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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).

References

  1. Maiolino, R. & Mannucci, F. De Re Metallica: the cosmic chemical evolution of galaxies. Astron. Astrophys. Review 27, 3 (2019).

    ADS  Google Scholar 

  2. Kewley, L. J., Nicholls, D. C. & Sutherland, R. S. Understanding galaxy evolution through emission lines. Annu. Rev. Astron. Astrophys. 57, 511–570 (2019).

    ADS  Google Scholar 

  3. Wyse, A. B. The spectra of ten gaseous nebulae. Astrophys. J. 95, 356 (1942).

    ADS  CAS  Google Scholar 

  4. Ferland, G. J. Quantitative spectroscopy of photoionized clouds. Annu. Rev. Astron. Astrophys. 41, 517–554 (2003).

    ADS  CAS  Google Scholar 

  5. Peimbert, M., Peimbert, A. & Delgado-Inglada, G. Nebular spectroscopy: a guide on H ii regions and planetary nebulae. PASP 129, 082001 (2017).

    ADS  Google Scholar 

  6. Peimbert, M. Temperature determinations of H ii regions. Astrophys. J. 150, 825 (1967).

    ADS  CAS  Google Scholar 

  7. Arellano-Córdova, K. Z. et al. A first look at the abundance pattern—O/H, C/O, and Ne/O—in z > 7 galaxies with JWST/NIRSpec. Astrophys. J. Lett. 940, L23 (2022).

    ADS  Google Scholar 

  8. Curti, M. et al. The chemical enrichment in the early Universe as probed by JWST via direct metallicity measurements at z ~ 8. Mon. Not. R. Astron. Soc. 518, 425–438 (2023).

    ADS  Google Scholar 

  9. Katz, H. et al. First insights into the ISM at z > 8 with JWST: possible physical implications of a high [O iii] λ4363/[O iii] λ5007. Mon. Not. R. Astron. Soc. 518, 592–603 (2023).

    ADS  Google Scholar 

  10. Peimbert, M. & Costero, R. Chemical abundances in Galactic H ii regions. Bol. Obs. Tonantzintla Tacubaya 5, 3–22 (1969).

    ADS  Google Scholar 

  11. Peimbert, A. & Peimbert, M. Densities, temperatures, pressures, and abundances derived from O ii recombination lines in H ii regions and their Implications. Astrophys. J. 778, 89 (2013).

    ADS  Google Scholar 

  12. García-Rojas, J. & Esteban, C. On the abundance discrepancy problem in H ii regions. Astrophys. J. 670, 457–470 (2007).

    ADS  Google Scholar 

  13. Méndez-Delgado, J. E. et al. Gradients of chemical abundances in the Milky Way from H ii regions: distances derived from Gaia EDR3 parallaxes and temperature inhomogeneities. Mon. Not. R. Astron. Soc. 510, 4436–4455 (2022).

    ADS  Google Scholar 

  14. Esteban, C., Peimbert, M., Torres-Peimbert, S. & Rodríguez, M. Optical recombination lines of heavy elements in giant extragalactic H ii regions. Astrophys. J. 581, 241–257 (2002).

    ADS  CAS  Google Scholar 

  15. Peimbert, A., Peña-Guerrero, M. A. & Peimbert, M. A classification of H ii regions based on oxygen and helium lines: the cases of TOL 2146-391 and TOL 0357-3915. Astrophys. J. 753, 39 (2012).

    ADS  Google Scholar 

  16. Toribio San Cipriano, L. et al. Carbon and oxygen in H ii regions of the Magellanic Clouds: abundance discrepancy and chemical evolution. Mon. Not. R. Astron. Soc. 467, 3759–3774 (2017).

    ADS  Google Scholar 

  17. Stasińska, G. The interest of high spatial resolution observations of presumed metal-rich H ii regions. Astron. Astrophys. 85, 359–361 (1980).

    ADS  Google Scholar 

  18. Garnett, D. R. Electron temperature variations and the measurement of nebular abundances. Astron. J. 103, 1330 (1992).

    ADS  CAS  Google Scholar 

  19. Pérez, E. Temperature fluctuations and starburst evolution. Mon. Not. R. Astron. Soc. 290, 465–470 (1997).

    ADS  Google Scholar 

  20. Ercolano, B., Bastian, N. & Stasińska, G. The effects of spatially distributed ionization sources on the temperature structure of H ii regions. Mon. Not. R. Astron. Soc. 379, 945–955 (2007).

    ADS  CAS  Google Scholar 

  21. Esteban, C., Mesa-Delgado, A., Morisset, C. & García-Rojas, J. The chemical composition of Galactic ring nebulae around massive stars. Mon. Not. R. Astron. Soc. 460, 4038–4062 (2016).

    ADS  CAS  Google Scholar 

  22. Walborn, N. R. The space distribution of the O stars in the solar neighborhood. Astron. J. 78, 1067–1083 (1973).

    ADS  Google Scholar 

  23. Peimbert, A. The chemical composition of the 30 Doradus Nebula derived from Very Large Telescope echelle spectrophotometry. Astrophys. J. 584, 735–750 (2003).

    ADS  CAS  Google Scholar 

  24. López-Sánchez, Á. R., Esteban, C., García-Rojas, J., Peimbert, M. & Rodríguez, M. The localized chemical pollution in NGC 5253 revisited: results from deep echelle spectrophotometry. Astrophys. J. 656, 168–185 (2007).

    ADS  Google Scholar 

  25. Esteban, C. et al. Keck HIRES spectroscopy of extragalactic H ii regions: C and O abundances from recombination lines. Astrophys. J. 700, 654–678 (2009).

    ADS  CAS  Google Scholar 

  26. Esteban, C. et al. Carbon and oxygen abundances from recombination lines in low-metallicity star-forming galaxies. Implications for chemical evolution. Mon. Not. R. Astron. Soc. 443, 624–647 (2014).

    ADS  CAS  Google Scholar 

  27. Toribio San Cipriano, L., García-Rojas, J., Esteban, C., Bresolin, F. & Peimbert, M. Carbon and oxygen abundance gradients in NGC 300 and M33 from optical recombination lines. Mon. Not. R. Astron. Soc. 458, 1866–1890 (2016).

    ADS  CAS  Google Scholar 

  28. Esteban, C., Bresolin, F., García-Rojas, J. & Toribio San Cipriano, L. Carbon, nitrogen, and oxygen abundance gradients in M101 and M31. Mon. Not. R. Astron. Soc. 491, 2137–2155 (2020).

    ADS  CAS  Google Scholar 

  29. Domínguez-Guzmán, G., Rodríguez, M., García-Rojas, J., Esteban, C. & Toribio San Cipriano, L. The homogeneity of chemical abundances in H ii regions of the Magellanic Clouds. Mon. Not. R. Astron. Soc. 517, 4497–4514 (2022).

    ADS  Google Scholar 

  30. García-Rojas, J. et al. Chemical abundances of the Galactic H ii region NGC 3576 derived from Very Large Telescope echelle spectrophotometry. Astrophys. J. Supplement. 153, 501–522 (2004).

    ADS  Google Scholar 

  31. García-Rojas, J. et al. Deep echelle spectrophotometry of S 311, a Galactic H ii region located outside the solar circle. Mon. Not. R. Astron. Soc. 362, 301–312 (2005).

    ADS  Google Scholar 

  32. García-Rojas, J. et al. Faint emission lines in the Galactic H ii regions M16, M20 and NGC 3603. Mon. Not. R. Astron. Soc. 368, 253–279 (2006).

    ADS  Google Scholar 

  33. García-Rojas, J. et al. The chemical composition of the Galactic H ii regions M8 and M17. A revision based on deep VLT echelle spectrophotometry. Rev. Mex. Astron. Astrofis. 43, 3–31 (2007).

    ADS  Google Scholar 

  34. Esteban, C., Fang, X., García-Rojas, J. & Toribio San Cipriano, L. The radial abundance gradient of oxygen towards the Galactic anti-centre. Mon. Not. R. Astron. Soc. 471, 987–1004 (2017).

    ADS  CAS  Google Scholar 

  35. Esteban, C. et al. A reappraisal of the chemical composition of the Orion Nebula based on Very Large Telescope echelle spectrophotometry. Mon. Not. R. Astron. Soc. 355, 229–247 (2004).

    ADS  CAS  Google Scholar 

  36. Mesa-Delgado, A. et al. Properties of the ionized gas in HH 202 – II. Results from echelle spectrophotometry with Ultraviolet Visual Echelle Spectrograph. Mon. Not. R. Astron. Soc. 395, 855–876 (2009).

    ADS  CAS  Google Scholar 

  37. Delgado-Inglada, G., Mesa-Delgado, A., García-Rojas, J., Rodríguez, M. & Esteban, C. The Fe/Ni ratio in ionized nebulae: clues on dust depletion patterns. Mon. Not. R. Astron. Soc. 456, 3855–3865 (2016).

    ADS  CAS  Google Scholar 

  38. Méndez-Delgado, J. E. et al. Photoionized Herbig-Haro objects in the Orion Nebula through deep high-spectral resolution spectroscopy – I. HH 529 II and III. Mon. Not. R. Astron. Soc. 502, 1703–1739 (2021).

    ADS  Google Scholar 

  39. Méndez-Delgado, J. E. et al. Photoionized Herbig-Haro objects in the Orion Nebula through deep high spectral resolution spectroscopy. II. HH 204. Astrophys. J. 918, 27 (2021).

    ADS  Google Scholar 

  40. Méndez-Delgado, J. E., Esteban, C., García-Rojas, J. & Henney, W. J. Photoionized Herbig-Haro objects in the Orion Nebula through deep high-spectral resolution spectroscopy – III. HH 514. Mon. Not. R. Astron. Soc. 514, 744–761 (2022).

    ADS  Google Scholar 

  41. Luridiana, V., Morisset, C. & Shaw, R. A. PyNeb: a new tool for analyzing emission lines. I. Code description and validation of results. Astron. Astrophys. 573, A42 (2015).

    ADS  Google Scholar 

  42. Storey, P. J. & Hummer, D. G. Recombination line intensities for hydrogenic ions-IV. Total recombination coefficients and machine-readable tables for Z=1 to 8. Mon. Not. R. Astron. Soc. 272, 41–48 (1995).

    ADS  CAS  Google Scholar 

  43. Storey, P. J., Sochi, T. & Bastin, R. Recombination coefficients for O ii lines in nebular conditions. Mon. Not. R. Astron. Soc. 470, 379–389 (2017).

    ADS  CAS  Google Scholar 

  44. Froese Fischer, C. & Tachiev, G. Breit-Pauli energy levels, lifetimes, and transition probabilities for the beryllium-like to neon-like sequences. At. Data Nucl. Data Tables 87, 1–184 (2004).

    ADS  CAS  Google Scholar 

  45. Wiese, W. L., Fuhr, J. R. & Deters, T. M. Atomic transition probabilities of carbon, nitrogen, and oxygen: a critical data compilation. J. Phys. Chem. Ref. Data https://srd.nist.gov/JPCRD/jpcrdM7.pdf (1996).

  46. Storey, P. J. & Zeippen, C. J. Theoretical values for the [O iii] 5007/4959 line-intensity ratio and homologous cases. Mon. Not. R. Astron. Soc. 312, 813–816 (2000).

    ADS  CAS  Google Scholar 

  47. Irimia, A. & Froese Fischer, C. Breit Pauli oscillator strengths, lifetimes and Einstein A coefficients in singly ionized sulphur. Phys. Scr. 71, 172–184 (2005).

    ADS  CAS  Google Scholar 

  48. Fritzsche, S., Fricke, B., Geschke, D., Heitmann, A. & Sienkiewicz, J. E. Forbidden transitions in the ground-state configuration of low-Z phosphorus-like ions. Astrophys. J. 518, 994–1001 (1999).

    ADS  CAS  Google Scholar 

  49. Mendoza, C. Recent advances in atomic calculations and experiments of interest in the study of planetary nebulae. In Planetary Nebulae. IAU Symposium 103 (ed. Flower, D. R.) 143–172 (Reidel Publishing, 1983).

  50. Kaufman, V. & Sugar, J. Forbidden lines in ns2npk ground configurations and nsnp excited configurations of beryllium through molybdenum atoms and ions. J. Phys. Chem. Ref. Data 15, 321–426 (1986).

    ADS  CAS  Google Scholar 

  51. Mendoza, C. & Zeippen, C. J. Transition probabilities for forbidden lines in the 3p3 configuration. Mon. Not. R. Astron. Soc. 198, 127–139 (1982).

    ADS  CAS  Google Scholar 

  52. Quinet, P. Transition probabilities for forbidden lines of Fe iii. Astron. Astrophys. Suppl. Ser. 116, 573–578 (1996).

    ADS  CAS  Google Scholar 

  53. Kisielius, R., Storey, P. J., Ferland, G. J. & Keenan, F. P. Electron-impact excitation of O ii fine-structure levels. Mon. Not. R. Astron. Soc. 397, 903–912 (2009).

    ADS  CAS  Google Scholar 

  54. Storey, P. J., Sochi, T. & Badnell, N. R. Collision strengths for nebular [O iii] optical and infrared lines. Mon. Not. R. Astron. Soc. 441, 3028–3039 (2014).

    ADS  CAS  Google Scholar 

  55. Tayal, S. S. Electron excitation collision strengths for singly ionized nitrogen. Astrophys. J. Suppl. 195, 12 (2011).

    ADS  Google Scholar 

  56. Tayal, S. S. & Zatsarinny, O. Breit-Pauli transition probabilities and electron excitation collision strengths for singly ionized sulfur. Astrophys. J. Suppl. 188, 32–45 (2010).

    ADS  CAS  Google Scholar 

  57. Butler, K. & Zeippen, C. J. Effective collision strengths for fine-structure forbidden transitions in the 3p3 configuration of Cl iii. Astron. Astrophys. 208, 337–344 (1989).

    ADS  CAS  Google Scholar 

  58. Galavis, M. E., Mendoza, C. & Zeippen, C. J. Atomic data from the IRON Project. X. Effective collision strengths for infrared transitions in silicon- and sulphur-like ions. Astron. Astrophys. Suppl. Ser. 111, 347 (1995).

    ADS  CAS  Google Scholar 

  59. Ramsbottom, C. A. & Bell, K. L. Effective collision strengths for electron-impact excitation of triphy ionized argon. At. Data Nucl. Data Tables 66, 65 (1997).

    ADS  CAS  Google Scholar 

  60. Zhang, H. Atomic data from the Iron Project. XVIII. Electron impact excitation collision strengths and rate coefficients for Fe iii. Astron. Astrophys. Suppl. Ser. 119, 523–528 (1996).

    ADS  CAS  Google Scholar 

  61. Torres-Peimbert, S., Peimbert, M. & Peña, M. Planetary nebulae with a high degree of ionization: NGC 2242 and NGC 4361. Astron. Astrophys. 233, 540 (1990).

    ADS  CAS  Google Scholar 

  62. Zhang, Y., Ercolano, B. & Liu, X. W. Temperature fluctuations in H ii regions: t2 for the two-phase model. Astron. Astrophys. 464, 631–634 (2007).

  63. Nicholls, D. C., Dopita, M. A. & Sutherland, R. S. Resolving the electron temperature discrepancies in H ii regions and planetary nebulae: κ-distributed electrons. Astrophys. J. 752, 148 (2012).

  64. Ferland, G. J., Henney, W. J., O’Dell, C. R. & Peimbert, M. The abundance discrepancy factor and t2 in nebulae: are non-thermal electrons the culprits? Rev. Mex. Astron. Astrofis. 52, 261 (2016).

    ADS  CAS  Google Scholar 

  65. Rodríguez, M. & García-Rojas, J. Temperature structure and metallicity in H ii regions. Astrophys. J. 708, 1551–1559 (2010).

    ADS  Google Scholar 

  66. Rubin, R. H. Noncollisional excitation of low-lying states in gaseous nebulae. Astrophys. J. 309, 334 (1986).

    ADS  CAS  Google Scholar 

  67. Guseva, N. G. et al. VLT spectroscopy of low-metallicity emission-line galaxies: abundance patterns and abundance discrepancies. Astron. Astrophys. 529, A149 (2011).

    Google Scholar 

  68. Peimbert, A., Peimbert, M. & Ruiz, M. T. Chemical composition of two H ii regions in NGC 6822 based on VLT spectroscopy. Astrophys. J. 634, 1056–1066 (2005).

    ADS  CAS  Google Scholar 

  69. Peña-Guerrero, M. A., Peimbert, A., Peimbert, M. & Ruiz, M. T. Analysis of two Small Magellanic Cloud H ii regions considering thermal inhomogeneities: implications for the determinations of extragalactic chemical abundances. Astrophys. J. 746, 115 (2012).

    ADS  Google Scholar 

  70. Valerdi, M., Peimbert, A., Peimbert, M. & Sixtos, A. Determination of the primordial helium abundance based on NGC 346, an H ii region of the Small Magellanic Cloud. Astrophys. J. 876, 98 (2019).

    ADS  CAS  Google Scholar 

  71. Peimbert, M., Peimbert, A. & Ruiz, M. T. The chemical composition of the Small Magellanic Cloud H ii region NGC 346 and the primordial helium abundance. Astrophys. J. 541, 688–700 (2000).

    ADS  CAS  Google Scholar 

  72. Binder, B. A. & Povich, M. S. A multiwavelength look at Galactic massive star-forming regions. Astrophys. J. 864, 136 (2018).

    ADS  Google Scholar 

  73. Asplund, M., Amarsi, A. M. & Grevesse, N. The chemical make-up of the Sun: a 2020 vision. Astron. Astrophys. 653, A141 (2021).

    ADS  CAS  Google Scholar 

  74. Peimbert, A. & Peimbert, M. On the O/H, Mg/H, Si/H, and Fe/H gas and dust abundance ratios in Galactic and extragalactic H ii regions. Astrophys. J. 724, 791–798 (2010).

    ADS  CAS  Google Scholar 

  75. Sánchez, S. F. et al. PPAK integral field spectroscopy survey of the Orion Nebula. Data release. Astron. Astrophys. 465, 207–217 (2007).

    ADS  Google Scholar 

  76. Mesa-Delgado, A., Esteban, C. & García-Rojas, J. Small-scale behavior of the physical conditions and the abundance discrepancy in the Orion Nebula. Astrophys. J. 675, 389–404 (2008).

    ADS  CAS  Google Scholar 

  77. García-Rojas, J. Physical Conditions and Chemical Abundances in Photoionized Nebulae from Optical Spectra 89–121 (Springer International Publishing, 2020).

  78. Liu, X. W. et al. NGC 6153: a super-metal-rich planetary nebula? Mon. Not. R. Astron. Soc. 312, 585–628 (2000).

    ADS  CAS  Google Scholar 

  79. Wesson, R., Liu, X. W. & Barlow, M. J. Physical conditions in the planetary nebula Abell 30. Mon. Not. R. Astron. Soc. 340, 253–263 (2003).

    ADS  CAS  Google Scholar 

  80. Storey, P. J. & Sochi, T. The continuum emission spectrum of Hf 2-2 near the Balmer limit and the ORL versus CEL abundance and temperature discrepancy. Mon. Not. R. Astron. Soc. 440, 2581–2587 (2014).

    ADS  CAS  Google Scholar 

  81. Corradi, R. L. M., García-Rojas, J., Jones, D. & Rodríguez-Gil, P. Binarity and the abundance discrepancy problem in planetary nebulae. Astrophys. J. 803, 99 (2015).

    ADS  Google Scholar 

  82. García-Rojas, J. et al. MUSE spectroscopy of planetary nebulae with high abundance discrepancies. Mon. Not. R. Astron. Soc. 510, 5444–5463 (2022).

    ADS  Google Scholar 

  83. Richer, M. G. et al. NGC 6153: reality is complicated. Astron. J. 164, 243 (2022).

    ADS  Google Scholar 

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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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