Re-examining the Bayesian colour excess estimation for the local star-forming galaxies observed in the HETDEX pilot survey

In my previous reanalysis of the local star-forming galaxies observed in the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) pilot survey, I reported that the overestimation of E(B-V), hence the star formation rate (SFR), undermined the claim of new galaxy population discovery in the original study. Herein, I re-examine whether the E(B-V) overestimation problem can be alleviated in the Bayesian parameter estimation framework by adopting scientifically motivated new priors. I modelled the emission-line fluxes of galaxies using the strong-line method and four model parameters-metallicity $12 + \text{log {}(O/H)}$, nebula emission-line colour excess E(B-V), intrinsic [O iii] λ5007 line flux, and intrinsic [N ii] λ6584 line flux. Based on mock data tests, I found that all input values can be recovered within and around the 1σ credible interval by adopting suitable priors for the intrinsic [O iii] λ5007 and [N ii] λ6584 line fluxes: The inverse gamma distribution reflecting the logical constraint that an intrinsic emission-line flux must exceed the observed (reddened) emission-line flux. The mock data tests were performed for two metallicity calibrations, three colour excess input values [E(B-V) = 0.1, 0.3, and 0.5] and two metallicity input values [$12 + \text{log {}(O/H)}$ = 8.0 and 8.5]. I also found that the new prior can diminish the SFR overestimation eightfold. This study demonstrates how the Bayesian parameter estimation can achieve more accurate estimates with no further observations when the likelihood does not constrain the model parameters correctly.