4.1. Contamination with compact HII regions
At the distance of M33, low-excitation PNe can be misidentified with compact HII regions. We used the R=I([O III ])/I(H+[N II ]) line ratio to estimate the possible contamination of HII regions in our sample of candidate PNe. The distribution of R for the 127 objects in Table 2 in which both the [O III] and H+[N II] fluxes have been measured is shown in the upper box of Fig. 3. In the lower box, we show for comparison the distribution of 808 Galactic PNe whose fluxes are quoted in the Strasbourg-ESO Catalogue of Galactic PNe (Acker et al. 1992). The two distributions are very similar for , as expected since HII regions have generally a lower excitation class than PNe. In the sample of M33 there is an excess of objects with as compared to the Galaxy, indicating possible contamination by compact HII regions. Since the percentage fraction of PNe with in the Galaxy is 25 while it raises to 35 in the sample of M33, assuming that the distributions of R are the same in the Galaxy and in M33, we expect that around 15 objects in Table 2 could be in fact HII regions.
4.2. The luminosity function (PNLF)
In recent years it has been shown that the PNLF is a good extragalactic secondary distance indicator (Jacoby 1997).
In order to build the PNLF, we have converted [O III] fluxes into equivalent V-band magnitudes following Jacoby (1989):
We have then estimated the completeness of our sample for the 131 candidate PNe with measured [O III] fluxes. We calculate the signal to noise ratio (S/N) for our candidates. Ciardullo et al. (1987) found a linear relationship between S/N and completeness, putting the limit of completeness at S/N10. This would correspond in our frames to a limiting [O III] magnitude of about 23.
We note a lack of PNe in the central zone and in the densest regions along the spiral arms. This is likely due to the high stellar background in the inner disc/bulge and to the presence of many giant HII regions in the spiral arms, which make difficult to detect PNe. Another effect causing incompleteness is the galactic background emission and the presence of large complexes of HII regions. Faint PNe can be missed because of the bright background of the inner disc, bulge and spiral arms of M33. The bulge of M33 is small, having a characteristic de Vaucouleurs' radius (defined as the radius within which half the total light is emitted) of 110 arcsec (Baggett et al. 1998). Even at much shorter distances from the centre, however, the light from the disc of M33 dominates the galaxy background emission, with its tight spiral-arm design highly populated by HII regions. To avoid this high background and crowded region, we rejected from the study of the PNLF the 6 candidate PNe closer than 180 arcsec from the centre of M33. We also conservatively lowered the limiting magnitude to 22.6 mag, slightly more luminous than the point at which our observational PNLF turns down indicating incompleteness. This magnitude corresponds to a S/N of about 20.
Using the luminosity parameters for M33 derived by Baggett et al. (1998) by means of bulge-disc decomposition of its brightness profile, we expect that the total luminosity of the region of M33 used to build our PNLF comes from the disc. From that, adopting the specific planetary luminosity density for M31 (Ciardullo et al. 1989), we estimate a total of about 180 objects within 2.3 mag from the PNLF cutoff of about 20.3 mag. This figure has to be compared with the 75 candidate PNe that we effectively detected in M33 within the adopted completeness limit.
We applied the Eddington formula (Eddington 1913) to our data in order to correct for the effects of observational errors, and fit the resulting luminosity function for the complete sample of 75 PNe to the "universal" PNLF
In Eq. (2) m is the observed [O III ] magnitude from Eq. (1), and is the apparent magnitude of the PNLF cutoff of M31 (Jacoby 1989).
This sample of 75 objects contains all candidate PNe within the established completeness limits regardless of their R ratio, since we already noticed that a substantial number of PNe are observed in the Galaxy with . Their luminosity function is presented in the upper panel of Fig. 4. In order to check whether exclusion of the objects with large H+[N II] over [O III] fluxes produces some effects on the PNLF, we also fit the theoretical formula to objects with only (Fig. 4, lower panel). Although the amplitude of the PNLF changes somewhat, in both cases we found the same apparent distance modulus of 24.62. This is because the most luminous objects in [O III] have generally also large R values (apart from few, but noteworthy exceptions). In fact, 80% of the candidates in the complete sample have , and if we restrict to the most critical luminosity range of the PNLF of M33, i.e. to magnitudes smaller than 21.6, 90% of the objects have and some 80% have . Thus the shape of the high luminosity tail of PNLF is not changed significantly by excluding objects with low R values, as confirmed by a further test in which we obtain the same results as above by considering objects with only.
The apparent distance modulus need to be corrected for foreground, Galactic reddening (, Burstein & Heiles 1984) as well as for dust extinction within M33. The latter is an important source of uncertainty in the present analysis. Freedman et al. (1991) derived (foreground + internal) for Cepheids in M33. Cepheids, however, are population I objects, and are located close or within the thin dust layer of M33. PNe are instead generally associated with an older disc population; in the Galaxy, for instance, they have a scale height above the disc two or three times larger than the dust layer (cf. Corradi & Schwarz 1995). Then some of our PNe will lie in front of the dust layer of M33 (which is seen relatively face-on), and will have a very small reddening; other objects will instead lie behind it, and will be characterized by a reddening similar (or only slightly larger) to that of the Cepheids. As a consequence, the average reddening for PNe is likely to fall between the foreground value () and that of Cepheids (). The effect is difficult to quantify. As a test, we have computed the PNLF for PNe which are located at a galactocentric distance larger than one scale length of the exponential disc of M33 (530", Baggett et al. 1998). Results obtained for other spiral galaxies (Xilouris et al. 1999) indicate that at such a distance the average, face-on extinction of a spiral galaxy is expected to be lower than 0.35 mag in V, corresponding to . In addition, most of the selected PNe are located in the inter-arm region, where extinction is expected to be even lower. By considering this subsample of PNe which is less affected by extinction within M33, we obtain the same apparent distance modulus as above, suggesting that our results are not strongly affected by dust internal to M33. Lacking of better estimates, we correct the apparent distance modulus using the value indicated by Freedman et al. (1991), and obtain a corrected modulus of . The error is obtained by combining the error associated with our best least mean square fits ( mag) in quadrature with those associated with the photometric zero point (0.03 mag) and the adopted extinction (0.09 mag from Freedman et al. 1991). In addition, two systematic errors come from the uncertain definition of the empirical PNLF (0.05 mag) and the distance of the calibration galaxy M31 (0.10 mag).
All that finally leads to a distance to M33 of kpc in excellent agreement with the value derived from the Cepheids method ( kpc, Freedman et al. 1991).
© European Southern Observatory (ESO) 2000
Online publication: March 9, 2000