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Astron. Astrophys. 347, 169-177 (1999)

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3. Preliminary analysis of the nebula spectra

Because of the low surface brightness of the nebulae and their large angular diameters, spectral information on the nebulae is still rather unsatisfactory: though all objects were observed by Stenholm for the catalogue of Acker et al. (1992), the [FORMULA] aperture was usually placed on a bright portion, and thus is neither representative for the object as a whole nor sufficient to allow reasonable photoionization modeling. Three objects (PNe G231.8+04.1, G277.1-03.8, and G283.6+25.3) were observed by Kingsburgh & Barlow (1992) with a 18" long slit centered on the CS and analyzed by plasma diagnostics for their chemical compositions.

Therefore, we limit ourselves to an overall test whether the nebula spectra and data are consistent with the properties found for the CSPN. We deduce how many hydrogen recombinations take place in the shell and what must be the minimum luminosity for a central star to ionize it, and how this agrees with the one derived from the atmospheric analysis of the CS. Nebulae which require low stellar luminosities must be substantially optically thin in the hydrogen Lyman continuum which implies that the nebula spectra should be dominated by high stages of ionization.

We assume a spherical, homogeneous, and isothermal nebula of density n and electron temperature [FORMULA] at a distance d. Given the angular diameter (in arc sec) D, the measured H [FORMULA]-flux [FORMULA]), and the interstellar extinction c, one obtains a relation between nebula density and distance:


with the effective recombination coefficient [FORMULA] for the H [FORMULA] line (cf. Osterbrock 1974). We set [FORMULA], which suffices for the estimates we want to do here. This relation we use to get an estimate for either n or d from the other quantity. For some objects the electron density can be derived from the [S II [FORMULA]Å line ratio, for others we have available the distance on the basis of the CSPN analysis.

Then the number of recombinations [FORMULA] is


with the total recombination coefficient [FORMULA] for hydrogen. As the nebulae are most likely optically thin, we should use [FORMULA]. An average electron temperature of 20 kK is used, as appropriate for high excitation objects.

Table 3 summarizes our results: we give for each object the adopted data. the number of hydrogen recombinations, and the luminosity for a CSPN at [FORMULA] kK to ionize the nebula, if it were optically thick. The latter figure is quite insensitive to the adopted value of [FORMULA] in this temperature range. In some objects, we give several results based on fixing either the distance or the density. It is worth pointing out that given the distance, one has


so [FORMULA] depends strongly on d but only weakly on [FORMULA]. But with a given density


one notes an extremely strong sensitivity to the angular diameter, and also strong dependences on the flux and electron temperature. Therefore, guessing a reasonable distance gives more reliable results than depending on an uncertain estimate for the electron density. Table 3 shows that the resultant densities all are in the range of [FORMULA] as one would expect for highly evolved nebulae.


Table 3. Analysis of the nebular spectra: given are the H [FORMULA] fluxes (in [FORMULA]) (Acker et al. 1992 except for G249.3-05.4 which was estimated from Stenholm's measured flux), used angular diameter, extinction derived from the Balmer lines, adopted electron density (cm-3) and distance (values in brackets are derived from Eq. 1) the number of H recombinations (sec-1) in the nebula, the necessary minimum luminosity (in [FORMULA]) for a CSPN with [FORMULA], the luminosity derived from our photospheric analysis, and the He II and [O III ] line intensities (I(H [FORMULA])=100) from the spectra of Stenholm (S, normal exposure time 10 min., for faint objects, in a few case, longer exposures were done) or Kingsburgh & Barlow (KB).
a: exposure time 30 min, no He II
b: exposure time 40 min, no He II
c: exposure time 30 min, no He II , H [FORMULA] very faint
d: exposure time 10 min, He II visible, but uncertain 20:

Let us discuss first the nebulae with circular or elliptical nebulae. PNe G214.9+07.8, G283.6+25.3, and G293.6+10.9 all require a stellar luminosity smaller than is obtained from the CSPN analysis. Thus all are substantially optically thin in the hydrogen Lyman continuum. The nebula spectra are consistent with this: PN G214.9+07.8 has a He II [FORMULA]Å line as strong as H [FORMULA] while the [O III ] line is rather weak. This nebula thus is probably optically thin in the He II Lyman continuum as well, like e.g. K 1-27 (Rauch et al. 1994). PN G283.6+25.3 is not so extreme an object with a smaller difference in luminosities, and a lower excitation spectrum (from Kingsburgh & Barlow 1992). The moderate [O III ] intensity is also found in Stenholm's spectrum which lack any indication for He II . Since in all three objects with spectra from both sources one notes that Stenholm's spectra always give lower or absent He II lines, it is most likely that Stenholm's smaller aperture was placed at some bright condensation of lower excitation. Finally, PN G293.6+10.9 shows [O III ] typical for high excitation objects, but lacking He II because of the reasons just mentioned.

The other elliptical nebulae also tend to have quite low required stellar luminosities, and nebula spectra characteristic of high excitation, optically thin nebulae: PN G249.3-05.4 has rather strong [O III ] lines (but no He II) in Stenholm's spectrum, which implies that it might be only moderately optically thin; this would be in accordance with the somewhat high lower limit of 1700 [FORMULA] for the CS. PNe G253.5+10.7 and G324.1+09.0 must be extremely optically thin: the very low required stellar luminosity as well as the very strong He II but fairly weak [O III ] lines clearly indicate this.

There seems to be one exceptional object among the circular nebulae: PN G231.8+04.1 requires about ten times as many ionizing photons as its analyzed CSPN can provide. The nebula spectra are indicative for an optically thin high excitation object (though Stenholm's spectrum probably underestimates the He II line, as before). Critical inspection of the data of this object has not revealed any obvious cause for the seemingly high nebular luminosity. We therefore consider this object to be included in further studies.

The amorphous nebula PN G257.5+00.6 would be rather similar to the elliptical PN G253.5+10.7, if only Stenholm's spectrum would not lack the He II . A clarification must avait the analysis of a good quality long slit spectrum.

Finally, the large, bipolar PN G277.1-03.8 is difficult to analyze in our simple fashion, as the determination of a characteristic angular diameter is not without problems. Thus, the required stellar luminosity cannot be reliably constrained. Stenholm's spectrum would indicate a optically thin high excitation object similar to the circular nebulae discussed above. However, the spectrum of KB is somewhat unusual, in that He II is 1.5 times stronger than H [FORMULA] which indicates a nebula not only optically thin in the He II Lyman continuum but also with a high helium abundance. The former would be difficult to reconcile with the rather strong [O III ] lines. Preliminary attempts to interpret this object with (spherical) photoionization models have so far failed to give even a roughly satisfactory reproduction of the spectrum.

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Online publication: June 18, 1999