3. Comparison with wind models
3.1. The model
The observed HI line emission has been compared with a wind model which considers a spherically symmetric and fully ionized envolope where the gas is moving with a constant rate of mass loss (). The gas is assumed to have a constant temperature of K and to be in LTE; the adopted gas velocity law is:
where =20 km s-1, is the maximum wind velocity (derived from the H observed profiles), and is the stellar radius. By increasing the parameter , the radius at which the gas velocity approaches its maximum value decreases. A detailed discussion on the validity of the model assumptions for the analysis of ionized winds in Herbig Ae/Be stars, is given in Nisini et al. (1995).
An important parameter to be considered is the amount of extinction for which the line fluxes need to be corrected. The adopted extinction law is that of Rieke & Lebofsky (1985). CoD 11721 has an estimate visual extinction () ranging from 5 mag (Mc Gregor et al. 1988) to 7 mag (de Winter & Thé 1990), while for MWC1080 a value of 5.4 mag has been determined (Cohen & Kuhi 1979). To account for the indetermination, we checked that, changing by a factor of two, the observed line ratios in the wavelength range we are considering do not change significantly.
We first compared the observed line ratios in a given recombination series (line decrement) with the standard model in which the envelope is completely ionized (density bounded ionized flow). In Fig. 2 we show the behaviour of the Pfund series decrement as a function of the different parameters. It turns out that the decrement does not change very much by varying any of the considered parameters, with the only exception being the mass loss rate; for very low values of all the lines become optically thin and then their ratios approach the Case B values (Hummer & Storey 1987). In any case, the higher lines in each series are more sensitive to variations in the model parameters than the lower lying lines.
The ratios observed in CoD 11721 are much above the Case B line ratios, which means that optical depth effects start to play a significant role. They are however also in disagreement with the wind model predictions, independently of the choice of the input parameters. We have therefore modified the assumption of a fully ionized envelope by introducing, as a separate parameter, the relative physical dimension of the ionized region (R=), where represents the radius at which the hydrogen atoms recombine. Fig. 3 shows how the line decrement significantly changes with this parameter. The behaviour of the line ratios decrement is essentially due to the different optical depths in the lines. For very small values of R, the lines are all emitted from the same optically thick surface and the emission can be approximated as proportional to S()R2, with S() the Planck function at Tgas. As R increases, the external part of the envelope starts to be optically thin and the line emission become proportional to , where is the radius at which the optical depth approaches unity (Smith et al. 1987, Simon et al. 1983). This radius depends on the transition and it is therefore different for the lines of the same spectral series; this is the reason why the line decrement slope changes with the dimension of the ionized region. The ratios observed in CoD 11721 are much better fitted with models which assume a relatively small dimension of the ionized region (ionization bounded flow).
From the line decrement we can constrain the mass loss rate and the ionized region dimension; the distance to the star (D) is then derived from the absolute line fluxes. Table 2 summarizes the model parameters of the best fits for the two stars; the errors quoted for the three considered parameters are derived by taking into account the spread in the line ratios of the different decrements. In the following sections we discuss separately the results obtained.
Table 2. Model paramaters of the best fit.
3.2. CoD 11721
CoD 11721 is an emission line star embedded in a diffuse nebulosity whose physical parameters are rather uncertain, mainly because its distance is poorly known. Indeed, distance estimates range between 2600 pc (Brooke et al. 1993) and only 220 pc (Pezzuto et al. 1997); in turn the estimate of the spectral type ranges between O9 and B8. H emission is observed towards the source, with a FWHM of 500 km s-1, indicating the presence of a strong wind (Hutsemekers & Van Drom 1990). Because of the lack of a defined estimate of the spectral type and luminosity of the star, its stellar radius is also not known a-priori. We have assumed a radius of 31011 cm (considering that the model, as shown in Fig. 2, does not strongly depend on this parameter), and checked a posteriori that this value is consistent with the physical quantities derived by our fit. The visual extintion towards the source has been taken equal to 7.1 mag (de Winter & Thé 1990).
We have already shown that the line decrements for this star suggest a very compact ionized region (R=12) with a rather high rate of mass loss . In Fig. 4a we show the best fit to the data for the line ratios of Brackett, Pfund and Humphreys series with respect to the Br line and in Fig. 5a the predicted absolute line fluxes are compared with the observed ones. The estimated distance is 500 pc; at this distance the star luminosity is , which indicates a spectral type B4 - B5. These estimates of distance and spectral type are in agreement with those found by Pezzuto et al. (1997) by fitting the continuum emission of the source.
Emission from the Brackett series was observed by McGregor et al. (1988), who estimated from the Br luminosity a mass loss rate , positioning the star at D2000 pc and assuming a fully ionized envelope model. They however do not check for the consistency of their derived parameters with the observed Brackett line decrement; their measured lines in the Brackett series agree with the model we derive from the SWS data (Fig. 4a).
MWC1080 shows H emission with strong P-Cygni profile, indicating a wind with velocity of 400 km s-1 (Finkenzeller & Mundt 1984). The spectral type is estimated to be B0 and the distance ranges between 1000 pc (Hillenbrand et al. 1992) and 2500 pc (Cantó et al. 1984). This source drives a powerful molecular outflow from which a wind mass loss rate of about has been derived. From the absolute flux of some recombination lines, Nisini et al. (1995) find a wind mass loss rate in agreement with this value.
We have assumed an =5.4 mag (Cohen & Kuhi 1979) and a stellar radius of 3.21011cm (Nisini et al. 1995). Also in this case the ionized region has a finite size of . Despite that, the derived mass loss rate is consistent with that computed assuming a fully ionized envelope. At our estimated distance of 2100 pc, the star has a luminosity of and a B0 spectral type, confirming the values quoted in Berrilli et al. (1992). The comparison between the observations and the model are shown in Fig. 4b for the line ratios of Brackett and Pfund series with respect to the Br line and in Fig. 5b for the absolute line fluxes.
© European Southern Observatory (ESO) 1998
Online publication: September 30, 1998