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Astron. Astrophys. 342, 395-407 (1999)

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6. Photoionization models

In order to estimate the ionization state of the absorbing clouds, photoionization models have been calculated using Ferland's program CLOUDY (Ferland 1993). The absorber clouds were modelled as plane-parallel slabs of constant density, illuminated on one side by the ionizing radiation field. Solar abundances specified by number relative to hydrogen as given by Gehren (1988) were used: He: 0.1, O: 8.32 10-4, C: 4.68 10-4, N: 9.77 10-5, Mg: 3.98 10-5, Si: 3.72 10-5, Fe: 3.39 10-5, S: 1.86 10-5, Ar: 6.31 10-6, Al: 3.16 10-6, Ca: 2.29 10-6, Na: 2 10-6, Ni: 1.78 10-6. The solar neon abundance 1.26 10-4 from Grevesse & Anders (1989) was chosen instead of the uncertain Ne abundance 6.3 10-5 given by Gehren (1988).

For the intensity of the ionizing background at the Lyman limit Haardt & Madau (1996) found from model calculations 4 10-22 erg s-1 cm- 2 Hz-1 sr-1 at [FORMULA], while Bechtold found 3 10-21 erg s-1 cm- 2 Hz-1 sr-1 (Bechtold 1994) for [FORMULA] using the proximity effect. We adopt throughout log [FORMULA] erg s-1 cm- 2 Hz-1 sr-1. If the flux at the Lyman limit is indeed a factor 30 larger as demanded by the proximity effect we have to choose a 30 times higher density resulting in smaller cloud sizes.

The H I column density was fixed to the value derived from Si II (see Sect. 5) and the total hydrogen density was varied until the best agreement with the column density ratios was found.

We tried several radiation fields: a) a simple power law with [FORMULA] (model M1), b) the radiation field calculated by Haardt & Madau (1996) at [FORMULA] (model M2) or c) a power law with [FORMULA] and a break by a factor of 10 at the He II ionization edge to account for absorption by intervening absorber systems (model M3; see Fig. 5). C, Si and Al abundances were chosen individually dependent on the radiation field.

[FIGURE] Fig. 5. Radiation fields adopted in the photoionization models. The solid line represents a power law with [FORMULA] and a break by a factor of 10 at the He II ionization edge (model M3). The dashed line is a simple power law with [FORMULA] (model M1). The dotted line yields the radiation field calculated by Haardt & Madau (1996) at [FORMULA] (model M2). J is given in erg s-1 cm-2 Hz-1 sr-1.

6.1. Description of model results

6.1.1. Results on carbon, silicon and aluminum

In Table 2 model results for the different radiation fields are compared with the observed column densities. Errors in the derived column densities as given by FIT/LYMAN are normally in the range from 0.02-0.12 dex, but larger variations might exist between different fit results for a single line. For the "low ionization" components 3 and 6 best agreement is found for model M3. The Haardt & Madau (1996) model (M2) is too soft and does not produce enough C IV . The simple power law with [FORMULA] overestimates Si III and Si IV . C and Si abundances are identical for both components ([C/H][FORMULA], [Si/H][FORMULA]), but the Al abundances differ slightly. Since component 2 appears also of low ionization it was fitted with M3 and is well reproduced with the abundances found for component 3. For component 1 the H I column density is unknown, but H I and the hydrogen density have been varied for the radiation field M3 and abundances as given above until the Si II /Si III ratio was reproduced, but then C IV is underestimated. Unless we know the C II column density we are not able to decide between differences in the carbon abundance and the ionizing mechanism.

For the highly ionized components we used the ratio Si II / Si IV to constrain the hydrogen density. The carbon abundance was then varied until the observed C IV column density was reproduced. For component 9 best agreement is found for model M2. The carbon abundance is slightly smaller than found for the components of low ionization, but the Si abundance is identical. Also, the better representation of C II favours the radiation field as calculated by Haardt & Madau (1996). For component 10 the same parameters yield satisfactory agreement for Si II and C IV , but a too small Si IV column density. However, the observed value of Si IV is quite uncertain. Nearly similar results are obtained for the radiation field M3 when adopting lower C and Si abundances. The relative abundances [Si/C] obtained for the latter model are then larger by a factor of [FORMULA]. For component 11 we find similar results as for component 10. As can be seen in the calculation for component 9 the simple power law with [FORMULA] (model M1) has problems in reproducing the Si IV column density.

Components 4, 5, 7 and 8 of intermediate ionization are also best reproduced adopting model M3 but with different abundances [C/H] and [Si/H]. For components 4 and 5 model M1 is overestimating Si III .

Components of low and intermediate ionization (components 2 to 8) show a smaller Si overabundance relative to C ([Si/C][FORMULA], 0.16, 0.23, 0.28, 0.32) in comparison to 0.5 for the highly ionized components. If all components were ionized by the same radiation field (model M3) the [Si/C] overabundance would be even larger for the highly ionized components. The aluminum abundance is nearly the same for all models. It was varied between [Al/H][FORMULA]0.97 and -1.17 in order to reproduce the observed Al II column density with the exception of component 8, where [Al/H][FORMULA]1.3/-1.34 had to be chosen. No overabundance of Al with respect to C is found, but no measurements of Al II are available for the highly ionized components. However, a 3 [FORMULA] upper limit for the Al II equivalent width of component 9 yields [Al/H][FORMULA] and thus [Al/C][FORMULA]. The derived Al abundances agree well with the results found for Halo stars: no overabundance of Al relative to Fe is found at [Fe/H][FORMULA] and the ratio [Al/Fe] is decreasing with decreasing [Fe/H] while Si is overabundant relative to Fe with a mean ratio [Si/Fe] of 0.5 (McWilliam et al. 1995).

6.1.2. Results on oxygen, nitrogen and sulphur

Abundances of N, O, S and Ne are in principal constrained by absorption lines observed in the ultraviolet. Due to the low resolution we could not derive individual abundances, but adopted instead common values for all components. As mentioned above all neon lines are located in strong blends, thus, the neon abundance was set to [Ne/H][FORMULA]0.7 as found for [Si/H] in most components. The oxygen abundance is determined by several O II and O III lines. Only weak absorption is visible for N and S, thus, the resulting abundances are stronger influenced by the chosen continuum level. All other abundances were set to one tenth their solar values.

For comparison of the model results with the HST spectra we need information about the line broadening mechanism. No uniform b-values were found for the different elements. Most reliable b-values or the mean of the measured b-values of carbon and silicon were taken to derive turbulent und thermal velocity parameters. For components 10 and 11 we take the values found for component 9, because the measured values yield no meaningful results. For half of the components (4, 5, 6, 7 and 9) the derived temperatures are then in the range 25 000-33 000 K. These temperatures are consistent with those found in the CLOUDY photoionization calculations. For component 1 we find a very high temperature of 65 000 K, but the silicon b-values are poorly determined. For component 3 and 8 we find very low temperatures of 2000 and 3800 K, respectively, but the b-values are also poorly constrained. For all components we have to introduce an additional turbulent component with values between 2-12 km s-1.

With the parameters derived from the optical data we started the model calculations for all 11 components with very small O, N and S abundances. A UV spectrum is then synthesized from the model results with individual b-values as mentioned above and convolved with the instrumental profile for comparison with the UV observations (see Fig. 4). The observed C III 977 and C II 903.6, 903.9 absorption is well explained by the model parameters derived from the optical absorption lines. The O III 832, O II 833, 834, 832 and O III 702 resonance lines are well reproduced for [O/H][FORMULA]. As can be seen from the 1 [FORMULA] noise level in Fig. 4 O IV 553, 554, O III 507, O II 539.0, 539.5, 539.8 and He I series lines are located in noisy regions with uncertain continuum definitions. This might be the reason why the predicted absorption is slightly stronger than observed. S III 677 is blended with Ly[FORMULA] at [FORMULA] and Si II 989 is blended with Ly[FORMULA] of the MLS at [FORMULA]. S III 724 and S II 765, 764, 763 yield [S/H][FORMULA]. In the presence of dust we expect null depletion for S as it is found in the Galaxy, while Si should be strongly affected. The ratio [S/Si][FORMULA] derived for the low ionization components hints at the absence of noticable amounts of dust.

With [N/H][FORMULA] the predicted absorption is too weak in comparison with the observations, while [N/H][FORMULA] predicts slightly too much absorption in case of N III 685, 685.5, 763 (see Fig. 4). But due to the high line density and the low resolution the continuum level might be underestimated.

With the O abundance determined from the UV absorption lines of O II and O III , our models cannot reproduce the observed O I absorption. In order to explain the O I absorption one has to invoke further mainly neutral components with relatively low H I column densities. Also, the photoionization models do not predict significant absorption by O VI . However, if the observed absorption is indeed O VI there is still the possibility of a collisionally ionized phase as found in our Galaxy. Kirkman & Tytler (1997) favoured collisional ionization for a component with strong O VI and C IV absorption in a LLS at [FORMULA], too. Since for the "highly ionized" components (9, 10 and 11) in the LLS at [FORMULA] we do detect absorption by C II , the observed C IV absorption might be related to both a collisionally ionized and a photoionized phase, thereby making model calculations more difficult.

6.1.3. Results on helium

Absorption lines of neutral helium were first discovered in HST spectra of the UV-bright, high-redshift ([FORMULA]) QSO HS 1700+6416 (Reimers & Vogel 1993). Ultraviolet spectra of the [FORMULA] QSO HS 1307+4617 also reveal He I 584, 537, 522 absorption lines for all LLS with a suitable redshift. We found column density ratios [FORMULA]H I )/[FORMULA]He I ) of 35 to 43 adopting turbulent line broadening and 4 to 10 for pure thermal line broadening, respectively (see Reimers et al. 1998).

Both the absence of knowledge of the splitting into subcomponents and the unknown ionization conditions, however, made it impossible to perform a more quantitative analysis of He I lines, e.g. in terms of the He abundance.

For the LLS discussed here He I resonance series lines up to He I 508 are clearly visible in the UV spectra. In our model calculations for the 11 components we fixed the He abundance He/H to 0.079 ([FORMULA]) and found surprisingly good agreement between the synthesized and the observed spectrum (see Fig. 4), although the predicted absorption is throughout a little bit stronger than the observed one. According to the photoionization models column density ratios [FORMULA]H I )/[FORMULA]He I ) for the components of low and intermediate ionization range from 13.5 to 15 and 16.6 to 18.2, respectively. For the highly ionized components we found ratios of 21, 31 and 35.

It can also be seen from Fig. 4 that in comparison with the synthesized spectrum the observed He I absorption lines all reveal an additional absorption component in the red wing ranging at least up to [FORMULA] km s-1 relative to [FORMULA] km s-1 ([FORMULA]). Also, from Fig. 3 it is obvious that Ly[FORMULA] and C II 1334 absorption is more extended to the red than indicated by the components identified. At [FORMULA] km s-1 we detect absorption which might be related to O I 1302. A Voigt profile fit yields N(H I )[FORMULA] cm-2 and [FORMULA] km s-1 rather indicating a H I Ly[FORMULA] absorption line. A higher signal-to-noise ratio could help to distinguish between multiple O I 1302 absorption lines and Ly[FORMULA] forest absorption.

More quantitative constraints for the He abundance are difficult due to the low signal-to-noise ratio of the spectra. In combination with the blending problem at low resolution it is extremely difficult to reliably determine the continuum level. Having this in mind, the near agreement of model calculations with [FORMULA] with the observed He I series can be considered as fully consistent with the expectation of big bang nucleosynthesis (see Boesgaard & Steigman, 1985). With the planned COS spectrograph on HST there is a chance to really measure the He abundance at [FORMULA].

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© European Southern Observatory (ESO) 1999

Online publication: February 22, 1999