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Chemical Abundances of Planetary Nebulae in M33

Using spectroscopic data presented in Magrini et al. (2003), we have analyzed with the photoionization code CLOUDY 94.00 (Ferland et al. 1998) 11 Planetary Nebulae belonging to the spiral galaxy M 33. Central star temperatures and nebular parameters have been determined. In particular the chemical abundances of He/H, O/H, N/H, Ar/H, and S/H have been measured and compared with values obtained via the Ionization Correction Factors (ICFs) method, when available. Chemical abundance relationships have been investigated; in particular, a correlation between N/H and N/O similar to the Galactic one (Henry 1989), and a feeble anti-correlation between O/H and N/O have been found. A gradient in O/H across the disc of M~33 is indicatively consistent with the one found from HII regions in this galaxy (Vilchez et al 1988). Further studies in the more external parts of M~33 are however needed to ascertain this point. The present result shows that oxygen and helium abundances (with lower accuracy also nitrogen, argon and sulphur) can be actually estimated from the brightest PNe of a galaxy, even if the electron temperature cannot be measured. We also found that the oxygen abundance is quite independent of the absolute magnitude of the PN and consequently the brightest PNe are representative of the whole PN population. This represents an important tool to measure the metallicity of galaxies at the time of the formation of PNe progenitors.


Introduction
Chemical abundances in extragalactic Planetary Nebulae (PNe) have been derived so far only in a small number of galaxies. Inside the Local Group they are: the irregular galaxies LMC, SMC (cf. Leisy et al. 2000;Jacoby & De Marco 2002), and NGC 6822 (Richer & McCall 1995), the dwarf spheroidal and spheroidal galaxies Fornax (Maran et al. 1984), Sagittarius (cf. Walsh et al. 1997), NGC 185, andNGC 205 (Richer &McCall 1995), the elliptical galaxy M 32 (Stasinska et al. 1998) and finally the two spiral galaxies M 31 and M 33 that have been studied by Jacoby & Ciardullo (1999, hereafter JC99) and Magrini et al. (2003, hereafter M03), respectively. There is a substantial lack of information about chemical abundances of PNe in dwarf irregular galaxies of the Local Group (e.g. Sextans B. Sextans A, Leo A, IC 10), where no PN has been investigated so far. Outside the LG, only PNe in the giant elliptical galaxy NGC 5128 (Centaurus A) at the distance of 3.5 Mpc were analyzed by Walsh et al. (1999).
In most of the previous cases, with the exception of NGC 5128, the abundances have been obtained by direct determination of the T e , derived from the [O iii] λλ 4363/5007 A or, in the worst cases when the λ 4363Å is not measured, using its upper limit, thus obtaining lower limits for the [O iii] ionic abundance and then for the total O abundance, which was calculated from the ICFs (Ionization Correction Factors) procedure (cf. e.g. Kingsburgh & Barlow 1994, hereafter KB94).
In M 31, in addition to the ICFs method, JC99 have modeled the observed PNe using the photoionization code CLOUDY 90 (Ferland et al. 1998) with simplified assumptions: blackbody central stars and spherical nebulae with constant density. They have derived abundances and central star parameters for 15 PNe of M 31. In eight cases they could compare the results from the nebular models built with CLOUDY with abundances based on the ICFs method. They found good agreement between abundances derived with these two different methods. From this comparison, CLOUDY resulted to be a useful tool to measure chemical abundances, particularly when direct electron temperature measurements are not available.
M03 studied 48 emission line objects in M 33 spectroscopically, and recognized, via diagnostic diagrams, 26 of them to be bona fide PNe. They presented the observed fluxes for 42 of the 48 objects, deriving chemical abundances with the ICFs method for the three brightest PNe.
In the present paper, we re-analyze with CLOUDY 94.00 (Ferland et al. 1998)  already studied with ICFs by M03 are also included, in an effort to clarify their observed low N/O.
In Section 2 we summarize the observations and data reduction. In Section 3 the derivation of nebular and stellar properties is illustrated. In Section 4 we discuss the derived quantities and correlations among them. Summary and Conclusions are in Section 5.

Observations and data reduction
The observations were taken at the 4.2 WHT telescope (La Palma, Spain) in October, 2001 with AF2/WYFFOS, with a setting producing a dispersion of 3.0Å per pixel in the spectral range 4300Å to 7380Å. A detailed description of spectroscopic data and of the reduction procedure are in M03.  strength. Therefore the assumption of BB central stars might introduce uncertainties in the determination of chemical abundances. We will also check in the next sections in a specific case the BB assumption vs. the use of a model atmosphere. We will see that differences in resulting abundances are quite small.
The aim of our procedure is to match the intensity of the observed emission lines with that predicted by CLOUDY. The spirit of our procedure is similar to the one adopted by JC99 to determine the chemical abundances of PNe in M 31. In the following we briefly describe how our analysis works.
CLOUDY needs the following input parameters: the central star energy distribution and luminosity, the nebular geometry, the electron density, and the chemical abundances.
Because of the lack of information in our objects on the morphology and on the density distribution, we set the geometry to be spherical and the density to a constant value, although we will explore the effect of a r −2 density distribution in some PNe. The central star energy distribution was set to that of a BB. For the three PNe (PN91, 93, 101) with the best S/N spectra and with chemical abundances derived also with the ICFs method (M03), we will compare nebular abundances from the blackbody central star with those from the model atmospheres by Rauch (2003) (see Table2).
The first run is done setting the input parameters as follows. We varied the external radius from 10 16 cm (0.0032 pc) to 10 18 cm (0.32 pc). This range corresponds to a reasonable interval of sizes of Galactic PNe. The electron density is evaluated from the [S ii] λλ6717/6731 line ratio. We have assumed the average non-Type I galactic PNe abundances from KB94 as initial chemical abundances and dust grains, with composition and size considered to be typical of Galactic PNe dust (cf. Ferland 1998). The addition of dust in the model does not vary substantially the derived chemical abundances.
Further iterations make the following adjustments. First the BB T ⋆ is altered to match the He i/He ii line ratio. When the He ii λ4686 line was too weak to be measured, we determined its upper limit so as to derive an upper limit to the central star temperature.
These cases correspond to T ⋆ marked with b in Table 1 In the other cases, models with different nebular radii were built. For these PNe, we found the smallest and the largest radius for which the model converged. Final quantities are the averages of quantities from models spanning over these nebular radius intervals (cases marked with d in Table 1).
1 Gurzadyan (1988) indeed distinguishes between low and high excitation objects. We prefer to use the term 'medium' in place of low because when the He ii λ4686 line is measured, the excitation cannot be really regarded as low. We think this specification is more appropriate to PNe where the line is not detectable.  1983). When the central star temperature is derived from the upper limit of the He ii λ4686 line, only upper limit to the helium and other metal abundances can be derived.
The derived central star temperatures and nebular quantities are shown in Table 1.
We recall that the T ⋆ derived from the upper limit of the He ii λ4686 are marked with b, whereas the directly measured T ⋆ are marked with a. Derived nebular radii are marked with c, and upper limit nebular radii with d.
In Table 2

Chemical Abundances
We have applied the procedure above described to 11 PNe of M 33. In four cases we could determine the temperature of the central star within 5,000 K using He i and He ii lines. In the remaining cases we estimated an upper limit to the central star temperature  Table 1. Chemical abundances previously obtained for the three PNe with the ICFs method (M03) are shown in Table 2 together with the new determinations, both with BB and model atmosphere (Rauch 2003  PNe whose T ⋆ could be measured, see  considering the same distance. The Pearson correlation coefficient for our relationship is 0.6. ON the other hand our result is quite dependent on a single PN (n. 8). Therefore the study of more PNe at high galactocentric distances is needed to clarify this aspect.
In Figs. 5c and 5d the relationship between N/O and N/H are presented. In Fig. 5c the dashed line represents the correlation found by Henry (1990) for the Galactic PNe.
Our data, shown in Fig Fig.6). The sample of Milky Way PNe consists of objects in common between PNe whose chemical abundances have been re-determined by P04 and PNe whose distances have been recently obtained by Phillips (2002), whereas the LMC sample consists of PNe with chemical abundances and relative fluxes from the work of Leisy & Dennefeld (2004), and the absolute fluxes from Jacoby et al. (1990). (as from any PN) is representative of the total PNe population. This is particularly useful when deriving chemical abundances from PNe belonging to external galaxies, where only the brighter tip of their luminosity function is observed. luminosity is clearly independent of the oxygen abundance. Therefore it is possible to use every PN, and particularly the brightest PNe, in external galaxies as representative of the whole PN population.