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On the O/H, Mg/H, Si/H and Fe/H Gas and Dust Abundance Ratios in Galactic and Extragalactic H II Regions

We derive the Mg/H ratio in the Orion nebula and in 30 Doradus. We also derive the O/H and the Fe/O ratios in the extremely metal poor galaxy SBS 0335-052. We estimate the dust depletions of Mg, Si, and Fe in Galactic and extragalactic H II regions. Based on these depletions we estimate the fraction of O atoms embedded in dust as a function of the O/H ratio. We find an increasing depletion of O with increasing O/H. The O depletion increases from about 0.08 dex, for the metal poorest H II regions known, to about 0.12 dex, for metal rich H II regions. This depletion has to be considered when comparing nebular with stellar abundances.


Introduction
To determine the primordial helium abundance and to study the chemical evolution of galaxies it is necessary to derive the total N (O)/N (H) ratio in H II regions; in this paper the abundances are given by number following the usual definitions X/H = 12 + log N ( N (X)/N (O) = X/H − O/H, and X +i /H + = 12 + log N (X +i )/N (H + ). To obtain the total O/H ratio in H II regions it is necessary to add the dust-phase to the gas-phase component of the O/H value. We presented elsewhere a preliminary discussion on the fraction of O trapped in dust grains, (Peimbert, A. & Peimbert, M. 2010a). To find the fraction of O atoms embedded in dust grains we will estimate the depletions of Mg, Si, and Fe, and we will assume that the O atoms trapped in dust belong to molecules that include Mg, Si, and Fe atoms.
There are three results in favor of dust presence in low metallicity H II regions: a) Cannon et al. (2002) found significant enhancements of the I(Hα)/I(Hβ) value in some areas of I Zw 18 (one of the most metal-poor galaxies known) that are not due to underlying stellar absorption nor to the effect of collisional excitation of the Balmer lines, they conclude that the enhancements are more likely due to the presence of dust, b) Thuan et al. (1997) find that dust is clearly present in the extremely metal poor galaxy SBS 0335−052 E, and c) the Si/O versus O/H diagram of H II regions, where the Si/O ratio is almost independent of the O/H ratio and considerably smaller than the solar ratio implying that a substantial fraction of Si is embedded in dust grains (Garnett et al. 1995).
There are two arguments in favor of significantly lower depletion fractions of heavy elements into dust in metal poor H II regions: a) Izotov et al. (2006) find a slight increase of Ne/O with increasing metallicity, which they interpret as due to a moderate depletion of O onto grains in the most metal-rich galaxies, they conclude that this depletion corresponds to ∼ 20% of oxygen locked in the dust grains in the highest-metallicity H II regions of their sample, while no significant depletion would be present in the H II regions with lower metallicity, and b) Rodríguez & Rubin (2005) have estimated the fraction of Fe atoms in Galactic and extragalactic H II regions in the gaseous phase, and find that this fraction decreases with metallicity. The Fe depletions derived for the different objects define a trend of higher depletion at higher metallicities; while the Galactic H II regions show less than 5% of their Fe atoms in the gas phase, the low metallicity extragalactic regions (LMC 30 Doradus, SMC N88A, and SBS 0335−052 E) have somewhat lower fractions of Fe embedded in dust grains. Izotov et al. (2006) have produced a Fe/O versus O/H diagram that confirms the results by Rodríguez & Rubin. To estimate the dust fraction as a function of O/H we need to have good gaseous abundance determinations for a relatively O-rich H II region; for this purpose we will use the the Orion nebula, its gaseous abundances derived by Esteban et al. (2004), and the result by Mesa-Delgado et al. (2009) that from three different methods have estimated that the fraction of O atoms trapped in dust in the Orion nebula amounts to 0.12 ± 0.03 dex. We will compare the Orion nebula abundances with the protosolar abundances by Asplund et al. (2009), and the solar vicinity B stars abundances by Przybilla et al. (2008 Keenan et al. (2001). In section 5 we make use of the Si/O ratios for 5 extragalactic H II regions obtained by Garnett et al. (1995). In section 6 we compile Fe/O ratios from the literature for Galactic and extragalactic H II regions and estimate the Fe dust fraction as a function of O/H. In section 7 we discuss the observational results and estimate the fraction of O atoms trapped in dust grains as a function of O/H, and the conclusions are presented in section 8.

The Orion nebula
In Table 1 we present the solar neighborhood and Orion Nebula abundances that will be used as reference values to estimate the fraction of a given element in the dust phase. In column 2 we present the protosolar abundances (Asplund et al. 2009). In column 3 we present the solar neighborhood abundances by correcting the protosolar abundances due to the chemical evolution of the Galaxy since the Sun was formed; based on the Galactic chemical evolution models of Carigi (1996), Chiappini et al. (2003), and Carigi & Peimbert (2008, 2010 we added 0.09, 0.09, 0.13, and 0.20 dex to the protosolar values of O, Mg, Si, and Fe respectively. In column 4 we present the chemical abundances derived by Przybilla et al. (2008) from 6 B stars of the solar vicinity; Simón-Díaz (2010) has recently derived the O and Si abundances for 13 B stars from the Orion region, his results are in very good agreement with those by Przybilla et al.; note that B stars abundances do not need correction for Galactic chemical evolution since these stars are only a few million years old. In column 5 we present our adopted abundances for the ISM of the solar vicinity; we obtained these values from a simple average of columns 3 and 4. In column 6 we present the expected total abundances for the Orion Nebula; we obtained these values by considering the different galactocentric distances of the solar vicinity and the Orion Nebula and subtracting to the O, Mg, Si, and Fe solar neighborhood abundances 0.02, 0.02, 0.03, and 0.04 dex respectively to account for the presence of Galactic abundance gradients; the Galactic gradients are obtained from the Galactic chemical evolution models by Carigi, Chiappini and their collaborators; it is worth mentioning that the expected total, gas plus dust, O/H value for the Orion nebula is equal to the total derived O/H value from observations by Mesa-Delgado et al. (2009) (see below). In column 7 we present the gaseous abundances of the Orion nebula; the O/H abundance comes from Esteban et al. (2004), the Fe/H abundance from Esteban et al. (1998), and the Mg/H and Si/H abundances from this paper (see below). Baldwin et al. (1991) estimated an upper limit to the gaseous Mg/H value of 6.58 dex from an upper limit to the Mg II λ2800/Hβ line intensity ratio obtained by Perinotto & Patriarchi (1980). From the same raw data of the observations for Orion by Esteban et al. (2004), we have estimated -4 - c Galactic chemical evolution correction from Carigi (1996), Chiappini et al. (2003), and Carigi & Peimbert (2008, 2010, see text. d Solar vicinity B stars from Przybilla et al. (2008). e Adopted solar vicinity ISM abundances, average from B stars and protosolar values corrected for Galactic chemical evolution. Esteban et al. (2004) including the dust correction from Mesa-Delgado et al. (2009); values in parenthesis come from the ISM solar vicinity values presented in the fifth column and a small correction due to the larger galactocentric distance of Orion relative to the Sun predicted by the Galactic chemical evolution models mentioned above. Esteban et al. (2004), Fe from Esteban et al. (1998), Mg and Si from this paper. the gaseous Mg abundance in this region. From these data, we have measured the following line ratios: I(4481.22, Mg II)/I(Hβ) = (3.6±1.6) x 10 −5 and I(4482.17, Fe I])/I(H β) = (8.6±2.5) x 10 −5 . As we can see in Figure 1, high resolution spectra are needed to separate the Mg II line from the 4482.2 line, that is probably due to the Fe I] (a 5 -z 7 F o ). Under the assumption that the Mg II 3d-4f λ4481 line has an effective recombination coefficient equal to that of the C II 3d-4f λ4267 line (Liu et al. 2004), from the Mg II/Hβ intensity ratio and the C II line effective recombination coefficient we derive a gaseous Mg ++ /H + value of 6.54 ± 0.16 dex. By adding 0.02 dex due to the presence of Mg + (Baldwin et al. 1991), we obtain a total Mg/H gaseous component of 6.56 ± 0.16 dex. Our Mg/H ratio is in agreement with the upper limit obtained by Baldwin et al., this ratio together with the reference stellar value of Table 1, implies that (9±3)% of the Mg atoms are in gaseous form and (91±3)% are embedded in dust. Garnett et al. (1995), obtained UV observations of the Orion nebula with the HST, and found that Si/C = −1.46 ± 0.10 dex. From the C/O value of −0.25 dex derived by Esteban et al. (2004) and the previous result we find that the gaseous Si/O value amounts to −1.71 dex. By considering that 0.12 dex of O is tied up in dust grains it follows that the gaseous Si to the total (gas + dust) O abundance is equal to −1.83 dex, and consequently that Si/H = 6.94 ± 0.12 dex. This number together with the reference Si/H value implies that the fraction of Si atoms tied up in dust grains amounts to 76% in the Orion nebula (see Table 1). Similarly Esteban et al. (1998) obtained that the gaseous Fe/H = 6.07 ± 0.20 dex, this result together with the Fe/H reference value implies that about 97 % of the Fe atoms are tied up in dust grains.
The total O value for the Orion nebula presented in Table 1, O/H = 8.77 dex, was obtained from 2 different methods: a) By adding to the gaseous value derived by Esteban et al. (2004) for t 2 = 0.022 the dust correction of 0.12 dex estimated by Mesa-Delgado et al. (2009), where t 2 is the mean square temperature variation (Peimbert 1967). And b) by using the same procedure for O than the one used for the other elements of Table 1.
The use of the t 2 formalism presented by Peimbert (1967) and Peimbert & Costero (1969) will be used throughout this paper. As mentioned before the use of t 2 = 0.022 gives O/H = 8.65, a reasonable value for the estimated oxygen depletion. On the other hand under the simpler assumption, that H II regions have uniform temperature (t 2 = 0.000), Deharveng et al. (2000), Pilyugin, Ferrini, & Shkvarun (2003), and Esteban et al. (2004) obtain for the Orion nebula O/H values of 8.51, 8.49, and 8.51 dex respectively, a difference of 0.27 dex with respect to the total oxygen value presented in Table 1. A difference too large to be explained by the depletion of oxygen into dust grains. It should be noted that: of the well observed H II regions the Orion nebula presents one of the lowest t 2 values (e.g. Esteban et al. 2002, Peimbert 2003, therefore in general we expect larger abundance differences than in Orion between the T (4363/5007) method and the method with t 2 values different from zero.
We will assume that the fraction of O atoms tied up in dust grains of H II regions is proportional to the fraction of atoms of Mg, Si, and Fe tied up in dust grains of each nebula and that the constant of proportionality will be given by the Orion nebula results. This assumption is a first approximation to this problem and is based on the following ideas: a) as far as molecules -that survive as part of dust grains in an H II region -go, the elements that most frequently bind with O atoms are Mg, Si, and Fe; b) Na, Al, Ca, Cr, Mn, and Ni are less abundant than the previous three elements, and most of them have similar behaviors to those of either Mg, Si, or The error bars from equation 1 correspond to a systematic uncertainty that depends on the exact O depletion of the Orion Nebula; we will ignore this systematic error for most of the paper, and will look into it at the end of section 7.
We will estimate the O total for other H II regions from equation (1) and the next equation: Jenkins (2009) finds for some lines of sight of the ISM, that include mainly neutral material, that the O depletion reaches values in the 0.2 to 0.3 dex range. He concludes that O molecules that include Mg, Si, and Fe are not enough to account for these depletions, and suggests that ices might also be present. Equations (1) and (2) were calibrated with the Orion nebula, where according to Mesa-Delgado et al. (2009) the O depletion derived from the assumption that O is trapped by molecules, that include only Mg, Si, and Fe, agrees with: a) the O depletion estimated from the comparison of the stellar abundances of the Orion region with the nebular abundances; and b) with the O pre-shock nebular abundances and post shock O abundances associated with the H-H object 202, in this object after the shockwave passes dust grains are destroyed and most of the Fe trapped in grains is returned to the gaseous phase, they assume that also most of the O is returned to the ISM. Since the Orion nebula is one of the H II regions with the highest Fe depletion we consider unlikely that the O depletions of H II regions with lower Fe depletions are higher than in the Orion nebula, therefore we conclude that ices and O 2 molecules are practically absent in H II regions.

The 30 Doradus nebula
To obtain the fraction of O, Mg, Si and Fe in the dust phase of 30 Doradus we will follow the same procedure as for the Orion nebula.
Based on the raw data presented by Peimbert (2003) Table 2, due to the considerably higher degree of ionization of 30 Doradus relative to the Orion nebula we neglected the contribution to this value due to Mg + . Tsamis and Péquignot (2005), from the observations of λλ 4561 and 4571 of Mg I] by Peimbert (2003), also derived the Mg/H value for 30 Doradus and it is presented in  Peimbert (2003), the Si determination by Garnett et al. (1995), and the Mg determination presented in this paper (see Table 2 Table 2 we derived the fractions of the Mg, Si, and Fe atoms in the gas phase and the dust phase. The 30 Doradus Mg and Fe fractions are slightly lower than those of Orion, while Si is nearly constant; this result gives us an initial hint that the fraction of heavy elements trapped in dust diminishes at lower metallicities.

The Fe/H and O/H ratios in SBS 0335−052 E
It is important to obtain the Fe/O and the O/H ratio of the metal poorest H II regions to try to find out if a substantial fraction of Fe is tied up in dust grains and consequently also a non-negligible amount of O atoms. To reach this objective we will compute the abundances for SBS 0335−052 E. To calculate the total fraction of Fe in dust grains, we first need to obtain the Fe gas /O total value and then compare it to the reference value. To correct for the fraction of O in dust grains we will use equation 2 and the reference values derived for the Orion nebula. The gaseous Si/O ratio comes from Garnett et al. (1995) that obtain Si/O = −1.72 ± 0.20 dex. We will assume that the value of the Mg term of equation 2 lies between the values of the Si and Fe terms, we will discuss this point further in section 7. From the previous considerations we derive a correction of 0.08 ± 0.01 dex for the O abundance. Therefore we obtain an Fe gas /O total of −1.44 ± 0.03 dex. Taking as reference value the solar vicinity ISM abundances, the Fe/O ratio amounts to −1.20 ± 0.15 dex, and we obtain that the fraction of Fe in gaseous form amounts to (58 ± 20)% and that the rest is trapped in dust grains. To derive an accurate O/H value it is also necessary to consider the density dependence of the O II lines. The sum of the intensities of all the lines of the O II multiplet 1, I(total), has a temperature and density dependence that is proportional to T −0.9 N 2 , similar to the temperature and density dependence of the H I lines. However the fraction of the intensity due to each one of the lines of the O II multiplet 1 varies when N e < 10000 cm −3 . In Figure 3 we present the density dependence of the eight O II lines of multiplet 1 that were obtained empirically from observations of planetary nebulae and H II regions (Ruiz et al. 2003, Peimbert & Peimbert 2005a, and Peimbert et al. 2005b). Bastin and Storey (2006) from atomic physics computations obtain a similar behavior for the I(4649)/I(total) versus density relation to that derived empirically from observations. To obtain abundances from the O recombination lines it is necessary to take into account the possible blend of the O II lines when the resolution is not high enough. From the equations by Ruiz et al. (2003), Peimbert & Peimbert (2005a), and Peimbert et al. (2005b), for those cases where  the resolution is of the order of two to three angstroms, we recommend these equations:

The O/H ratio
In Figure 4 we present what fraction of the total intensity is present in each of these blends as a function of density.
Due to the importance and the faintness of the O II recombination lines we decided to reduce the FORS raw data for SBS 0335−052 E present in the VLT archive, an independent reduction of this data was made by Izotov et al. (2009). We obtain that I (4649 + 51)/I(Hβ) amounts to 0.0132 ± 0.0074, in addition we obtain that I(4639 + 42)/I(Hβ) amounts to 0.0085 ± 0.0074. From our two measurements we find that I(4639 + 4641 + 4649 + 51)/I(Hβ) = 0.0217±0.0104. We have subtracted to I(Hβ) the contribution due to collisional excitation, that according to Peimbert et al. (2007) amounts to 6.6%, and obtain that I(4639 + 4641 + 4649 + 51)/I(Hβ) rec = 0.0231 ± 0.0111. Based on the I(4639 + 42)/I(4649 + 51) line ratio and the very low N/O ratio in this object we consider that the feature at λλ4639 + 4642 is due to the O II lines and not to the 4642 N III line, contrary to the suggestion by Izotov et al. (2009). ¿From our measurements, equations (3) and (4), the recombination coefficients of O II by Storey (1994), and the H I recombination coefficients by Storey and Hummer (1995) we obtain an abundance of O ++ /H + = 7.36 +0.17 −0.28 dex. The total O/H value amounts to 7.41 +0.17 −0.28 dex and includes the O + contribution that amounts to 0.05 dex (Luridiana et al. 2003, Izotov et al. 2009). Our O/H value can be compared with the values for t 2 = 0.00 derived by Peimbert et al. (2007) and Izotov et al. (2009) that amount to 7.31 ± 0.04 dex and 7.23 ± 0.01 dex respectively, and also with the value derived by Peimbert et al. for t 2 = 0.04 that amounts to 7.47 ± 0.04 dex. In Table  3 we present the value for t 2 = 0.00 by Peimbert et al. (2007) Storey (1994), and Storey and Hummer (1995) and equation (4) Izotov et al. (2009) is not correct, their result probably has been affected by at least one of the following causes: a) that they did not consider the density dependence of the O II lines, and b) that they did not use the proper branching ratio for the O II lines.

The Si/O ratio in H II regions
Si and O are produced by core collapse supernovae and this production is expected to be independent of the O/H ratio. By comparing the Si/O ratio in H II regions with the Si/O ratio in B stars of the solar vicinity it is possible to estimate the fraction of Si in gas and dust phases in H II regions. Garnett et al. (1995) derived the Si/O ratio for eight Galactic and extragalactic H II regions with gaseous O/H abundances in the 7.2 to 8.7 dex range and found that the Si/O ratio was almost constant for these objects. ¿From the Orion and 30 Doradus data of sections 2 and 3, and the data of the other 6 objects of Garnett et al. (see Table 3) we derived an average gaseous Si gas /O gas = −1.66 ± 0.05 dex. The Si gas /O total versus O total /H for the 8 H II regions discussed in this paper are presented in Figure 5.
The reference value for Si/O amounts to −1.20 dex and is obtained from the protosolar + GCE Si/O value (Asplund et al. 2009;Chiappini et al. 2003;Carigi & Peimbert 2008, 2010 and the Si/O B stars values (Przybilla et al. 2008) that amount to −1.14 dex and −1.26 dex respectively.
Since the Orion nebula, the metal richest H II region of the sample, has an oxygen depletion of 0.12 dex, and SBS 0335−052 E, one of the 2 metal poorest H II regions of the sample, has an oxygen depletion of 0.08 dex, we can assume that most of the H II regions have an intermediate depletion value. As a first approximation we will adopt 0.10 dex for the fraction of O trapped in dust grains. In section 7 this point will be discussed further and we will see that 0.10 dex is a good representative value for most H II regions.
¿From the previous considerations we estimate that the average ratio of Si gas /O total amounts to −1.76 dex, from this estimate and the reference value of Si total /O total of −1.20 dex we obtain that in H II regions, about 28% of the Si is in the gas phase and 72% in the dust phase.
Note that the specific correction for oxygen in dust grains for the objects in Table 3 (except SBS 0335−052 E) follow the recipe derived in section 8.

The Fe/O ratio in H II regions
In Figure 6 we present the Fe/O versus O/H ratio compiled from many sources in the literature. The data comes from two different sets. In the first set the O/H determination comes from recombination line ratios which are independent of the temperature structure. In the second one the O/H ratios are derived in the traditional way, this depends on the ratio of collisionally exited to recombination lines which is strongly dependent on the temperature structure of the H II region (Peimbert, 1967;Peimbert & Costero, 1969;Peimbert, M. & Peimbert, A. 2010b).
To correct for the presence of temperature variations we have added 0.24 dex to the O/H ratio, this correction comes from the average value of 13 well observed extragalactic H II regions (Esteban  Peimbert (2003). Si from Garnett et al. (1995). Mg from this paper.
c Gaseous abundances for the inhomogeneous model by Tsamis & Péquignot (2005 Garnett et al. (1995); Peimbert et al. (2000Peimbert et al. ( , 2007; this paper. b Garnett et al. (1995).   Tables 1 and 3).   Izotov et al. (1997Izotov et al. ( , 1998Izotov et al. ( , 1999Izotov et al. ( , 2004, where the O/H values have been corrected for the presence of temperature variations, see text. The filled circles are from measurements by Esteban et al. (2002Esteban et al. ( , 2004Esteban et al. ( , 2009, García-Rojas et al. (2004, Peimbert et al. (2000), and this paper, where the O/H values are come from recombination lines. López-Sánchez et al. 2007). Note that the Fe/O ratio is almost independent of the temperature structure since it is determined from a ratio of collisionally excited lines that show a similar temperature dependence.
Part of the scatter in Figure 6 could be due to errors in the determinations of the gas-phase Fe/O ratios and part to the different star formation histories of the different galaxies. The closer in time to a recent burst of star formation the lower the total Fe/O ratio in their ISM. In the solar vicinity at present all the O abundance is due to core collapse supernovae, while about 40% of the Fe is due to core collapse supernovae and the other 60% to Type Ia supernovae ( e. g. Pagel & Tautvaisiene 1995, Pagel 2009). There is a time delay in the Fe formation relative to the O formation, and consequently the Fe/O ratio depends on the star formation rate, the initial stellar mass function, and the gas flows from and into the intergalactic medium. There are two well established Fe/O ratios from observations: the one when the Sun was formed, called the protosolar ratio that amounts to −1.19 dex (Asplund et al. 2009), and the present value in the solar vicinity based on observations of B stars that amounts to −1.32 dex (Przybilla et al. 2008); from the protosolar value plus the modification due to Galactic chemical evolution we find a value of Fe/O = −1.08 dex for the present ISM (see Table 1). From the average of the previous 2 values we obtain an Fe/O = −1.20 dex.
¿From Figure 6 and under the assumption that the total Fe/O ratio amounts to −1.20 dex, we obtain that for the Galactic and extragalactic H II regions with abundances in the 8.3 dex < O/H < 8.8 dex range the average fraction of Fe in the gaseous-phase is about 10%, with some of them reaching 3%. For the extragalactic H II regions with abundances in the 7.8 dex < O/H < 8.3 dex range the fraction of Fe in the gaseous-phase is about 25%. For the extragalactic H II regions in the 7.3 dex< O/H < 7.8 dex range the fraction of Fe in the gaseous phase is about 50%.

Discussion
The  Jenkins (2009) finds that in lines of sight dominated by neutral material the Mg and Si depletions are very similar and considerably smaller than those of Fe. From these results we will explore two possibilities for the H II region set: a) that Mg gas /H is equal to Si gas /H, and b) that Mg gas /H is intermediate between Si gas /H and Fe gas /H. We found that in the range of metallicities studied here there is a small but measurable trend in the sense that the depletion of O in dust grains increases with metallicity. The limiting values for the O depletion are: 0.08 dex for the O poorest objects, based on the observations of SBS 0335−052 E, one of the O poorest objects known; and 0.12 dex for the Orion nebula one of the richest objects with a good determination. Note that the upper limit given by equation (1) is 0.14 dex if no Mg, Si, or Fe atoms remain the gas phase.
We decided to divide the sample in three O/H groups: a) 7.3 < O/H < 7.8 dex, b) 7.8 < O/H < 8.3 dex, and c) 8.3 dex < O/H < 8.8 dex. We took the Fe gas /O total average of all the H II regions in each interval as representative of each group, and from equation (1) Table 4 we present our adopted values.
So far we have not included the systematic error present in equation 1 due the depletion determinations of the Orion nebula (our absolute calibrator). This systematic error is comparable to the trends that we have found, and makes any given absolute determination uncertain, but the differences derived between two objects are not affected by this error. The systematic error is about one fourth of the estimated O depletion and, including the possible errors in the reference values of Mg, Si, and Fe, translates to a final error of 0.03 dex for each of the 3 intervals discussed in this paper.

Conclusions
From the Mg II 3d-4f λ4481 recombination line intensities we have derived the Mg/H abundance ratio for the Orion nebula and for 30 Doradus. From this abundance ratio we have estimated that in the Orion nebula and in 30 Doradus about 9% and 27% of the Mg atoms are in the gas phase respectively, and that the rest of the Mg atoms are embedded in dust grains.
We have reduced the FORS raw data for SBS 0335−052 E and have measured four of the eight O II lines of multiplet 1 and from the I(4639 + 4641 + 4649 + 51)/I(Hβ) rec = 0.0231 ± 0.0111 value we obtain that 12 + log (O ++ /H + )= 7.36 +0.17 −0.28 and that the total O/H value amounts to 7.41 +0.17 −0.28 dex.