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Temperature inhomogeneities cause the abundance discrepancy in H ii regions

Nature volume 618, pages 249–251 (2023)Cite this article

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Abstract

H ii regions are ionized nebulae surrounding massive stars. They exhibit a wealth of emission lines that form the basis for estimation of chemical composition. Heavy elements regulate the cooling of interstellar gas, and are essential to the understanding of several phenomena such as nucleosynthesis, star formation and chemical evolution1,2. For over 80 years3, however, a discrepancy exists of a factor of around two between heavy-element abundances derived from collisionally excited lines and those from the weaker recombination lines, which has thrown our absolute abundance determinations into doubt4,5. Here we report observational evidence that there are temperature inhomogeneities within the gas, quantified by t2 (ref. 6). These inhomogeneities affect only highly ionized gas and cause the abundance discrepancy problem. Metallicity determinations based on collisionally excited lines must be revised because these may be severely underestimated, especially in regions of lower metallicity such as those recently observed with the James Webb Space Telescope in high-z galaxies7,8,9. We present new empirical relations for estimation of temperature and metallicity, critical for a robust interpretation of the chemical composition of the Universe over cosmic time.

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Fig. 1: Correlation of temperature inhomogeneities with temperature differences between ionization zones.
Fig. 2: Comparison of high- and low-ionization zone temperatures within extragalactic H ii regions.
Fig. 3: Extension of Fig. 1 considering H ii regions and RNe of the Milky Way.
Fig. 4: Revised metallicities when accounting for temperature inhomogeneities.
Fig. 5: Temperature–metallicity relation for extragalactic H ii regions.

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Data availability

All data included are publicly available and cited in the references. Source data are provided with this paper.

Code availability

Our results use the PyNeb code, publicly available on GitHub (https://github.com/Morisset/PyNeb_devel).

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Acknowledgements

J.E.M.-D. thanks A. Peimbert and S. Torres-Peimbert for fruitful discussions on the formalism of temperature variations and chemical inhomogeneities in the ionized gas and W. J. Henney for interesting discussions. J.E.M.-D. and K.K. gratefully acknowledge funding from Deutsche Forschungsgemeinschaft in the form of an Emmy Noether Research Group grant (no. KR4598/2-1, PI Kreckel). C.E. and J.G.-R. acknowledge support from Agencia Estatal de Investigación del Ministerio de Ciencia e Innovación under grant Espectroscopía de campo integral de regiones H ii locales, Modelos para el estudio de regiones H ii extragalácticas (no. 10.13039/501100011033) and support under grant no. P/308614 financed by funds transferred from the Spanish Ministry of Science, Innovation and Universities, charged to the General State Budgets and with funds transferred from the General Budgets of the Autonomous Community of the Canary Islands by MCIU. J.G.-R. acknowledges support from an Advanced Fellowship under the Severo Ochoa excellence programme CEX2019-000920-S and financial support from the Canarian Agency for Research, Innovation and Information Society of the Canary Islands Government, and the European Regional Development Fund under grant no. ProID2021010074.

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Authors and Affiliations

  1. Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Heidelberg, Germany

    J. Eduardo Méndez-Delgado & Kathryn Kreckel

  2. Instituto de Astrofísica de Canarias, San Cristóbal de La Laguna, Spain

    César Esteban & Jorge García-Rojas

  3. Departamento de Astrofísica, Universidad de La Laguna, San Cristóbal de La Laguna, Spain

    César Esteban & Jorge García-Rojas

  4. Instituto de Astronomía, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Manuel Peimbert

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Contributions

J.E.M.-D. conducted the study following the original idea, compiled appropriate data, recalculated the physical conditions and chemical abundances, created the figures, wrote the manuscript and interpreted results. C.E. checked the consistency of the spectroscopic analysis, contributed to the interpretation of results and edited the manuscript. J.G.-R. checked the consistency of the spectroscopic analysis and interpretation of the results and edited the manuscript. K.K. contributed to discussion on the impact of the results and edited the manuscript. M.P. reviewed the formalism of temperature inhomogeneities under the paradigm proposed in this work and edited the manuscript.

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Correspondence to J. Eduardo Méndez-Delgado.

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Extended data figures and tables

Extended Data Fig. 1 Similar relation to Fig. 1 but considering the electron temperature of [Ar iii].

Te([Ar iii]λ5192/λ7751) − Te([N ii] λ5755/λ6584) seems to have a similar correlation with t2(O2+) than Te([O iii]λ4363/λ5007) − Te([N ii] λ5755/λ6584). This indicates that Te([Ar iii] λ5192/λ7751) also suffers from a bias due to the presence of t2(O2+) > 0 and rules out recombination contributions to the [O iii] λ4363 CEL as the cause of the trend observed in Fig. 1. The color bar corresponds to the O/H abundance derived from CELs assuming a homogeneous temperature structure (t2 = 0). Error bars correspond to 1σ standard deviation.

Source data

Extended Data Fig. 2 Extension of Fig. 1 considering other extragalactic H ii regions from the literature.

Other spectra from extragalactic H ii regions of the literature with similar characteristics than our observational sample follow the same t2(O2+)-ΔTe correlation, ruling out that our findings are the effect of a selection bias. Equation (3) describes the best fit derived from Fig. 1 (blue). Error bars correspond to 1σ standard deviation.

Source data

Extended Data Fig. 3 Temperature-metallicity relation for ionized hydrogen in extragalactic H ii regions.

T0(H+)-metallicity relation considering t2(O2+) > 0 that permits the determination of metallicity in H ii regions observed at radio wavelengths. The color bar shows the derived t2(O2+) values. Equation (7) describes the best fit line (blue). The Pearson correlation coefficient of the fit (r) is -0.94. Error bars correspond to 1σ standard deviation.

Source data

Extended Data Fig. 4 Comparison between the global temperature and that derived from [O iii] emission lines.

T0(H+), which should be very similar to the temperature inferred from the Balmer jump in the optical continuum emission, can have a good consistency with Te([O iii] λ4363/λ5007), even though t2(O2+) > 0. This is because the emission of H I RLs arises from the whole nebula, including the volume of low degree of ionization, which does not present relevant temperature inhomogeneities and is hotter than the average temperature of the zone of high degree of ionization. The color bar shows the degree of ionization O2+/O. Error bars correspond to 1σ standard deviation.

Source data

Supplementary information

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Méndez-Delgado, J.E., Esteban, C., García-Rojas, J. et al. Temperature inhomogeneities cause the abundance discrepancy in H ii regions. Nature 618, 249–251 (2023). https://doi.org/10.1038/s41586-023-05956-2

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