TEMPERATURE & ABUNDANCES IN GASEOUS NEBULAE 277N(He)N(H)=∫Ne N(He 0 )dV + ∫ N e N(He + )dV + ∫ N e N(He ++ )dV∫Ne N(H 0 )dV + ∫ N e N(H + )dV,= ICF (He)∫Ne N(He + )dV + ∫ N e N(He ++ )dV∫Ne N(H + )dV. (1)Ionized Gaseous Nebulae (Mexico City, 21-24 November 2000)Editors: William Henney, José Franco, Marco Martos, & Miriam Peñations might be larger for objects with lower temperatures.To determine the N/O ratio often the temperaturederived from the λλ 4363/5007 ratio, T (O III),is used as representative of the O + and N + zones;from photoionization models it is found that for objectswith T (O III) > 12 360 K, the temperature ofthe O ++ region is higher than the temperature ofthe O + region, the opposite is found for objects withT (O III) < 12 360 K (e.g., Stasińska 1990); if this effectis not taken into account the N/O value for metalrich H II regions (those with T (O III) < 12 360 K)will be underestimated while for metal poor H II regions(those with T (O III) > 12360 K) N/O will beoverestimated.Often it is assumed that the N/O ratio is equal tothe N + /O + ratio (assuming that the O + zone coincideswith the N + one), while some photoionizationmodels indicate that this is the case, others indicatethat it is at best a fair approximation (Relaño et al.2001).Apparently there are environmental effectspresent in the N/O versus O/H relation, while Peimbert& Torres-Peimbert (1992) find an underabundanceof the N/O ratio for a given O/H ratio inthe Boötes Void galaxies, Vílchez & Iglesias-Páramo(2001) find that there is an overabundance of N/Ofor a given O/H in the dwarf galaxies of the Virgocluster.5. PRIMORDIAL HELIUM ABUNDANCEThe determination of the pregalactic, or primordial,helium abundance by mass Y p is paramountfor the study of cosmology, the physics of elementaryparticles, and the chemical evolution of galaxies(e.g., Boesgaard & Steigman 1985; Fields & Olive1998; Izotov et al. 1999; Peimbert & Torres-Peimbert1999; Olive & Skillman 2000 and references therein).We will call Y p (nHc) those Y p values in the literaturederived under the assumption of no contributionto the hydrogen Balmer lines due to collisionalexcitation.The best determinations of Y p (nHc) in the literatureare those of Izotov & Thuan (1998); Izotovet al. (1999); and Peimbert, Peimbert, & Ruiz (2000)that amount to 0.2443 ± 0.0015, 0.2452±0.0015, and0.2345 ± 0.0026, respectively. These determinationsare based on 45, 2, and 1 extragalactic H II regions,respectively, and the differences between the first twoand the last one amount to at least 3σ.To study the source of this discrepancy Peimbert& Peimbert (2001) and Peimbert, Peimbert, &Luridiana (2001) decided to compute Y p (nHc) basedon the data by Izotov & Thuan (1998) and Izotovet al. (1999). From two different subsamples of thebest observed objects, comprising 12 and 5 objects,found that Y p (nHc) amounts to 0.2371 ± 0.0015 and0.2360 ± 0.0025, respectively. These results are ingood agreement with the value derived by Peimbertet al. (2000) and are significantly smaller than thevalues derived by Izotov & Thuan (1998) and Izotovet al. (1999).The main source of the discrepancy between bothgroups of authors is due to the treatment of the temperaturestructure inside the nebulae; while Izotov &Thuan (1998) and Izotov et al. (1999) adopt T (O III)to derive the helium abundance, Peimbert & Peimbert(2001) and Peimbert et al. (2001) from the He Iline intensities and adopting t 2 > 0.00 determineT (He II) values 6–11% smaller than T (O III). In theself-consistent solutions the smaller T (He II) valuesimply higher densities; the higher the density thehigher the collisional contribution to the He I lineintensities and, consequently, the lower the heliumabundances.The baryon energy density, Ω b , values derivedby Peimbert & Peimbert (2001) and Peimbert etal. (2001) from the Y p (nHc) values are significantlysmaller than the Ω b value derived from the D p determinationby O’Meara et al. (2001). Before weconclude that a non-standard big bang nucleosynthesismodel is needed to reconcile the differencesit is necessary to analyze further two possible systematiceffects: (a) the ionization structure of theH II regions, and (b) the collisional excitation of thehydrogen lines.To determine very accurate He/H values of agiven H II region we need to consider its ionizationstructure. The total He/H value is given by equation(1) above.For objects of low degree of ionization it is necessaryto consider the presence of He 0 inside the H +zone, while for objects of high degree of ionization itis necessary to consider the possible presence of H 0
278 PEIMBERTIonized Gaseous Nebulae (Mexico City, 21-24 November 2000)Editors: William Henney, José Franco, Marco Martos, & Miriam Peñainside the He + zone. For objects of low degree of ionizationICF (He) might be larger than 1.00, while forobjects of high degree of ionization ICF (He) mightbe smaller than 1.00. The deviations from unity inthe ICF (He) value occur in and near the ionizationboundary of a given H II region, therefore those H IIregions that are density bounded in all directionshave an ICF (He) = 1.00. The ICF (He) problem hasbeen discussed by many authors (e.g., Shields 1974;Stasińska 1983; Peña 1986; Vílchez & Pagel 1988;Pagel et al. 1992; Armour et al. 1999; Peimbert & Peimbert2000; Viegas, Gruenwald, & Steigman 2000;Viegas & Gruenwald 2000; Ballantyne, Ferland, &Martin 2000; Sauer & Jedamzik 2001).Based on models of metal poor H II regions Luridianaet al. (2001) find that the ICF (He) for some ofthe best observed objects is very close to 1.00 andconsequently that the main difference between theΩ b value derived from Y p (nHc) and D p is not dueto the ICF (He). Relaño et al. (2001) from the spectraltypes of the ionizing stars of NGC 346 find thatabout half of the ionizing photons escape the nebulafavoring an ICF (He) = 1.00, this result is alsosupported by the fit of the lines of low degree of ionizationby their photoionization model. From thework by Zurita, Rozas, & Beckman (2000) on theionization of the diffuse interstellar medium in externalgalaxies it is expected that a large fractionof the ionizing photons escapes from the most luminousH II regions, which favors the assumption thatthe ICF (He) is very close to 1.00.Davidson & Kinman (1985) were the first to estimatethe collisional contribution to the Balmer linesand its effect on the determination of Y p ; they madea crude estimate for I Zw 18 and concluded that thecollisional contribution to I(Hα) may be roughly 2%.All the subsequent determinations of Y p in the literaturehave been derived under the assumption ofno contribution to the hydrogen Balmer lines due tocollisional excitation, I have referred to these determinationsin this paper as Y p (nHc).Notice that to a very good approximation the collisionalexcitation of the Balmer lines does not affectthe maximum likelihood method determinations ofN e (He II), T (He II) τ(3889), and T (O III).From a series of Cloudy models it is found thatthe collisional contribution to I(Hβ) for I Zw 18and SBS 0335-052 is in the 2% to 6% range, forH 29 and NGC 2363 in the 1% to 2% range, andfor NGC 346 in the 0.6% to 1.2% range. 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