🔬 atomic physics

Emissivity line ratios for [Mn III] and spectral diagnostics of H II regions

This paper presents the first theoretical study of Mn III emission lines, utilizing advanced relativistic Breit-Pauli R-matrix calculations to derive atomic data and collision strengths that enable the use of specific forbidden lines as temperature-density diagnostics and tools for determining cosmic manganese abundance in H II regions and supernova remnants.

Original authors: Zher Samak (Department of Physics, Al Aqsa University, Gaza, Palestine), Sultana N. Nahar (Department of Astronomy, The Ohio State University, Columbus, Ohio, USA 43210), Anil K. Pradhan (Department o

Published 2026-07-27

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Original authors: Zher Samak (Department of Physics, Al Aqsa University, Gaza, Palestine), Sultana N. Nahar (Department of Astronomy, The Ohio State University, Columbus, Ohio, USA 43210), Anil K. Pradhan (Department of Astronomy, The Ohio State University, Columbus, Ohio, USA 43210)

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Clockwork and the Missing Manganese

Imagine the universe as a giant, ancient library where every book is a star, and the ink used to write them is made of chemical elements. For decades, astronomers have been trying to read the history of this library by looking at how much iron is in the stars. Iron is like the library's most common paper; it's everywhere, and it tells a story about how stars are born and die. But there's another element, manganese, that acts like a special, rare ink that only appears in certain types of stories. While iron comes from massive stars that live fast and die young, manganese is produced more efficiently in a different kind of stellar explosion involving white dwarfs, which take billions of years to form. Because of this, the ratio of manganese to iron in a galaxy acts like a cosmic clock. It tells astronomers not just what the galaxy is made of, but when it was built.

To read this clock, scientists usually look at the light coming from stars. However, there's a problem: in the hot, glowing clouds of gas between stars (called H II regions) and in the debris of exploded stars (supernova remnants), the manganese isn't sitting quietly in a star; it's been blasted into a highly charged, ionized state. Until now, we've had a hard time seeing these charged manganese atoms because they don't shout as loudly as other elements, and the specific colors of light they emit are often hidden or too faint to catch with our telescopes. It's like trying to hear a whisper in a hurricane. Without a clear way to detect this "whisper," we've been missing a crucial piece of the puzzle in understanding how galaxies evolve over time.

The New Map to the Manganese Whisper

This paper is the first to create a detailed theoretical map for listening to that whisper. The authors, Zher Samak, Sultana Nahar, and Anil Pradhan, have performed massive computer simulations to figure out exactly how doubly ionized manganese ([Mn iii]) behaves when it gets bumped around by electrons in space. Think of the manganese atom as a complex, multi-story building with 1,421 different floors (energy levels). The team calculated what happens when an electron hits the building, knocking an atom up to a higher floor, and then what happens when it falls back down, releasing a flash of light. They focused specifically on the "forbidden" transitions—these are like secret staircases that atoms usually avoid, but in the thin, low-density vacuum of space, they become the main way the atom releases energy.

Using a powerful method called the Breit-Pauli R-matrix, they simulated collisions for 703 different transitions between the lowest 38 floors of this manganese building. They didn't just guess; they calculated the "collision strengths" (how likely a bump is to happen) and the "Einstein A-values" (how likely a light flash is to happen) for every single step. The result is a new set of tools for astronomers: a list of specific light ratios that act as diagnostic dials.

The paper finds that certain pairs of manganese light lines are incredibly sensitive to the density of the gas they are in, while others are sensitive to temperature. For instance, they identified a pair of ultraviolet lines (at 2996.42 Å and 2997.45 Å) and a pair of mid-infrared lines (at 4.35 μm and 4.33 μm) that change their brightness ratio depending on how crowded the gas is, but stay the same regardless of how hot it is. This makes them perfect "pure density" meters. Conversely, other line pairs change based on both temperature and density, allowing scientists to untangle the two variables if they measure them together. These findings suggest that with the James Webb Space Telescope (JWST), which can see these specific infrared colors, astronomers will finally be able to measure the manganese abundance in distant galaxies and supernova remnants.

However, the authors are careful to note that not everything is solved yet. They looked at a previous claim that a specific manganese line had been spotted at 6821.16 Å. After running their own simulations, they found that the closest candidate lines they calculated are actually hundreds of times weaker than the strong diagnostic lines they identified. While they cannot definitively say the 6821.16 Å line doesn't exist (because their model doesn't account for every possible real-world variable like the exact amount of manganese in that specific cloud), their calculations suggest that if it was seen, it was likely a very faint signal that is hard to explain with current atomic data.

Ultimately, this work doesn't just give us a list of numbers; it provides the key to unlocking the "Mn/Fe" ratio in the universe. By combining these new manganese diagnostics with existing iron data, astronomers can finally use manganese as a precise chronometer to trace the history of star formation and chemical evolution in the cosmos, turning a faint, previously ignored whisper into a clear voice in the story of the universe.

Technical Summary: Emissivity line ratios for [Mn III] and spectral diagnostics of H II regions

Problem Statement
While neutral manganese (Mn I) absorption lines are routinely used to determine Mn/Fe abundance ratios in stellar atmospheres, emission lines from ionized manganese have not been previously employed for astrophysical diagnostics in H II regions or supernova remnants (SNRs). This gap exists primarily because Mn abundance is approximately two orders of magnitude lower than iron, making spectral lines difficult to detect, and because singly ionized Mn II lines fall in the ultraviolet, limiting ground-based observation. However, with the advent of space-based observatories like JWST, red-shifted lines from high-redshift objects are becoming accessible. There is a need for theoretical atomic data to identify low-ionization stages of Mn (specifically [Mn III]) that emit in the UV/Optical/IR, which could serve as diagnostics for physical conditions and elemental abundances in nebular environments.

Methodology
The authors present the first systematic theoretical study of forbidden emission lines from doubly ionized manganese ([Mn III]). The computational framework involves three main stages:

Atomic Structure Calculations: Energy levels and Einstein $A$ -coefficients for forbidden electric-quadrupole ( $E2$ ) and magnetic-dipole ( $M1$ ) transitions were calculated using the SUPERSTRUCTURE (SS) code. The configuration interaction (CI) expansion included the ground configuration ( $3d^5$ ), the first excited configuration ( $3d^4 4s$ ), and correlation configurations up to $n=5$ . A total of 1421 fine-structure levels were computed. The lowest 38 levels, dominated by $3d^5$ and $3d^4 4s$ , were selected as target states for scattering calculations. The calculated energy levels were benchmarked against NIST experimental values, showing a mean difference of approximately 3%.
Collisional Excitation: Relativistic Breit-Pauli R-matrix (BPRM) calculations were performed for electron impact excitation. The close-coupling expansion included couplings among the 38 selected levels, covering an energy range up to 5.0 Ry. Collision strengths ( $\Omega_{ij}$ ) were computed for all 703 forbidden transitions among these levels. Maxwellian-averaged effective collision strengths ( $\Upsilon_{ij}$ ) were derived for electron temperatures ( $T_e$ ) ranging from 2,500 K to 40,000 K to smooth out resonance structures for astrophysical applications.
Collisional-Radiative (CR) Modeling: A CR model, utilizing the spectra code, was constructed to solve statistical equilibrium equations for coupled level populations. This model combined the calculated collision strengths and radiative decay rates to derive line emissivity ratios as functions of electron density ( $N_e$ ) and temperature ( $T_e$ ).

Key Results
The study provides a comprehensive dataset of atomic parameters and identifies specific line ratios with diagnostic utility:

Atomic Data: The authors computed collision strengths for 703 forbidden transitions and effective collision strengths over the relevant thermal range for H II regions.
Density Diagnostics: Two line ratios were identified as "pure" electron density diagnostics, showing negligible dependence on electron temperature ( $T_e$ $T_{e}$ ) across the range of 2,500–40,000 K:
- $R_1$ : The ratio of the 2996.42 Å line ( $4D_{5/2} \to 6S_{5/2}$ ) to the 2997.45 Å line ( $4D_{3/2} \to 6S_{5/2}$ ). This ultraviolet ratio is robust against interstellar reddening.
- $R_2$ : The ratio of the 4.35 $\mu$ m line ( $4D_{5/2} \to 4P_{3/2}$ ) to the 4.33 $\mu$ m line ( $4D_{3/2} \to 4P_{5/2}$ ). This mid-infrared ratio is accessible via JWST.
  Both ratios vary monotonically with electron density in the range $3 \lesssim \log_{10} N_e \lesssim 7$ cm $^{-3}$ .
Temperature-Density Diagnostics: Two additional ratios were found to be sensitive to both $N_e$ $N_{e}$ and $T_e$ $T_{e}$ , allowing for the breaking of degeneracy in plasma diagnostics when combined with $R_1$ $R_{1}$ and $R_2$ $R_{2}$ :
- $R_3$ : The ratio of the 4.40 $\mu$ m line to the 4.33 $\mu$ m line, showing strong temperature dependence at low densities.
- $R_4$ : The ratio of the 8213.52 Å line to the 8081.28 Å line, which increases monotonically with density and shows significant temperature sensitivity.
Line Identification: The authors re-examined a tentative identification of a Mn III line at 6821.16 Å reported by Esteban et al. (2004). Their calculations suggest the closest candidate transitions (at 6801.52 Å and 6796.42 Å) are significantly weaker (26–370 times) than established diagnostic lines. While the authors cannot definitively rule out the identification due to uncertainties in ionization fractions and abundance models, they conclude the identification remains highly uncertain.

Significance and Claims
The paper claims to provide the first theoretical framework for using [Mn III] emission lines as tools for astrophysical diagnostics. The primary significance lies in enabling the determination of physical conditions (temperature and density) in H II regions and SNRs, which are critical for understanding the chemical evolution of the Universe.

Specifically, the authors posit that these diagnostics could facilitate the measurement of cosmic Mn abundance relative to other elements, particularly iron. Since Mn and Fe have different nucleosynthetic origins and timescales (SNe II vs. SNe Ia), the Mn/Fe ratio serves as a chronometer for galaxy evolution. By combining the new [Mn III] diagnostics with existing [Fe II] data and JWST observations of high-redshift galaxies, it becomes possible to derive Mn/Fe abundance ratios. This would allow for a more detailed reconstruction of the star formation history and metallicity evolution of the Universe. The authors note that complete datasets will be made available through the NORAD online database.

The Cosmic Clockwork and the Missing Manganese

The New Map to the Manganese Whisper

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