Relaciones de temperatura para el ion de Cl2+ en regiones HII y la determinación de abundancias químicas
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H II regions and planetary nebulae are created when hot stars ionise nearby gas clouds. H II regions are ionised with high-energy UV radiation from young and massive stars, and they are primarily composed of hydrogen, but we can also find elements such as helium, carbon, nitrogen and oxygen, to name some of the most common ones. Although they may produce thousands of stars, generally less than the 10 % of the available gas is converted into stars, while the rest of it is dispersed by phenomena like stellar winds, radiation pressure and supernova explosions. Elements heavier than H and He are formed from stellar nucleosynthesis processes, and are sent back to interstellar medium through different mechanisms such as gas ejections, all of them based on the same idea: the outgassing of stars during the last stages of their lives. These stars in their initial and final phases emit photons that can ionize the surrounding gas, increasing the amount of free electrons that are in the ionized nebulae. These electrons interact creating what we call thermal equilibrium and photoionization equilibrium. Considering these processes, we can determine the chemical composition of the gas, which depends on three parameters: the electron density (ne), temperature (Te) and the chemical abundance of the ion that emits the radiation. So, if we can determine the first two parameters, ne and Te, we can obtain the ionic abundances, once we have the intensity of the appropiate emission lines. The main objective of this study is Chlorine (Cl), which belongs to group VIIA of the periodic table, known as halogens. Spectral lines of Cl are quite unusual in stellar spectra, so the determinations of its abundance in stars are very few. Because of this, most of the information that is available nowadays about Cl abundance comes from analyzing emission lines in ionized nebulae. The calculation of Cl abundance is based on measuring the intensity of the [Cl III] line doublet, at 5517 and 5537 ˚A, which are the brightest lines of Cl in the optical range. Moreover, in common conditions of an H II region, we expect that only Cl+ and Cl3+ have a significant contribution to total Cl abundance, as well as Cl2+, which is the dominant one. Nevertheless, the most common situation is that where we can only get [Cl III] lines to obtain total Cl abundance, and this is when we use the ionization correction factors (ICF), which correct the contribution to the total abundance of an element given by those ions we can not observe. But there is still one more problem to get through with Cl: the correct determination of the electron temperature representative of the nebular volume where Cl2+ is present. When it cannot be obtained through [Cl III] lines, we have to use valid diagnoses for other ions, such as O2+ and N+. First of all, we consider photoionization models, which through a numerical code, solve all the physical processes inside ionized nebulae, and calculate the physical conditions (Te, ne) and emitted spectra. In this case, we use the model grid from Vale Asari et al. (2016), available at the Mexican Million Models Database (3MdB) (Morisset, 2015). Moreover, we also use the constraints proposed by Amayo (2019) to this same grid, based on observational arguments, which, in the end, make the model grid a realistic one. One of the aims of this study, is to compare the results with real observations, in order to conclude if the temperature we choose is valid or not for representing Te(Cl2+). For it, we have an observational sample of 65 spectra of 33 extragalactic and 15 Galactic H II regions, obtained from different publications of our research group. For these spectra, we take the physical conditions calculated in M´endez-Delgado et al. (2022a). Through the photoionization models, we explore the behavior of Te as a function of the ionization degree, and, as we expected, we see that Te(N+) better represents zones with a lower ionization degree, and vice versa for Te(O2+). So we think about a temperature that can represent the most common conditions of ionized nebulae in the volume where Cl2+ is present, as a combination of Te(O2+) and Te(N+). We define the representative temperature, which depends on P instead of the ionization degree, since P is directly obtained through observational data, given by the ratio of line intensities. We represent Te(Cl2+) as a function of these three temperatures, Te(N+), Te(O2+) and Trep, and we see that Trep is the one that better fits the results. On the other hand, by analyzing the exact values of the standard deviation that results when we use Te(N+) or Te(O2+), we see that it is lower for Te(N+) for P ≤ 0.3, and lower for Te(O2+) for P > 0.3. This leads us to define a new temperature, named reference temperature. After representing Te(Cl2+) as a function of all the temperatures, we see that both, Trep and TP , are more appropiate for representing Te(Cl2+), since they both fit better than Te(N+) or Te(O2+). Once we establish the appropiate temperatures, we process the data of the 65 spectra and start determining the ionic abundances. For it, we use PyNeb (Luridiana et al., 2015), a numerical code made for calculus in ionized nebulae, which gives us the ionic abundance of an ion through the getIonAbundance() function. In order to obtain associated uncertainties, we also calculate these abundances through a Monte Carlo simulation of 500 experiments, so that we can use this value for the rest of the study. In our data, all the 65 spectra have intensities for [Cl III] emission lines, so we calculate the ionic abundance of Cl2+ for all of them. Moreover, there are 14 spectra in which the intensities for both [Cl II] and [Cl IV] emission lines are also given, so, for these, we can obtain the ionic abundances for Cl+ and Cl3+. This allows us to calculate the total abundance of Cl by just adding the ionic abundances of Cl+, Cl2+ and Cl3+, in addition to the method using the ICF. Moreover, we will also calculate the Cl/O ratio, which is particularly interesting, due to some studies reveal that its value must be constant. The reason for this is that Cl is produced in the same zones where the O burning happens, so both elements have a similar nucleosynthetic origin (Esteban et al., 2015). For a reference, we use the value proposed by Lodders (2019) for the Sun, log(Cl/O)⊙ = −3.50 ± 0.09. We start calculating the total abundance of Cl as the sum of the ionic abundances, for each proposed temperature, and the 14 spectra for which we have calculated the three needed abundances. In fact, we add one more spectrum to this case: the Herbig-Haro object HH204, from the Orion nebula, due to its ionization degree (parameterized by O2+/O) being nearly zero. For it, we expect Cl/H=Cl+/H++Cl2+/H+. Once we obtain the total abundance of Cl, we calculate the Cl/O ratio for these 15 spectra, for each proposed temperature. For analyzing all these results, we represent them graphically, as follows: 12 + log(Cl/H) as a function of 12 + log(O/H), log(Cl/O) as a function of O2+/O, and log(Cl/O) as a function of 12 + log(O/H). Although the results we obtain for this method seem to be correct, we cannot draw a strong conclusion, due to the low number of points available for this method. Next, we calculate the total abundance through the ICF. In this case, we use the ICF proposed by Amayo et al. (2021), who also gives mathematical expressions to estimate the uncertainties associated to this factor. Once we get Cl/O, we continue by calculating the total abundance of Cl. Then, we repeat the three representations described before, and analyze our results. We have to take into account that, with this method, the number of points is considerably higher, since we have used the 65 spectra available, excluding M42-HH204. In the results given in the ICF method, we see that the bias of the total abundance of Cl as a function of O is quite similar to the one obtained with the sum of ionic abundances, for all the 4 proposed temperatures. On the other hand, for the Cl/O ratio, we see that, even though the weighted average of the represented points is nearly -3.5, the ratio does not remain constant. We must also consider that the uncertainties given for this method are considerably higher, especially for those points with a lower ionization degree. Finally, we end our analysis by representing the total abundance of Cl obtained through the ICF, as a function of the one calculated as the sum of ionic abundances. This allows us to see how the ICF underestimates the total abundance of Cl, since nearly all the points, for the 4 used temperatures, are located under the line representing a 1:1 relationship. As we found at the beginning of this study, the temperatures that are more appropiate representing Te(Cl2+) are Trep and TP . However, the uncertainties given for TP are a bit higher than those obtained for Trep, especially for spectra with a low ionization degree. Trep is a linear combination of Te(N+) and Te(O2+), so the uncertainties are calculated using the error propagation, where the uncertainty associated to P takes part and, therefore, makes a difference.