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Astron. Astrophys. 322, 975-981 (1997)

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4. Chemical analysis

4.1. Extinction, density and temperature

Fluxes have been de-reddened using the extinction law of Mathis (1990) with [FORMULA] =3.1. The logarithmic extinction constant [FORMULA] has been determined, in each of the selected regions, from the Balmer decrement in the relative averaged spectrum. They are listed in Table 2. At the centre, [FORMULA] [FORMULA] 0.27, in good agreement with previous optical and radio determinations (Torres-Peimbert & Peimbert 1977; Cahn et al. 1992; Tylenda et al. 1992).

The electron densities [FORMULA] have been computed from the [SII]673.1/671.7 intensity ratio, and electron temperatures from the [OIII] 495.9/436.3 and [NII] 658.3/575.5 ratios. The atomic data used throughout this paper are the same as in Kingsburgh & Barlow (1994, hereafter KB94). The computed density and temperature profiles of IC 4406 are shown in the upper panels of Fig. 2, and listed in Table 3 with their errors. At the centre, [FORMULA] =860 cm-3 decreasing in the outer parts to [FORMULA] 100 cm-3 (note that in p3 and n3 the [SII] ratio approaches its low density limit, where it is no longer sensitive to density variations). [FORMULA] and [FORMULA] have a constant value, within errors, around [FORMULA] throughout the nebula. In regions n3 and p3 the [OIII] [FORMULA] 436.3 line is not detected, and [FORMULA] is assumed to be the same as in the neighbouring positions.

[FIGURE] Fig. 2. Density, temperature, and abundance profiles for IC 4406. [FORMULA] and [FORMULA] are indicated by filled and open circles, respectively (open squares are adopted [FORMULA]). Symbols are plotted slightly displaced in d in order to avoid overlapping. In the lower panels, ionic and total abundance profiles for He, O, N, Ne, Ar, and S are shown. The explanation of the symbols used is given in the Legenda at the bottom of the figure. Above the uppermost boxes, the limits of the regions into which the slit was divided are indicated by horizontal "errorbars".


Table 3. Electron density and temperature in IC 4406. In brackets are adopted temperatures.

4.2. Chemical abundances

Given the temperatures and densities, the ionic abundances relative to hydrogen in each of the selected regions are computed from the line fluxes relative to H [FORMULA]. The concentration of He ions relative to hydrogen has been derived from the usual recombination lines assuming case B with the effective recombination coefficients from Hummer & Storey (1987) for HeII and H [FORMULA] lines and from Brocklehurst (1971) for the HeI lines. Corrections of the HeI lines for the effect of collisional population of their upper states via excitation from the 23 S metastable level was evaluated using the prescriptions by Clegg (1987). Owing to the low densities, this contribution was found to be below 1-3  [FORMULA] and consequently no correction for the effect has been applied.

Errors on the ionic abundances from a single spectral line are derived by taking into account both the errors in the line ratios and those on the adopted temperature. To obtain the total abundances, the ionization correction factors (icf) from KB94 are used. Errors on the total abundances are obtained by propagating the errors on the mean ionic abundances as well as on the icf. Ionic and total abundances are listed in Table 4. Abundance profiles are shown in Fig. 2. We discuss the results for the different elements separately.
Helium. The He/H abundance is constant throughout the nebula around the value of 0.125 except for the extreme positions n3 and p3 where it apparently increases to [FORMULA] 0.15. Owing to the to larger errors in the outer positions, we cannot conclude that the effect is real. A confirmation by further observations would be however in order, considering the important implications of such a result. The mean He/H abundances throughout the nebula, obtained by weighting the determinations in the different positions with both their errors and a "mass" factor (proportional to the square root of the total H [FORMULA] flux from that region), is 0.126 [FORMULA] 0.015.
Oxygen. We measure a substantial amount of O0 particularly in the outer parts of the nebula. On the other hand, where O0 is abundant, the same could be inferred of the neutral hydrogen. Excluding O0 in the computation of the total O/H abundance, therefore, is to some extent compensated by the fact that also the neutral hydrogen is not taken into account. We have then derived the total O/H abundance by the formula [FORMULA] = [FORMULA] icf, as done by KB94, where icf (O) accounts for the contribution of the ionization stages higher than [FORMULA]. In this way, the total oxygen abundance results to be constant throughout IC 4406, with an average value of is 5.60 [FORMULA] 1.26 ([FORMULA] 10-4).
Nitrogen. Similarly to oxygen, the N/H total abundance is constant throughout the nebula. The weighted mean of N/H is 2.01 [FORMULA] 0.87 ([FORMULA] 10-4), and the average [FORMULA] (which is constant within 8 [FORMULA] throughout the seven positions). Both are quite modest values for bipolar PNe (CS95).
Neon, argon and sulphur. The situation for these elements is less clear. While the ionic abundances do not show dramatic variations along the nebulae, when icf are applied a significant increase of the total abundances toward the external regions appears. The effect, although systematic in the three elements, remains within the estimated errors for Ne and Ar, while it is larger than the errors for sulphur. Note that the sum of the argon abundances in three different ionic stages (Ar [FORMULA] [FORMULA] Ar [FORMULA] [FORMULA] Ar [FORMULA]) is on the other hand pretty constant. We then suspect that the used icf, in particular for sulphur, do not correctly describe the ionization structure of the nebula. The weighted means of Ne/H and Ar/H are 1.68 [FORMULA] 0.70 ([FORMULA] 10-4) and 3.19 [FORMULA] 1.12 ([FORMULA] 10-6), respectively.


Table 4. Chemical abundances of IC 4406. In brackets are the [FORMULA] errors on the total abundances.

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998