5 Discussion

The detailed photoionization model of G29.96 reproduces with good accuracy most of the atomic fine-structure line fluxes and radio flux densities. It allows one to derive the elemental abundances in the gas phase and the properties of the ionizing star(s). In the following, we will investigate how some of the less constrained parameters influence the results and discuss the reliability of the derived abundances.

   
5.1 Effect of the uncertainties of the observed line fluxes on the model parameters

The observed line fluxes are known with 10 to 20% accuracy (Paper I). The effect of these uncertainties on the model are not always linear. For example, changing $r_{[O {\sc iii}]}$ by $\pm$20% changes the electron density of component 1 by ⁺³⁴_-25%. On the other hand, as the stellar effective temperature diagnostics are extremely sensitive (as shown in Fig. 2), any change by $\pm$20% in any of these diagnostic line fluxes will have virtually no effect on the determination of the stellar temperature.

Concerning the number of ionizing photons, the product of the number of stars by the stellar luminosity is directly proportional to the 2 cm flux density.

One of the most critical parameters is the contribution of each component to the total line fluxes. Once the density of component 2 is determined from the 6 cm flux density, the ratio of the covering factors is derived by fitting the Br$\alpha$ line flux. However, this line is sensitive to attenuation and aperture size corrections. As given in Table 2, the nitrogen and oxygen lines are emitted mainly (96 to 99%) by the diffuse component where only 10% of the hydrogen lines emission is observed. Decreasing the observed line flux of Br$\alpha$ by 10% increases the contribution of component 1 from 36% to 48% and the density of component 2 from 5.2 $\times 10^4$ to 9.0 $\times 10^4$ cm^-3. The abundances of N, O, Ne, S, and Ar change by -25, -30, +10, 0,and +20 % respectively.

   
5.2 Filling factor and components geometry

The filling factor allows one to artificially increase the geometrical thickness of the ionized gas. The geometry affects both the low and high ionized species if the thickness of the nebula is of the order of its radius.

As component 1 represents the diffuse gas, a filling factor of 1.0 seems appropriate (the predicted extension of the gas is 35 $^{\prime\prime}$, i.e. comparable to the size of the observed surrounding molecular gas). Lowering this filling factor to 0.5 has an effect on the lines mainly produced by component 1, i.e. [N II] 121.8$~\mu$m, [N III] 57.3$~\mu$m, [O III] 51.8, 88.3$~\mu$m, [S III] 33.6$~\mu$m, and [S IV] 10.5$~\mu$m. The ratio $r_{[O {\sc iii}]}$ remains the same while the [N II] 121.8$~\mu$m/[N III] 57.3$~\mu$m ratio increases by about 15%. A small increase of the effective temperature from 29.7 to 30.1 kK is enough to recover the observed ratio. After the whole convergence process is performed, an increase of the N and O abundances of about 15% is found. Furthermore, as the geometrical thickness of component 1 increases up to 45 $^{\prime\prime}$, the effects of the finite size of the ISO SWS beam are amplified (the [S IV] 10.5$~\mu$m line significantly decreases). No value lower than 0.5, implying greater geometrical extension, would be acceptable.

For component 2, changing the filling factor from 1.0 to 0.5 increases the thickness by a factor of about two. No obvious effect is found on the line fluxes, but the radio flux densities are affected because the self absorption is decreasing with the filling factor. The predicted 6 cm value is then higher than the observed value by 8%, and we have to change the hydrogen inner density of component 2 from 5.2 to 9.2 $\times 10^4$ cm^-3 to recover it. The geometrical thickness of component 2 finally decreases from 1.5 to 1.0 $\times 10^{16}$ cm, the changes due to the filling factor being approximatively compensated by the increase of density imposed by the 6 cm flux density constraint. However, the line fluxes and the element abundances do not change significantly.

Decreasing further the filling factor of component 2 to a value of 0.1 leads to a different behavior. The hydrogen density needs to be increased to 5.5 $\times 10^5$ cm^-3 in order to recover the optical thicknesses of the radio continuum at various frequencies. Such a high density implies a collisional de-excitation of some lines in component 2 (see Paper II for the critical densities of all the lines). Finally, the abundances are greater than those given in Table 2 by 4, 7, 77, 83, 111% for N, O, Ne, S, Ar, respectively. Oxygen and nitrogen are not very affected as these lines are emitted in component 1. The geometrical thickness of component 2 becomes 1.6 $\times 10^{15}$ cm. We could interpret this model as a distribution of very dense, small clumps embedded in the low density medium.

In summary, modifying the filling factor leads to a change of the geometry of the ionized gas. The main effect is on the self-absorption of the radio free-free emission; changing the filling factor is the same as changing the optical depth at the different radio frequencies, in other words, changing the proportion of the gas seen tangentially with respect to the amount of gas seen radially.

Afflerbach et al. (1994) derived a filling factor between 0.03 and 0.4 combining the emission measure obtained from the continuum flux density with the local density obtained from the line-to-continuum ratio. They found high values for the density (some 10⁴ cm^-3) and they considered the gas as included in a sphere: "assuming that the line-of-sight depth is equal to the angular diameter from the continuum images''. In our case, the dense gas is located in a shell (in which the filling factor is $\sim$1.0) with a thickness 1/20 of its radius, leading to a total filling factor for the sphere of 0.13, compatible with the value obtained by Afflerbach et al. (1994). In the model presented in this paper, the gas is distributed in a shell, at fixed radius from the ionizing source. A more complex model could be constructed with a distribution of clouds at various radii, but the new free parameters introduced in such a model could not be constrained by any available observable.

   
5.3 Role of the inner radius

We fixed the inner radius of the H II region to $3\times 10^{17}$ cm, corresponding to 3 $^{\prime\prime}$, about the radio core size (e.g., Fey et al. 1995). This is also virtually the outer radius of the dense component, as the geometrical thickness is 1/20 times the inner radius. Lowering the value to e.g. 10¹⁷ cm will require to decrease the density of component 2 to $2.2\times 10^4$ cm^-3 in order to recover the radio flux densities break between 2 and 6 cm. The geometrical thickness of component 2 is now $\sim$ $2\times 10^{17}$ cm, still compatible with imaging observations. Oxygen and nitrogen abundances must be decreased by 10%. As the density of component 2 decreases, some lines previously de-excited by collisions in component 2 are now emitted: [Ne III] 15.5$~\mu$m and [S IV] 10.5$~\mu$m are predicted to be 3 and 5 times higher than the observed values.

Increasing the inner radius for component 2 will lead to an increase of the density of this component to recover the radio break. As the geometrical thickness will then decrease to less than one percent of the radius (it was 5% for the adopted model, see Table 1), the self absorption at 6 cm does not increase anymore. This is mainly due to the spherical geometry we used for the model. A more complicated geometry than such a thin shell could lead to more self-absorption. We then relax the constraint of the 6 cm flux density and perform a model where the 6 cm predicted flux density can be higher than the observation by some 10%. With a density of $8\times 10^4$ cm^-3 for component 2, and an increase or N, O, Ne, S, and Ar abundances of 12, 12, 24, 30, and 10% respectively, the result is close to the adopted model.

   
5.4 Role of dust

The effect of adding dust in the H II region is to increase the absorption of ionizing photons and to change the shape of the "apparent'' ionizing spectrum. We compared the emitted spectra of the dust to the observed infrared continuum, at wavelengths lower than 20 $\mu$m. At longer wavelengths, the emission is dominated by cold dust from the PDR and the outer H I region, which is not modeled by the photoionization code. We check that, whatever the dust type used (i.e. "astronomical'' silicates, olivines, amorphous carbon or graphite), the modeled emission does not exceed the observational data for any concentration of dust lower than $5 \times 10^{-4}$ (in mass, relative to hydrogen). This represents an upper limit of the amount of dust, as part of the 5-20 $\mu$m emission can be due to high temperature PAH's present in the PDR and behind. With this amount of dust, the models have to be adjust by changing the number of stars from 1.5 to 1.6 and the stellar effective temperature from 29.7 to 29.4 kK, without changes in the abundances. In this "maximum'' dust model, 8% of the incoming energy is absorbed by dust in the H II region, compared to 11% by ions. The relatively small amount of dust derived by our modeling is in agreement with the recent results of Aannestad & Emery (2001) who found that dust in the ionized region of S125 is severely depleted. A more detailed study of the dust emission observed in G29.96, including the H I region, is postponed to a future paper.

   
5.5 Number of stars versus luminosity and age

Figure 2: HR diagram showing the locations of the available CoStar models (crosses) and the four models discussed in text (filled diamonds with corresponding number of stars). The dotted lines show solar metalicity isochrones for ages 0, 1.6, 2.8, 3.5 and 4.0 Myr from left to right, from the tracks of Meynet et al. 1994.

The number of ionizing photons is constrained by the 2 cm radio flux density. It is a degenerated parameter since it is the product of the number of stars by the number of ionizing photons produced by one star. This degeneracy can be explored by changing the luminosity of the individual stars and by adjusting the corresponding value of the number of stars.

If one changes the luminosity of the individual stars, the effective temperature of each star must be changed in order to recover the [N II] 121.7$~\mu$m/[N III] 57.3$~\mu$m ratio. All the fluxes are then reproduced as in the adopted model presented in Table 2 within a few percent. Figure 3 shows in an HR diagram the locations of the available CoStar models (crosses) and the four models retained and discussed here (filled diamonds). The number of stars needed to reproduce the 2 cm flux density is given for each model. Although the range in effective temperature seems small (from 30 to 35 kK), it is large if one considers the strong constraint from the [N II] 121.7$~\mu$m/[N III] 57.3$~\mu$m ratio (see Fig. 2). Along the track between the four models with 1.5, 3.3, 8.6 and 19 stars, the stellar age varies approximatively from 2.8, 3.5, 4.0 to $1.6\times 10^6$ yr. Whatever the exact number of stars involved in the ionization of G29.96, we see that these stars occupy a rather small range in effective temperature (30 to 35 kK) and age (1.6 to 4 Myr). The obtained ages are quite old compared to "classical'' expectations for UCHII regions.

We cannot find a satisfying model corresponding to one single star, as the luminosity will then overstep the CoStar models grid and enter the post main sequence and/or Wolf Rayet (see Fig. 3). Once the temperature is derived from the diagnostic lines ratio [N II] 121.7$~\mu$m/[N III] 57.3$~\mu$m, we used the most luminous star available and multiply its flux by a factor 1.5 to reproduce the radio flux. As we know from NIR observations (see Sect. 2.4) that only one star is the primary source of ionization, we think our model with 1.5 star is better. We can interpret the value of 1.5 star as a consequence of mixing one main ionizing star with one or more lower luminous stars.

   
5.6 Dependence on atmosphere models

The derived parameters of the ionizing source depend on the adopted atmosphere models. Given the limited amount of constraints available on the ionizing fluxes (cf. Sect. 3.2) and the potential uncertainties of the CoStar models especially for cool stars with weak winds (Schaerer & de Koter 1997), we have also tested other non-LTE model atmospheres. A full description is given in Morisset et al. (2002). Here we summarize the main effects.

We have used the recent line blanketed models of Pauldrach et al. (2001) and test calculations for O stars based on the comoving frame code CMFGEN of Hillier & Miller (1998) which both include stellar winds. Spectra from the fully blanketed plane parallel non-LTE TLUSTY models of Hubeny & Lanz (1995) were also kindly made available to us by Thierry Lanz. The comparison of the predicted IR fine-structure line ratios with observations from the sample of Paper I and II shows that a consistent fit of all four ratios ([N  III]/[N  II], [Ar  III]/[Ar  II], [S  IV]/[S  III], [Ne  III]/[Ne  II]) within a factor of two is only obtained with the CoStar models. The scatter in the effective temperature determined with the CoStar models is due to the [Ar  III]/[Ar  II] ratio, which have a similar ionization potential than [N  III] (29.6 and 27.6 eV respectively), showing a potential problem in either the observed line fluxes, the attenuation correction process, or in the atomic data. The other three excitation ratio, tracing ionizing photons between 27.6 and 40.1 eV, are in a very good agreement.

Using the extreme excitation ratio of [N  III]/[N  II] and [Ne  III]/[Ne  II], we estimate effective temperatures of $\sim$32-35, 33-38 and 34-38 kK, using the models CMFGEN of Hillier & Miller (1998), TLUSTY of Hubeny & Lanz (1995), and WM-Basic of Pauldrach et al. (2001) respectively, while the same ratio leads to lower and less scattered effective temperatures (29.5-30.5 kK) using the CoStar models (see Fig. 2).

   
5.7 Other constraints and comparison with earlier studies of the exciting star

Various estimates of the properties of the dominant ionizing star of G29.96-0.02 have been obtained from the following observations/methods:

1.

the bolometric luminosity L, estimated from IR or multi-wavelength observations

2.

the photon flux in the Lyman continuum $N_{\rm Lyc}$ assuming a single star,

3.

the ratio $N_{\rm Lyc}/L$ for a stellar cluster,

4.

IR line ratios through nebular modeling,

5.

the He⁺ abundance derived from radio recombination lines,

6.

near-IR photometry, and

7.

K-band spectral classification of the central source.

The estimated spectral types quoted in the literature reach from O3 to O9.5 (e.g., Lacy et al. 1982; Doherty et al. 1994; Simpson et al. 1995; Afflerbach et al. 1997; Watson et al. 1997; Kaper et al. 2002). However, these estimates are partly based on incompatible hypothesis such as different assumptions on the source distance and different spectral type vs. $T_{{\rm eff}}$ calibrations. Furthermore only unevolved zero age main sequence (ZAMS) stars were considered in most cases, in conflict with recent evidence (Afflerbach et al. 1997, this paper). For these reasons we here briefly rediscuss these estimates using also up-to-date stellar models and homogeneous assumptions. In particular all observational constraints are scaled to a distance of 6 kpc (cf. Sect. 2.3). As $T_{{\rm eff}}$ is the physically most important parameter - independently of the exact spectral-type vs. $T_{{\rm eff}}$ relation - we essentially derive the constraint on this parameter.

1) The total bolometric luminosity of G29.96 obtained from the 12-100 $\mu$m IRAS flux and its overall SED in an arcminute sized region is $\log L/L_\odot$ $\sim$ 5.90 (Paper I, Afflerbach et al. 1997). Likely the major fraction of it is due to the main ionizing source (cf. Afflerbach et al. 1997, and below). Using the calibrations of Schmidt-Kaler (1982) yields the following $T_{{\rm eff}}$ : $\sim$44 kK (for luminosity class V), 41 kK (LC III), 37 kK (LC I). From Vacca et al. (1996) one obtains: $\sim$48 kK (LC V), 45 kK (LCIII), 36 kK (LC I). A very wide range of $T_{{\rm eff}}$ ( 20 kK to 50 kK) is allowed for main sequence stars with the given luminosity, as shown in Fig. 3. These $T_{{\rm eff}}$ represent upper limits as other stars contribute to the total bolometric (cf. below).

2) The ionizing photon flux derived for G29.96 from radio emission is $\log(N_{\rm Lyc}) \sim$ 49.-49.14 s^-1(Fey et al. 1995; Kim & Koo 2001). A somewhat higher value of $\log(N_{\rm Lyc}) \sim$ 49.29 was derived by Afflerbach et al. (1997) from the extinction corrected Brackett-$\gamma$ map. Based on the Vacca et al. (1996) calibrations this corresponds to $T_{{\rm eff}}$ $\sim$ 40-43 kK (LC V), 35-38 kK (LC III), and 30-32 kK (LC I). Similarly, the stellar models of Schaerer & de Koter (1997) (based on the tracks shown in Fig. 3) reproduce the observed $N_{\rm Lyc}$ for a temperature range between $\sim$30 and 46 kK, depending on the evolutionary state.

3) Given the obvious importance of small number statistics for the number of massive stars observed in the cluster associated with G29.96 (see Afflerbach et al. 1997; Pratap et al. 1999) standard evolutionary synthesis models cannot be used for comparisons of $N_{\rm Lyc}/L$(Cerviño et al. 2000). However, an analysis of the resolved stellar content provides further insight. As discussed by Afflerbach et al. (1997); Pratap et al. (1999) we have taken the objects with $H-K \ge 1.$ as cluster members. Assuming a mean extinction A_H=3.6 (Afflerbach et al. 1997) and using the synthetic photometry of Lejeune & Schaerer (2001) we have determined from the H-band magnitude m_H the luminosity of the individual stars assuming all members to be on the same isochrone with ages between $\sim$0 and 4 Myr. From this we derive the fraction of L provided by the ionizing star, which is found to be $\sim$70-50% for ages 0-4 Myr. A somewhat smaller fraction (70-30%) is found using m_K (and A_K=2.14). This quantitative estimate confirms the expectations of Afflerbach et al. (1997) of a contribution of at least 50% from the ionizing star to L. Correcting for $\sim$50% of L due other cluster members and assuming that one star dominates the ionization, we obtain a revised $N_{\rm Lyc}/L$ of the ionizing star which should be comparable to predictions for single stars. The comparison with the stellar models used earlier yields $T_{{\rm eff}}$ between $\sim$31 and 38 kK.

4) Simpson et al. (1995) and Afflerbach et al. (1997) used line measurements from KAO and photoionization models including plane parallel LTE Kurucz model atmospheres. Their analysis (method 4) yields $T_{\rm eff}=$35.7 and 37.5 kK respectively, rather similar to our values derived with different atmosphere models, but larger than the value obtained with the CoStar atmosphere models. The main difference with their result likely originates from the use of more sophisticated model atmospheres.

5) The He⁺/He ionization fractions derived for the best model presented in Table 2 are 50% (35%) for Component 1 (2) respectively, slightly lower than the values obtained by Kim & Koo (2001): 68 to 76%. Using hottest stars with CMFGEN at 33 kK and WM-Basic at 36 kK atmosphere models, we found He⁺/He to be 60% (48%) and 77% (68%) respectively, in better agreement with the value obtained by Kim & Koo (2001) (but see the discussion on the Xⁱ⁺¹/Xⁱ ratios for Ar, Ne, N and S in Sect. 5.6).

6) From photometric observations and constraints on the total luminosity of G29.96 (Afflerbach et al. 1997) derive an allowed temperature range for the ionizing star of $T_{{\rm eff}}$ $\sim$28-37 (23-43) kK for 1 (3) $\sigma$ uncertainties valid for source distances between approx. 5-9 kpc. Our above analysis of the cluster photometric data, taking the contribution of all individual objects to L into account, yields consistency only for ages $\sim$3-4 Myr. Despite this, the permitted $T_{{\rm eff}}$ range based the H or K band data remains fairly large, and essentially identical to the above values.

7) Watson & Hanson (1997) obtained the first K-band spectrum of the ionizing star of G29.96, whose spectral type was found between O5 and O8 (luminosity class undetermined; cf. Watson & Hanson 1997), based on the presence of He  II absorption, and C  IV and N  III emission lines. They note, however, that a O7 or O8 spectral type would require some enhancement of the C  IV and N  III features - attributed to a higher metallicity - compared to "normal'' objects of these types. While the recent VLT spectrum presented in the preliminary work of Kaper et al. (2002) appears to be consistent with the data of Watson & Hanson (1997), the former authors deduce a spectral type as early as O3 based on the presence of the C  IV and N  III emission lines. From this it appears that a more detailed analysis of the data of Kaper et al. (2002) should be awaited before more firm conclusions on the spectral type of G29.96 can be drawn.

In any case, given the unknown luminosity class the following temperature ranges are obtained for O5-O8 (O3): $\sim$38.5-46 kK (51 kK) for LC V, intermediate values fo LC III, and $\sim$36-45 kK (50 kK) for LC Ia using the Vacca et al. (1996) compilation based on analysis using pure H-He atmosphere models. Recent fully line blanketed non-LTE calculations including stellar winds show, however, that - as already suspected earlier - the $T_{{\rm eff}}$ scale of O stars must be cooler (e.g., Fullerton et al. 2000; Martins et al. 2002).

The models of Martins et al. (2002) yield a reduction of $T_{{\rm eff}}$ by 4 to 1.5 kK for O3-O9.5 dwarfs compared to the Vacca et al. (1996) scale, and larger reductions are expected for giants and supergiants. Taking these effects into account we estimate for O5-O8 types $T_{{\rm eff}}$ $\sim$36-43 kK for LC V and $\sim$33-40 kK for LC Ia.

Combining the available data it appears that the preliminary spectral classification by Kaper et al. (2002) is the only information which is incompatible with most other constraints (points 3-6, possibly also 1 and 2). Good consistency is obtained, however, from the intersection of the above constraints 1) to 6), yielding an allowed $T_{{\rm eff}}$ between $\sim$31 and 37 kK, overlapping with the spectral type derived by Watson & Hanson (1997). We thus conclude that overall the parameters derived from our photoionization modeling are compatible with all the available observational data.

 

 

Table 3: Abundances determined by previous authors and in the present work.

Element	Herter et al. (1981)	Simpson et al. (1995)		Afflerbach et al. (1997)		Paper II		This work	Solar2
	G29.96	G29.96	4.5 kpc1	G29.96	4.5 kpc1	G29.96	4.5 kpc1
N/H (10-4)	-	2.3	1.8	1.8	1.2	1.9	-	2.0	0.8
O/H (10-4)	-	8.5	6.6	5.6	7.3	5.1	-	4.6	6.8
Ne/H (10-4)	2.7	2.6	1.8	-	-	2.5	2.2	1.7	1.2
S/H (10-5)	3.2	1.9	1.6	2.2	1.8	0.8	-	2.2	2.1
Ar/H (10-6)	23.	-	-	-	-	4.8	5.0	5.0	2.5
N/O	-	0.27	0.27	0.32	0.17	0.37	0.33	0.43	0.12
Ne/S	8.4	13.	11.	-	-	36.	-	7.5	5.7

¹ Values obtained applying the gradients from the corresponding authors at the galactocentric distance of Paper II.

² From Grevesse & Sauval (1998).

   
5.8 Implications of the advanced age of G29.96

However, an age of $\simeq$ $3\times 10^6$ years for the star is very high compared to the expected dynamical lifetime of UCHII regions ( $5\times10^5$ years, see e.g., Wood & Churchwell 1989a, based on the number of UCHII regions in the Galaxy and their expected lifetime). Two main models have been developed to explain the cometary morphology which is common for UCHII regions. Models of stellar-wind bow shocks (see e.g., Mac Low et al. 1991), due to an O star moving supersonically through a molecular cloud, were first studied and applied to G29.96 (Wood & Churchwell 1991; van Buren & Mac Low 1992; Lumsden & Hoare 1996). Champagne flow models (see e.g., Yorke et al. 1983), resulting from the expansion of an H II region into a molecular cloud exhibiting a density gradient, are also able to reproduce the cometary morphology. These models were applied more recently to G29.96 (Fey et al. 1995; Lumsden & Hoare 1996, PMB99) and were found to give results more consistent with the radio observations.

It is important to note that assuming a reasonable projected proper motion of 1 kms^-1, the star should have moved away from its birth place by about 3 pc (1.75 arcmin) in $\sim$ $3\times 10^6$ years. This rules out the Champagne flow model as a complete description of G29.96 and strongly favors the random meeting of an older star with an interstellar cloud. The ionizing star may also have left its birthplace, irradiating molecular gas further out which could still be part of the larger parental cloud from which it was formed.

5.9 Reliability of the abundances determination

The determination of the elemental abundances from the infrared fine-structure lines depends on many physical parameters, such as the filling factor, which are poorly constrained. Nevertheless,we can assert that there are two groups of elements. On one hand, oxygen and nitrogen, whose lines, all observed by the LWS spectrometer, are mostly emitted by the extended component 1, due to their low critical densities. Uncertainties in the attenuation correction and then in the Br$\alpha$ line flux by, e.g., 10% leads to an uncertainty on the N and O abundances of 25 to 30% (see Sect. 5.1).

The elements neon, argon and sulfur group, whose lines are observed by the SWS spectrometer (as the H I lines) with all the subsequent aperture corrections, are emitted by both components. The presence of high density clumps (filling factor of 0.1 - see Sect. 5.2) in the core will lead to abundances two times higher than what we determined in the presented model for the Ne, Ar, S group.

Whatever the uncertainties could be on the filling factor, the geometry of the source, the attenuation or the actual value of the radio emission, the determination of the abundance ratios in each group are robust: the N/O ratio on one hand, and the Ne/Ar, Ne/S and Ar/S ratios on the other.

Table 3 compares the abundances determined here and by Herter et al. (1981), Simpson et al. (1995), Afflerbach et al. (1997) and Paper II. The solar abundances from Grevesse & Sauval (1998) are also given. Afflerbach et al. (1997) used the Simpson et al. (1995) observations to model G29.96, but with a core/halo description. They both made semi-empirical models (using icf's) and adopted an higher effective temperature ($\sim$36 kK, see discussion in Sect. 5.7). The method used in Paper II is semi-empirical, based on the same observed line fluxes as the present work. For those previous works, we give the values effectively determined for G29.96 and the values obtained using the abundance gradient law they found, applied at the position of G29.96: 4.5 kpc from the galactic center.

The set of abundances, exepted for oxygen, shows that G29.96 is overabundant compared to the solar values, in agreement with its inner position in the Galaxy. The abundances determined in the present work are compatible with the previous determination within a factor of 2, except with the Ar/H ratio from Herter et al. (1981) and S/H ratio from Paper II.

The determination of the sulfur abundance relative to hydrogen in Paper II is very different from what the previous authors and the present work found. From the results presented in Table 2 we see that the [S III] 18.7$~\mu$m and [S IV] 10.5$~\mu$m lines on which the sulfur abundance is based in Paper II are mostly emitted by the extended component 1. The effect of the finite aperture size of the SWS instrument is crucial in this case. As there was no correction for this effect in Paper II, the sulfur emission and its abundance are underestimated.