4. Spectral analysis of the central stars
For the spectral analysis we used H-He NLTE models (Werner 1986, 1996). Atmospheric parameters of our CSPN are obtained by fitting profiles of the observed hydrogen and helium lines with the model spectra. We use the least-square routines developed by Bergeron et al. (1992) and Saffer et al. (1994).
The observed and theoretical Balmer line profiles are normalized to a linear continuum in a consistent manner. The synthetic spectra are convolved with a Gaussian to match the observational resolution and interpolated to the actual parameters with bicubic splines. The atmospheric parameters and are then determined by minimizing the value.
The Balmer line problem reported in Napiwotzki & Rauch (1994) is also present in these hot stars: the fit of different Balmer lines results in different temperatures. The results of Napiwotzki (1993) and Werner (1996) indicate that the temperature derived from the highest observable Balmer line (H or H ) is close to the real value. Thus we used the following recipe: g was computed from the average of all Balmer lines and is derived from H (Fig. 10). A comparison of our final models to the spectra is shown in Fig. 12.
Finally, an estimate of the internal errors can be derived from the covariance matrix. In contrast to Bergeron et al. 1992, we estimate the noise of the spectra () used for the fit from the neighbouring continuum of each line. Results are given in Table 4. The error margins on are quite high, even in the case of well exposed spectrum of the central star of PN G214.9+07.8. This is explained by a particular low sensitivity of the Balmer lines in the parameter range of our central stars. However, the Balmer lines are the only temperature indicator available for our sample.
Table 4. Photospheric properties of our CSPN. The He/H is given as a number ratio.
In the case of the CS of PN G283.6+25.3, there might be a flux contribution from a cool companion (Fig. 12) which may have an influence on the derived parameters.
None of the spectra of the CS of PN G257.5+00.6 and PN G277.1-03.8 could be consistently fitted by one of our models. A comparison to Kurucz models (1979, 1991) shows that these spectra are most likely of F-type main-sequence stars (an example is shown in Fig. 11). It appears likely that we obtained composite spectra which are dominated by the F star.
4.1. Masses and distances
The masses of the analyzed CSPN were determined by comparison with theoretical evolutionary tracks (Fig. 13, Table 5). In analogy to Rauch et al. 1994, the distances are determined by using the flux calibration of Heber et al. (1984) for :
with the Eddington flux , M given in , and . Since nothing is known about the extinction, we assume c ranging between 0.0 and 0.5 which has a slight influence on the error range (Table 5).
Table 5. Masses and distances of our CSPN. The linear size of the PN () is calculated from the measured angular diameter (Table 2). For the expansion times (in 103 a) we employ velocity measurements by Meatheringham et al. 1988 (PN G214.9+07.8: 21.4 km/sec, PN G231.8+04.1: 23 km/sec), Smith & Gull 1975 (PN G283.6+25.3: 28 km/sec), otherwise we assume an expansion velocity of . The evolutionary times (in 103 a) for the central stars are derived by comparison with the evolutionary tracks of Fig. 13
The expansion times () for the PN (Table 5) are significantly longer than the evolutionary times () of their CS. One reason for this might be that we used the faintest detected nebula emissions on our images in order to measure the size of the PN and thus may have considered a part of the AGB wind matter which is now ionized by the CS. However, we do not find a discrepancy like reported by McCarthy et al. (1990) and Rauch et al. (1994) for other low-mass () H-rich central stars.
© European Southern Observatory (ESO) 1999
Online publication: June 18, 1999