Reply to: Effects of density and temperature variations on the metallicity of Mrk71

In Chen et al., 2023 (C23; arXiv:2304.09898), we introduced a new method to directly measure temperature fluctuations and applied it to a nearby dwarf galaxy, Mrk 71, finding a temperature fluctuation parameter t^2 = 0.008± 0.043. This result is lower by ∼ 2σ than the value required to explain the abundance discrepancy (AD) in this object. In the Matters Arising article submitted by Mendez-Delgado et al. (arXiv:2310.01197), the authors claim that using the same data presented in C23 in a different way, it is possible to conclude that the measurements are consistent with a larger t^2 ≃ 0.1 inferred indirectly from recombination lines (RLs). However, this requires a higher density such that the infrared [O III] 52 μm and [O III] 88 μm lines – which form the basis of the direct measurement method – are mutually inconsistent. Moreover, to reach agreement between the direct t^2 measurement and the larger t^2 value inferred from RLs requires systematically varying four parameters by ∼ 1σ from their best-determined values, which collectively amount to a ∼2σ difference, consistent with the significance (∼ 2 σ) originally reported in C23. Therefore, we conclude that the results of C23 hold, and that the combined optical and infrared [O III] data disfavour t^2 ≃ 0.1 at the ≈2σ level in Mrk 71. Future work is nonetheless warranted to better understand the AD associated with both optical and infrared emission line analysis.