[Paper Review] On the universal validity of Case B recombination theory

Claudia Scarlata, Matthew Hayes+4 more|arXiv (Cornell University)|Apr 13, 2024

Healthcare Policy and Management11 citations

TL;DR

The paper reports a Hα/Hβ ratio of 2.620±0.078 in SXDF308, argues Case B can fail for some high-excitation galaxies due to Balmer self-absorption and non-spherical scattering, and tests this with SDSS data and Cloudy modeling.

ABSTRACT

In an ongoing search for low-mass extreme emission line galaxies, we identified a galaxy with a Ha/Hb Balmer line ratio of 2.620 +- 0.078. Ha/Hb Balmer ratios lower than the dust-free Case~B value appear relatively frequently in extreme emission line galaxies. These low values suggest that the Case~B assumption may not be valid in these objects. After ruling out the possibility that the low Ha/Hb ratio is due to systematic errors introduced by observational effects, we use constraints from the total Hb luminosity, the [OIII]/[OII] line ratio and the Balmer line equivalent widths, to suggest that the gas is optically thick to both Ha and Lya photons, and the geometry and orientation of the scattering gas causes Ha photons to be preferentially removed from the line of sight with respect to higher order Balmer series photons. Finally, we use data from the SDSS survey to show that Balmer self-absorption may be more important than previously assumed in high excitation emission line galaxies, where Lya pumping of the hydrogen excited state can be effective. If not recognized, Balmer self-absorption could lead to inaccurate estimates of galaxy physical properties. As an example, the effect of dust extinction could be over-estimated, for spherically symmetric scattering medium, or under-estimated, for a not spherically-symmetric distribution.

Motivation & Objective

• Motivate re-evaluating Case B applicability in extreme emission line galaxies (EELGs).
• Determine physical conditions (Te, ne) of SXDF308 to interpret Balmer line ratios.
• Assess whether non-spherical Balmer photon scattering/self-absorption can explain low Hα/Hβ values.
• Explore observational/systematic effects and alternative mechanisms (Case C, fluorescence) against Case B.
• Evaluate implications for dust extinction estimates and LyC escape fractions in high-excitation systems.

Proposed method

• Obtain and analyze deep optical spectrum of SXDF308 with Hectospec (MMT) to measure Balmer lines and [O III]/[O II].
• Compute Te from [O III] 4363/4959+5007 using PyNeb and derive ne from [S II] and [Ar IV] diagnostics.
• Compare observed Hα/Hβ to Case A/B predictions across Te and ne, using PyNeb.
• Perform Cloudy photoionization modeling to test Case C and fluorescence contributions for Balmer ratios.
• Use SDSS MPA-JHU data to assess Balmer self-absorption signatures in a large galaxy sample.
• Discuss radiative transfer implications for geometry and viewing angle on Balmer line emissivities.

Figure 1: Main panel: MMT spectrum of SXDF308. The full wavelength and flux range is shown to emphasize the line ratios between the strongest emission lines. In particular, note the large [O iii ]5007/H $\beta$ line ratio, indicating the presence of a hard ionizing radiation field. Insets: zooms in

Experimental results

Research questions

• RQ1 Does SXDF308 exhibit Balmer line ratios inconsistent with Case B across plausible Te and ne?
• RQ2 Can Case C or Balmer self-absorption in non-spherical gas reproduce the observed Balmer ratios and luminosities?
• RQ3 What role does geometry (e.g., edge-on disk-like scattering) play in preferentially removing Hα along the line of sight?
• RQ4 Are Balmer self-absorption signatures present in SDSS star-forming galaxies, implying non-negligible transport effects broadly?
• RQ5 What are the consequences for dust extinction estimates and LyC escape fraction calculations if Case B is not universally valid?

Key findings

• SXDF308 shows Hα/Hβ = 2.620±0.078, significantly below Case B (2.863 for Te≈1e4 K, ne≈100 cm^-3).
• Te(O2+) is 15380±850 K and ne(S+) ≈ 10 cm^-3, with an upper limit ne(Ar3+) < 10^3 cm^-3, indicating high excitation conditions.
• Case B predicted Hα/Hβ ≈ 2.79, higher than observed; Case A remains unable to reach the observed value, suggesting non-standard physics.
• Cloudy models with Case C and fluorescence can reproduce Balmer ratios at certain depths but struggle to match all observed constraints (e.g., Hβ luminosity).
• Balmer self-absorption in non-spherically symmetric gas can explain low Hα/Hβ if Hα photons are preferentially scattered out of the line of sight; SDSS data show galaxies with Balmer ratios not explainable by dust alone, consistent with self-absorption effects.

Figure 2: Full emission line profiles for both the H $\alpha$ and H $\beta$ lines. The inset zooms in on the continuum around the lines. The solid curve indicate the best-fit Gaussian profiles to the emission lines.