3 Line intensities and reddening

Tables 6 to 9 (at end) list the adopted reddening-corrected line intensity ratios and reddening values for the planetary nebulae in M 32 and the bulge of M 31. We use the object designations from Ciardullo et al. (1989). The line intensities were measured using the software described by McCall et al. (1985). The uncertainties quoted for the line ratios are $1\sigma$ uncertainties that incorporate the uncertainties in both the line and H$\beta$ fluxes. The uncertainties in the line fluxes include contributions from the fit to the line itself and from the noise in the continuum. In those instances where there is no line intensity value, but there is a line intensity uncertainty, e.g., He II$\lambda$4686 in PN5 in M 32, the uncertainty" is a $2\sigma$upper limit to the strength of undetected lines, and is based upon the noise observed in the continuum. Note that PN4 and PN17 in the M 32 field have radial velocities indicating that they belong to the background disk of M 31 (Ford & Jenner 1975). The H II region in the background disk of M 31 that we observed in the M 32 field is that denoted H II 1 by Ford & Jenner (1975).

  

Table 9: Line intensities for PNe in the bulge of M 31

For the planetary nebulae in M 32, Tables 6 to 8 list the reddening-corrected O300, B600, and U900 line intensities, in addition to our adopted line intensities. The adopted intensities are those listed under the object name. Generally, we adopted the U900 line intensities in the blue and the O300 line intensities in the red, with the dividing line being He II$\lambda$4686. He II$\lambda$4686 is the only common exception to this rule. For He II$\lambda$4686, we normally chose the line intensity from the spectrum in which the line was measured with the lowest relative error.

The reddening-corrected line intensities in Tables 6 through 9 are related to those we observed via

$$\log\frac{I\left(\lambda\right)}{I\left({\mathrm H}\beta\rig... ...t(A\left(\lambda\right) - A\left({\mathrm H}\beta\right)\right)$$

where $F(\lambda)$ and $I(\lambda)$ are the observed and reddening-corrected line intensities, respectively, E(B-V) is the reddening, and $A(\lambda)$ is the extinction for E(B-V)=1.0mag from the reddening law of Schild (1977). All of the line intensities for the planetary nebulae in M 32 in Tables 6, 7, and 8 have been corrected for reddening using E(B-V) determined from the O300 H$\alpha/\mathrm{H}\beta$ ratio. For the U900 spectra that did not extend to H$\beta$, we corrected intensities relative to H$\gamma$ using the O300 reddening, then adopted $I(\mathrm{H}\gamma)/I(\mathrm{H}\beta)=0.47$. For the planetary nebulae in the bulge of M 31, we determined the reddening from the H$\alpha/\mathrm{H}\beta$ ratio in the two cases when it was available, but used the reddening calculated from the $\mathrm{H}\gamma/\mathrm{H}\beta$ ratio otherwise. In all cases, we assumed intrinsic ratios of $I(\mathrm{H}\alpha)/I(\mathrm{H}\beta)=2.85$ and $I(\mathrm{H}\gamma)/I(\mathrm{H}\beta)=0.47$, which are appropriate for an electron temperature of 10⁴K and an electron density of $10^4\,{\rm cm}^{-3}$ (Osterbrock 1989). The reddening uncertainties reflect the $1\sigma$ uncertainties in the H$\alpha$ or H$\gamma$ line intensities.

Note that the line intensities for PN408 in M 31 are not corrected for reddening. For this faint object, we did not detect H$\gamma$, and H$\alpha$ fell outside our spectral window.

Since our reddenings are based upon different line intensity ratios for different objects, we consider them in greater detail before proceeding. All of our H$\alpha$- based reddenings in Tables 6 through 9 are positive. The overwhelming majority of our H$\gamma$-based reddenings in Table 9 are also either positive or consistent with no reddening, but our $1\sigma$H$\gamma$ line intensity uncertainties do allow negative reddenings in four cases (PN3, PN43, PN48, and PN53). We considered not using H$\gamma$ to determine the reddening, but rejected this option for four reasons. First, for the four planetary nebulae in M 32 for which we measured an H$\gamma$ intensity from the B600 spectrum, the reddening-corrected H$\gamma$ intensity has the expected value of approximately 47% that of H$\beta$ after correcting for reddening using the O300 H$\alpha$ intensity. In these four cases, then, H$\alpha$ and H$\gamma$ would yield similar reddenings. Second, our ultimate aim is to calculate electron temperatures and oxygen abundances from these line intensities. If we measured the intensity of [O III]$\lambda$4363 relative to H$\gamma$ and [O III]$\lambda\lambda$4959, 5007 relative to H$\beta$, and assumed $I(\mathrm{H}\gamma)/I(\mathrm{H}\beta)=0.47$,we would obtain final intensities for the [O III] lines that would be statistically indistinguishable from those obtained by correcting for reddening using the H$\gamma$ intensity. Applying a negative reddening correction does affect the oxygen abundance we derive by reducing the [O II]$\lambda$3727 intensity, but this effect has less impact on the oxygen abundance than the uncertainty in the electron temperature since there is so little oxygen in the form of O⁺. Third, forcing $I(\mathrm{H}\gamma)/I(\mathrm{H}\beta)=0.47$ via a reddening correction, even if negative, accounts for any errors in the sensitivity calibration that might otherwise systematically affect the [O III] lines and the subsequent oxygen abundances. Fourth, on average, our H$\alpha$- and H$\gamma$-based reddenings agree. The mean H$\alpha$-based reddening for all objects (both M 31 and M 32) is $E(B-V)=0.18\pm 0.04$mag, while the mean H$\gamma$-based reddening for all of the planetary nebulae in the bulge of M 31 is $E(B-V)=0.18\pm 0.08$mag, if negative reddening values are included, or $E(B-V)=0.25\pm 0.06$mag, if negative reddening values are set to zero (the uncertainties are the standard errors in the means). Thus, the reddenings computed from H$\alpha$ and H$\gamma$ are similar. For comparison, the foreground reddening to M 31 is $E(B-V)=0.093\pm 0.009$mag (mean of McClure & Racine 1969; van den Bergh 1969; and Burstein & Heiles 1984). It is not surprising that the mean reddening for the planetary nebulae is 0.10mag greater than the foreground value, for planetary nebulae suffer additional reddening due to internal dust and dust within M 31 and M 32. Consequently, we have chosen to correct for reddening" even when E(B-V) is negative.

Tables 4 and 5 present the electron temperatures and the oxygen abundances for the planetary nebulae in M 32 and in the bulge of M 31, respectively. We only observed two ionization stages of oxygen, O⁺ and O⁺⁺. We accounted for unseen stages in our oxygen abundance calculations using the ionization correction factors (ICF) computed according to the prescription of Kingsburgh & Barlow (1994), which employs the line intensities of He II$\lambda$4686 and HeI$\lambda$5876 to correct for unseen ionization stages of oxygen. Further details may be found in Stasinska et al. (1998). Tables 4 and 5 present two oxygen abundance calculations. The abundances in Col. 3 are simply the sum of the O⁺ and O⁺⁺ ionic abundances. The abundances in Col. 4 are those from Col. 3 corrected for the ICF. The ICF is normally small because He II$\lambda$4686 is weak. The oxygen abundances in Col. 4 will be adopted in future work.

In calculating the oxygen abundances, we assumed an electron density of $4000\,{\rm cm}^{-3}$ in all cases. With electron densities of $1\,{\rm cm}^{-3}$ and $2\,10^{4}\,{\rm cm}^{-3}$,the oxygen abundance changes by a maximum of - 0.02dex and +0.07dex, respectively, for the planetary nebulae in M 31, and by a maximum of - 0.03dex and +0.11dex, respectively, for the planetary nebulae in M 32.

In instances where only upper limits to intensities were available, we adopted the following approach. When we had upper limits for the intensities of the helium lines these limits were used to calculate the ICF. If we did not observe He I$\lambda$5876 (because it was outside our spectral window), we made no correction for unseen stages of oxygen regardless of the intensity of He II$\lambda$4686. (Only in two cases, PN29 and PN30 in M 31, did we detect He II$\lambda$4686 when He I$\lambda$5876 was outside our spectral window.) When we only had an upper limit to [O III]$\lambda$4363, we used this to derive an upper limit to the electron temperature, and this temperature limit was then used to derive a lower limit to the oxygen abundance. In these instances, we did not compute an error for either the electron temperature or the oxygen abundance, and have indicated the results listed in Tables 4 and 5 as limits. When we had an upper limit for [O II]$\lambda$3727, we adopted this limiting intensity for the line. In this case, the O⁺ ionic abundance is over-estimated, but its contribution to the total oxygen abundance was normally small.

Our uncertainties for the electron temperatures and oxygen abundances reflect the uncertainties in the [O III] line intensities alone. As noted earlier, reddening introduces a further uncertainty through its effect upon [O II]$\lambda$3727, but this has less influence upon the oxygen abundance than the uncertainty in the electron temperature. The electron temperature uncertainty that we quote is simply the temperature range permitted by the ($1\sigma$) limiting values of the [O III] line intensities. Similarly, our oxygen abundance uncertainties are derived from the abundances calculated using the extreme values of the electron temperature.