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Astron. Astrophys. 335, 421-430 (1998)

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4. Determining the oxygen abundances

The standard method to determine the oxygen abundance in a direct way is described by Osterbrock (1989) and involves determining the electron temperature of the gas in the HII region by measuring the ratio of intensities of the strong [O III ] [FORMULA] lines and the faint [O III ] [FORMULA] line. However, as can be seen in Table 2, this line was detected only with certainty in two of the best spectra (F563-1[2-3] and U5005[2-2]). We will determine the oxygen abundance of these two HII regions using the standard method in Sect. 4.1. For the other spectra the standard method does not suffice and in Sect. 4.2 we will use an empirical oxygen abundance indicator to estimate the oxygen abundances.

4.1. The standard method

We used the FIVEL program (De Robertis et al. 1987) as implemented in the IRAF package to iteratively solve for the electron temperature for the [FORMULA] region and the electron density. We refer to Table 4 for a listing of the relevant values. To determine the temperature the [O III ] [FORMULA] / [O III ] [FORMULA] ratio was used; for the density the [S II ] [FORMULA] / [S II ] [FORMULA] ratio. The values thus derived are consistent with the standard values for a low-density nebula of [FORMULA] K and [FORMULA] cm-3.


Table 4. Oxygen: standard method

The temperature of the [FORMULA] region was calculated using the relationship given in Campbell et al. (1986):


with [FORMULA] expressed in units of 104 K. The FIVEL program was used to calculate the [FORMULA] and the [FORMULA] ratios, given the values of the electron density and the fluxes in the [O II ] [FORMULA] line (which is blended with [O II ] [FORMULA]) and the [O III ] [FORMULA] line. The total oxygen abundance is then given by O/H [FORMULA] [FORMULA].

We thus derive values of log(O/H) [FORMULA] for F563-1 region 2-3, and log(O/H) [FORMULA] for U5005 region 2-2. This should be compared with the empirical values derived for these regions (in the next section) of -3.99 and -3.93 respectively. The empirical values are consistent with the true values within 0.2 dex, which, as we will show in the next section, is the typical uncertainty of the empirical method.

4.2. The strong line method

For spectra where the faint [O III ] [FORMULA] line was not detected the empirical oxygen abundance indicating line ratio R23 was used. This ratio is defined as


Pagel et al. (1979) were the first to investigate the behaviour of this line ratio. The main problem with this empirical method is the calibration: reliable measurements of the faint [O III ] [FORMULA] line have to be available. For our purposes, we will use the calibration and models presented in McGaugh (1991).

For HII regions with low abundances 23 does not depend solely on oxygen abundance, but also on the degree of ionization of an HII region. This degree of ionization is given by the volume averaged nebular ionization parameter [FORMULA], which is defined by


where Q is the ionizing luminosity, N the gas density, and R the distance from the ionizing source.


for constant density models, where [FORMULA] is the Str"omgren radius. [FORMULA] is then essentially the ratio of ionizing photon density to mass density.

In order to distinguish between the different degrees of ionization of the nebulae the ionization sensitive line ratio o32, defined as


is introduced.

This results in a model surface (Fig. 2) defined by contour lines with constant oxygen abundance and ionization parameter, as a function of 23 and o32. The exact position of the grid in the 23-o32-plane depends slightly on the assumed upper mass cut-off [FORMULA] of the IMF. The model presented here assumes [FORMULA].

[FIGURE] Fig. 2. Model grid of McGaugh (1991). The solid lines represent the upper branch; the dashed lines the lower branch. The vertical lines are lines of constant abundance; the horizontal lines of constant [FORMULA], with log [FORMULA] = -4 at the bottom, and log [FORMULA] = -1 at the top. The squares represent the values found for HII regions in our sample.

The oxygen abundance on the upper branch (drawn with solid lines) is relatively independent of the degree of ionization, while on the lower branch (dashed lines) the oxygen abundance cannot be determined reliably without taking o32 into account.

It is clear that most of this model surface is degenerate: once 23 and o32 are determined, there is still a choice between the low-abundance lower branch and the high-abundance upper branch. Especially for low 23 the difference between the two possibilities can be quite large.

The [N II ] [FORMULA] line can be used to find out if a point lies on the upper or lower branch. The ratio [N II ]/[O II ] varies monotonically with abundance, and is not very sensitive to [FORMULA] (see McCall et al. 1985). HII regions with [FORMULA] are on the upper branch. Most HSB spiral HII regions are found there (McCall et al. 1985). If [FORMULA] the HII regions are on the lower branch.

The model surface has a turnover region or fold at [FORMULA] [FORMULA] [FORMULA]. In this region a large change of oxygen abundance corresponds to only a small interval in 23. For HII regions occupying that part of the diagram an at least partly artificial crowding will occur around [FORMULA].

McGaugh (1991) showed that on the upper branch (solid lines; [FORMULA] [FORMULA] or [FORMULA]) the uncertainty in the calibration of [FORMULA] is [FORMULA] dex, and the uncertainty in the calibration of [FORMULA] is [FORMULA] dex. On the lower branch (dashed lines; [FORMULA] or [FORMULA]) the calibration uncertainties are smaller, as the oxygen lines dominate the cooling process. The uncertainty in calibrating [FORMULA] is [FORMULA] dex, and that in [FORMULA] is [FORMULA] dex. To get an idea of the true uncertainties in the abundance determinations, these calibration uncertainties should thus be added to the observational uncertainties (see Sect. 5). For a more complete discussion of the calibration see McGaugh (1991).

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Online publication: June 18, 1998