Line Ratio in the C-like Ion Spectrum O III: Testing Atomic Theory Predictions Through the Observation of Galaxies

Abstract

The progress made in atomic structure computations has indicated that certain line ratios of forbidden transitions may be slightly different from earlier assumptions. In order to check this theory, we evaluate previous observations of dwarf galaxies by the UVES spectrograph at the VLT telescope on ESO Paranal for the line ratios of branched decays in C-like oxygen ions [O III] that are insensitive to the local environment. Our findings show that the observed line ratio for [O III] ($r=3.005\pm 0.237$) aligns with recent theoretical predictions based on more sophisticated models, while it deviates from older computations. Additionally, the analysis of line profiles suggests that, in some cases, the spectral resolution was insufficient to fully resolve dynamic substructures within the galaxies. Our results emphasize the importance of improved data quality and consistency for future studies, especially for future searches of finestructure constant variations at higher redshifts using this method.

1. Introduction

The observed line ratios (LR) of celestial objects are regularly compared to line ratios from collisional-radiative models in order to derive information on the plasma conditions (density, temperature) at source [1]. It would be good to test the predictive power of theory on line ratios that do not depend on external parameters. Such line ratios are available for branched decays of a given upper level.

For example, the [N II] 2s²2p^{2 3}P_1,2–${}^1\mathrm{D}_2$ lines bracket the astrophysically prominent H_α line and may distort the H_α line profile [2]. For a reliable spectrum analysis, it should be of key importance to ascertain the line ratio of the two [N II] lines. [O III] has similar lines in the blue part of the visible spectrum and with a wider line separation [3]. A spectrum that contains both line pairs ([N II], [O III]) is reproduced in [4]. The predicted branching ratio in both spectra is close to 3.00, but how reliable is such a prediction?

For a timeline and examples of C-like ions, see [5,6,7,8,9,10,11,12,13,14]. According to a literature search by Dojčinović et al. [15], most of the predictions for [N II] say LR 2.96, with only a small scatter by 1 or 2%. For example, the extensive computations by Tachiev and Froese Fischer [13] agree with LR 2.96. In the evaluation of the distortions of the H_α line profile, some authors use a line ratio of 3, others of 2.96 (see [15]). Actually, the observations of AGNs evaluated by Dojcinovic et al. [15] point at a slightly higher line ratio of 3.05 for [N II], which comes close to the results of a theoretical study by Storey and Zeippen [14] that are more complex than the earlier work and yield a flux ratio of 3.07 for [N II], some 3% higher than the “traditional” value.

At the same time as the ratio of the predicted transition rates appears to be well established within better than 3%, the sum of the same transition rates (which is the inverse of the upper level lifetime) scatters by some 20%. The question arises whether the reproducibility of the line ratio is a proof of the high quality of theoretical prediction, or whether the much larger scatter of the individual transition rates points to intrinsic problems.

The 2s²2p² ${}^1\mathrm{D}_2$ level lifetime has been predicted to amount to about 250 s in [N II], and about 37 s in [O III]; see [14]. These values are too long to be measured directly at present [16]. However, a measure of the line ratio should be straightforward by astrophysical observations, of which many are preserved in archival data. For observations of the decays of very long-lived levels (of multi-second lifetimes), planetary nebulae should do well, for which ample data of high statistical reliability are available. Acker et al. [17] find LR 2.92 for [N II] in planetary nebulae, which is a little lower than usually predicted. Dojčinović et al. [15] have evaluated the spectra of active galactic nuclei (AGN) and find (for [N II]) some line ratios to be a little higher than most earlier predictions. This variation may seem surprising in the light of so many earlier predictions that seemed to agree perfectly with each other. However, one has to be aware of the substance of such predictions.

The [O III] lines of interest are among those that in the 19th century had been ascribed to the hypothetical element nebulium, because they appeared in the spectra of the (misnamed) planetary nebulae and could not be reproduced in terrestrial laboratories. Almost half a century later, Bowen recognised their origin as electric-dipole ($E1$) forbidden transitions in ordinary elements, such as low charge state ions of oxygen [18]. Bowen’s key insight was that only a very low particle density of the emitter zone would permit the radiative decay to be observable, whereas at higher densities, collisional quenching reduces the populations of excited levels and thus their radiative emission. The dominant $E1$-forbidden decay channels are via magnetic dipole ($M1$) and electric quadrupole ($E2$) radiation.

Basically, the prediction of $M1$ transition rates consists of combining the transition energy and a factor from Racah algebra [19]. The wavelengths are well known from observation, and Racah algebra ($6j$-symbols etc.) is mathematically strict, often with simple fractions of small integers that appear to leave little leeway for uncertainty. However, computations of the transition energy (or of the fine structure splittings) often do not agree with the precisely known experimental wavelength data, which is why “predictions” are often adjusted “semi-empirically”. Moreover, the seemingly exact, simple Racah factors apply to a single-configuration model. The above examples, however, deal with transitions between the five fine structure levels in the ground configuration of a C-like ion, and it has to be expected that a single-configuration ansatz may be insufficient. The recent multi-configuration computations by Storey and Zeippen (using the SUPERSTRUCTURE code and introducing relativistic corrections to certain transition operators) yield a transition rate (flux) ratio of 3.01 for [O III] [14], in good agreement with the analysis of the AGN observations (LR ≈ 3.05) [15].

It seems worthwhile to expand the astrophysical sample size by using observations of dwarf galaxies and to test the validity of computed line ratios in a relatively simple case, such as the C-like spectrum [O III]. Another motivation to investigate the ratio stems from the the occurence of unusual line ratios in spectra of dwarf galaxies, e.g., [20]. Earlier observations have already led to the speculation that the ratios might hint at difference in the finestructure constant $\alpha$ [21], an idea that has been discussed in the context of intergalactic absorption lines for quite a while (see, for example, ref. [22] for the currently best limits from intergalactic absorption lines). In this context, a critical evaluation of the [O III] ratio based on high quality, high dispersion spectra is of additional interest.

Using data obtained by a high-resolution spectrograph (for example, UVES at ESO Paranal [23]) should ascertain a high data quality. At the same time, a survey of available data may reveal problems with the recorded data and their interpretation. The joint evaluation of two lines of an expected line ratio helps to critically evaluate the data quality. Only deviations from the instrumental line profile that appear in both lines may relate to the object structure. The data depository, the data evaluation and quality assessment, and the interpretation in terms of line ratios are described below.

2. Data

The Ultraviolet and Visual Echelle Spectrograph (UVES) at the Very Large Telescope VLT-UT2 at the ESO observatory on Cerro Paranal is a crossdispersed echelle spectrograph [23]. Incoming light is divided into two arms, the blue arm ($\lambda \lambda$ 3000–5000 Å) and the red arm ($\lambda \lambda$ 4200–11,000 Å). Both arms work similarly, with a collimator focusing the light beam at first. The focused beam is then diffracted in one plane by an R4 echelle grating (which resembles stairs) with a blaze angle of 76°. A crossdisperser splits this diffracted light beam in an orthogonal plane so that initially overlapping diffraction orders are spatially separated from each other. This crossdisperser grating unit consists of two gratings mounted back to back on a grating turn-table. For the red arm, which was used to gather the data for this work, the groove densities of the crossdisperser gratings are 600 g/mm and 316 g/mm. The echelle spectra are accumulated on CCDs and can then be extracted [23].

The UVES spectrograph achieves a reciprocal dispersion of about 0.014 $\frac{\text{Å}}{\mathrm{px}}$. While the resolving power of the instrument was designed to be on the order of $\lambda /\Delta \lambda =R\approx$ 40,000 for a slit width of 1 arcsecond, the actually achieved resolution depends on the slit settings used and other parameters. For the presently evaluated data, a slit width of 2” was used in order to improve the signal-to-noise ratio (S/N) and to sample as much of the target galaxy as possible, all while preserving sufficient spectral solution. This results in a spectral resolution of about R $\approx 8000$. However, even at this spectral resolution, the observed [O III] lines show a velocity structure (several partly blended components), which broadens the apparent line width FWHM (full width at half maximum) to about 1.5 Å.

The data used in this work were originally recorded by Chávez et al. from 15 April to 18 April 2009, and they have been analyzed and discussed in [24]. Each data set consists of two spectra that cover wavelength ranges from 4750 Å to 5750 Å and from 5850 Å to 6850 Å, respectively. The [O III] wavelengths 4958.911 Å and 5006.843 Å [25] fall into the working range of the blue arm of the double spectrograph, as well as into that of the red arm. However, the stored catalog data are those obtained by the red arm. The data include 86 data sets from 57 different [H II] galaxies and the scientific goal was the study of the velocity dispersion of giant H II regions as a distance indicator. This sample of [H II] galaxies, which are low-mass galaxies undergoing a current burst of star formation and therefore often consist of a single galaxy-wide H II region, is also perfect for our program. According to the mass-metallicity relation (e.g., [26]), these galaxies are generally metal-poor and contain many young, massive, and therefore hot, stars. This leads to high electron temperatures and extremely strong [O III] lines as the main cooling lines under these conditions. Due to the slit spectrograph set-up of UVES, we can further control the measured extent of the H II region and can exclude areas of shock-ionized gas (outflows) from the photo-ionization dominated giant H II regions. An analysis of the outflows will be deferred to a later paper.

At the time of measurement, the galaxies were in a young starburst phase. Their spectra show distinct emission lines of the Balmer series, especially the H_β line at $4861.3$ Å. They also show distinct [O III] emission lines and other emission lines indicating a high electron temperature. The data sets include galaxies with redshifts of up to $z=0.2$. Color images of the target galaxies generated from the Sloan Digital Sky Survey (SDSS) or the PanSTARRS survey can be seen in Appendix A. The images document that our sample is strongly dominated by compact blue objects consistent with their classification as Blue Compact Dwarf Galaxies (BCDGs) and starbursting irregular dwarf galaxies.

In the data depository, the galaxies are named by their respective coordinates. For the purpose of this study, we use a simpler unique identifier (ID) for each galaxy. As some galaxies were observed multiple times, the data sets are distinguished by letters behind the ID. In total, 23 of the 57 galaxies were observed multiple times, with 18 of them being observed two times, 4 three times, and 1 galaxy four times.

Table A1. Presently used identifiers of the observed galaxies.

ID	Galaxy	ID	Galaxy	ID	Galaxy
1	074806+193146	19A	131235+125743	39	092918+002813
2	081403+235328	19B	131235+125743	40	091652+003113
3A	074947+154013	20	144805-011057	41	105040+342947
3B	074947+154013	21A	133708-325528	42A	101042+125516
4	082722+202612	21B	133708-325528	42B	101042+125516
5A	082520+082723	22	162152+151855	43A	103226+271755
5B	082520+082723	23	not declared	43B	103226+271755
6A	084000+180531	24	192758-413432	44	103726+270759
6B	084000+180531	25A	212043+010006	45	110838+223809
7	094000+203122	25B	212043+010006	46	105331+011740
8	095023+004229	25C	212043+010006	47A	102732-284201
9	095226+021759	25D	212043+010006	47B	102732-284201
10	101136+263027	26A	221823+003918	47C	102732-284201
11A	100720+193349	26B	221823+003918	48	114212+002003
11B	100720+193349	27A	051519-391741	49	132549+330354
12A	101430+004755	27B	051519-391741	50A	121329+114056
12B	101430+004755	28A	064650-374322	50B	121329+114056
13A	103412+014249	28B	064650-374322	51	130119+123959
13B	103412+014249	29	080000+274642	52	142342+225728
13C	103412+014249	30	083946+140033	53	125305-031258
14	104755+073951	31	084219+300703	54	132347-013252
15	104829+111520	32A	084414+022621	55	134531+044232
16A	105210+032713	32B	084414+022621	56A	171236+321633
16B	105210+032713	33	090531+033530	56B	171236+321633
17A	115023-003141	34	090506+223833	56C	171236+321633
17B	115023-003141	35	090418+260106	57A	211527-075951
18A	121717-280233	36	093424+222522	57B	211527-075951
18B	121717-280233	37	092540+063116	58A	222510-001152
18C	121717-280233	38	092749+084037	58B	222510-001152

shows the data sets and their respective ID.

3. Data Evaluation

Data reduction has been carried out with the official UVES pipeline by the ESO (European Southern Observatory). The installation and use of the pipeline was carried out in close cooperation with ESO support. We used the Reflex workflow, a graphical user interface that allows the user to adjust the reduction cascade at will.

Conceptually, the data comprise two well-established spectral lines that have been known for more than a century and are connected by the same initial (upper) atomic level. Thus, any spectral features that may result from the structure and dynamics of the individual galactic light source must affect both lines equally. This tie yields a powerful tool for judging the data quality of each observation. The [O III] ${}^1\mathrm{D}_2$→${}^3\mathrm{P}_{1,2}$ line ratio determined from the observation is close to 1/3, which is usually called “3” (in favour of the stronger line). Because of the (small) wavelength difference and the constant instrumental line width (on a wavelength scale), the band pass (on the energy flux scale) is slightly larger for the shorter-wavelength line, causing an apparent reduction in the line ratio by 0.959%. Wavelength and energy are inverse to each other (E = h$\nu$ = h$c/\lambda$). For a comparison of the data with theory (transition rates), the apparent line ratio has to be slightly enlargened correspondingly.

In fact, the original observation was not focused on the [O III] lines, and only 49 out of 86 data sets turned out to be suitable for this work. Out of the 37 rejected data sets, 15 were missing at least one of the analyzed [O III] lines because of redshift or other data corruption. A further 22 data sets failed to qualify for evaluation, as either their reduced ${\chi }^2$ values were too high (and thus appeared suspect, without necessarily showing an obvious cause), the line widths of the [O III] lines deviated too much (which is an indicator for contamination), or the signal-to-noise ratio fell below a value of five (our criterion). Data sets were also excluded when one of the lines happened to be saturated or coincided with a background sky line that interferes with the [O III] lines.

The data were fitted and analyzed by the Levenberg–Marquardt algorithm implemented in the python package astropy. A home-made python script employed this algorithm and performed several different fits to the data, based on the structure of the [O III] emission lines. This allowed the algorithm to fit the data with up to three different profiles: a single line Gaussian profile, a broadened line profile which uses wing fits on both sides of the emission line, and a multi-line Gaussian profile. Before fitting the profiles, an algorithm was used to determine the amount of distinguishable peaks in the [O III] lines. Based on this evaluation, the lines were fitted, and the fit with the lowest reduced ${\chi }^2$ value identified. Fits using multiple Gaussians will usually be chosen as the best, because with more fit parameters their reduced ${\chi }^2$ value is lowest. The algorithm is hard-coded to only allow the same fit profile for both analyzed [O III] lines, as any deviation would increase the error values. In theory, both [O III] lines need to show the exact same features and consist of an identical number of components. Differences in the profile strongly hint at a contaminated sample, suggesting that the data set should be excluded from evaluation. Figure 1 shows both [O III] lines for object 44 in comparison. Despite their rather unique appearance, the data sets are identical both in structure as well as in width.

Most of the data sets feature line profiles which visually consist of at least two components. However, in some cases, those components are so close to each other that multi-line profiles instantly over-fit the line and the respective individual component fits become unstable. Consequently, these individual line components should not be identified with specific physical features of the emitter galaxy, nor are the line ratios of individual components reliable. Nonetheless, the components are useful to derive the total line flux, because the combined components fit the emission line more precisely than a single-line profile. However, the resulting [O III] line ratio becomes stable only when looking at the total line flux.

A good example for a data set that is difficult to fit is object 44. Figure 2 shows examples of all fits, from a single Gaussian to several Gaussians without or with extra wings. Figure 1A shows the fit considered best for this specific line. The two-component Gauss profile fit resembles a partly merged double-line Doppler-broadened profile, possibly the red- and blue-shifted emissions of a rotating object. If two or more components are merged to a degree that the algorithm cannot resolve them as multiple components, the respective data set has to be fitted “by hand”. In this case, the fit software package Origin was used.

Some of the seemingly best (statistically most robust) line ratios are, significantly, of the expected value of about three. These cases could be considered as outliers of a statistical distribution, as indicators of technical problems in the observation or the data reduction pipeline, or as indicators of an unresolved structure at the source. This ambiguity introduces an element of human judgement and bias into the analysis of line ratio data. Such a bias can only be removed by future improved observations.

4. Results

The line ratio r of the [O III] lines at wavelengths $\lambda \lambda 4959,5007$ has been calculated as follows:

$$r={\displaystyle \frac{F\left([\mathrm{O}{\mathrm{III}]}_{5007}\right)}{F\left([\mathrm{O}{\mathrm{III}]}_{4959}\right)}}$$

(1)

The data sets are split into two categories. K1 data sets feature only one component per line, whereas K2 data sets have emission lines that can be split into multiple components. These components can be considered individually when calculating the line ratio. Figure 3 shows the calculated line ratio plotted against the respective redshift for every line component. Black dots represent a single-component data set (K1), while blue dots represent one of multiple components from a K2 data set.

The red line shows the line ratio average and has a value of

$$r=2.977\pm 0.237$$

(2)

After a small correction of about 0.96% for the non-linear inter-dependence of wavelength and energy (see above), the apparent line ratio is

$$r_{corr}=3.005\pm 0.237$$

(3)

An error value of almost 8% is rather high. Instead of taking every component into account individually, it is also possible to summarize all components of a single data set and take the resulting complete line profile instead. Figure 4 shows this plot, in which black dots are unchanged and still show the K1 data sets, while green dots are a cumulation of all components of one K2 data set. When comparing the figures, it is noteworthy that the [O III] ratio scale has changed.

The scattering now is significantly smaller than before. The line ratio has a value of

$$r_{\mathrm{cumulative}}=2.964\pm 0.095$$

(4)

With the necessary correction mentioned earlier, the corrected value is

$$r_{\mathrm{cumulative},\mathrm{corr}}=2.992\pm 0.095$$

(5)

The roughly 3% scatter in Figure 3 suggests that in this data sample even supposedly stable components cannot be fitted without an unfavourably high ambiguity. With an even higher spectral resolution than presently available, the line components could probably be interpreted individually and then yield more precise results for the line ratios.

For the representation of the complete line profiles, the statistics show a normal distribution (see Figure 5) without outliers. An increased sample size would possibly yield an even better error value for the [O III] line ratio.

5. Discussion

A treatise on atomic data assessment including the computation and interpretation of line ratio data in astrophysics has recently been presented by Morisset et al. [27]. For a critical view on theoretical predictions of atomic transition rates, see [28]. It seems intriguing to look at archival data from astrophysical observations without time resolution as a way to extract information on atomic levels that are too long lived to be measured for their lifetime (so far) [16], and to learn something about computations that differ notably from each other in their outcome on transition rates while a certain ratio of transition rate results (the line ratio) appears to be highly reproducible.

The approximate LR ≈ 3 of the 2s²2p^{2 3}P_1,2–¹D₂ lines in the [C I] isoelectronic sequence is misleading, because it applies to the lowest members of the isoelectronic sequence only. According to Galavis et al. [12] and Storey and Zeippen [14], the flux ratio decreases by about 13% along the isoelectronic sequence from [C I] to [Mg VII] (and it increases by about as much in the isoelectronic sequence [O I] up to [Mg V]). The transition rate predictions of these two computations differ by several percent. Both computations use an atomic structure model with experimental level energies. The difference in the newer results from the majority of earlier ones can be traced to a single origin; the introduction of a relativistic correction to the $M1$ transition operator by Storey and Zeippen [14].

However, a fraction of the data in the selected astrophysical data sample (from UVES observations at ESO Paranal [24]) meet most of the quality and consistency criteria, but show a significant deviation from the bulk of the LR values. Here, an additional signal has to be suspected, that at the resolving power of the UVES spectrograph at ESO Paranal cannot be separated from the [O III] lines. In these cases, the data pair has to be excluded from the statistical analysis of the LR values. After such filtering, the quality of the present data sample permits an estimate of the line ratio of interest, but that estimate does not test the predictions as well as one might hope for. A certain ambiguity emerges: on one hand, the spectral resolution of the presently evaluated data is high enough to show that the dynamical substructures of the observed galaxies must be contributing to the line widths, but the spatial and spectral resolution is not high enough to model the galaxies from the data. The uncertainties of photometry and line profile interpretation combine at the level of a few percent and thus they limit the quantification of the line ratio of interest by data from galaxies. Overall, the LR in [O III], as seen from the present sample of emission galaxies (LR = 3.005 ± 0.237), is compatible with the results of recent more complex computations rather than with earlier ones. Concerning a possible variation in the LR with age/distance, such a trend is not seen in the present redshift range, z = 0.01–0.2. Certainly, a much larger sample would facilitate an improvement in the data statistics. However, the present study highlights a need for data quality and consistency assessment, such as has resulted in the rejection of about a third of the envisioned data sample here.

A concurrent publication [29] discusses the hypothetical variation in the finestructure constant $\alpha$ over times that are commensurate with the age of the universe. That study uses the same [O III] line pair as lies at the core of the present manuscript. However, their search for a variation in the finestructure constant utilizes accurately measured wavelengths, i.e., the wavelength splitting of the line doublet, whereas our issue is the determination of line intensity ratios. The measured wavelengths yield a measure of the redshift. At high redshifts, the wavelengths differ substantially from those observed from the cosmic neighbourhood, which brings about a number of calibration problems as detailed in [29]. It is difficult to resolve line profiles to high detail on such distant objects. The problems we have encountered in the data set used here [24] (which led to our rejection of about a third of our intended data sample) are recognized in the other study, but are believed to be outdone by the very large number of objects included in their study. In principle, it should be feasible to extend our type of evaluation of line ratios to such a large sample. However, the very large redshifts involved imply a need to establish accurate high resolution spectroscopy in the near-infrared.