stars are obtained from clumped models of Nugis & Niedzielski (1995), or smooth models of Hamann et al. (1995) and Crowther et al. (1995a, b) if these were unavailable. N/He abundances are set to 0.005 for WN stars following estimates from Nugis (1991) and Crowther (1993). Throughout this paper, abundance ratios are presented by number. The chemical composition of the star WR 145 (WN7/CE+OB) is taken from Crowther et al. (1995c) and the composition of the star WR 98 (WN8/C7) is adopted to be the same as for WR 145. In the case of WC stars, we take C/He=0.5 for WC4-5 stars, 0.4 for WC6 stars, 0.3 for WC7 stars, 0.2 for WC8 stars and 0.1 for WC9 stars, and O/C=0.1 following Nugis (1991).

The ionic charge (numbers of valence electrons ), number of electrons per ion and asymptotic value of the electron temperature () depend on the ionization conditions in the outer wind. For smooth winds, the ionic charge is readily obtained from the lowest observed ionization state in optical subordinate lines (e.g. (He)=1 if He I is observed in the spectrum). Estimates for individual stars are given in Table 2 for the clumped case - where either no interaction takes place between clumps or this is too weak to cause additional ionization in the radio emitting region.

2.4. Spectral indices

We now turn to the IR-mm-cm spectral indices () for our program stars, using the fluxes tabulated in Table 1. Individual values between IR-mm and mm-cm wavelengths are presented in Table 3 for those stars with two measurements at mm-cm wavelengths. We find spectral indices 0.9-1.1 in the IR spectral range, tending towards 0.6 at centimetre wavelengths.

Table 3. Observed spectral indices () for those WR stars which have been observed at least two radio frequencies. Radio "maximum" fluxes have been used for WR 89, while spectral indices derived from extrapolated IR fluxes are given in parenthesis

The average spectral index between IR and centimetre wavelengths is 0.75 (0.65 0.87) for 20 WN stars and a trend towards lower values at later spectral type (see Fig. 1). In the case of WC stars the derived spectral index between IR and cm wavelengths is 0.82 (0.73 0.95) for 17 stars, with no clear trend to lower values at later WC subtypes.

Fig. 1. The dependence of the 12µm-6cm spectral index with spectral subtype for individual WN (filled) and WC (open) stars. The decrease in mean spectral index at later WN spectral types (solid) is not repeated for WC stars (dashed)

For those WR stars also observed at millimetre wavelengths, the average spectral index between mm-cm wavelengths is 0.77 for 9 WN stars (0.53-0.94) and 0.75 for 3 WC stars (0.66-0.85). Observed spectral indices over the IR-mm-cm range show substantial variations, even amongst similar spectral types as illustrated by WN7-8 stars in Fig. 2. In cases where dust contaminates IR fluxes (e.g. WC9 stars, Williams et al. 1987), we have restricted our study to the use of extrapolated fluxes.

Fig. 2. The spectral indices versus for WN7-8 stars which indicate a complicated structure of clumped WNL winds (an open circle corresponds to the predictions of the smooth WNL wind model)

© European Southern Observatory (ESO) 1998

Online publication: April 28, 1998

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