Reply to: Effects of density and temperature variations on the metallicity of Mrk 71

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 $t^2=0.008\pm 0.043$. This result is lower by $\sim 2\sigma$ 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 $t^2\simeq 0.1$ inferred indirectly from recombination lines (RLs). However, this requires a higher density such that the infrared [O III] 52 $\mu$m and [O III] 88 $\mu$m 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 $\sim 1\sigma$ from their best-determined values, which collectively amount to a $\sim 2\sigma$ difference, consistent with the significance ($\sim 2\sigma$) originally reported in C23. Therefore, we conclude that the results of C23 hold, and that the combined optical and infrared [O III] data disfavour $t^2\simeq 0.1$ at the $\approx 2\sigma$ level in Mrk 71. Future work is nonetheless warranted to better understand the AD associated with both optical and infrared emission line analysis.