A Comprehensive multi-species comparison of rotational temperature probes in a DC Ar/N$_2$ micro-hollow cathode discharge

Accurate gas temperature ($T_{\rm Gas}$) determination in microplasmas is critical for optimizing their applications, yet isolated diagnostic approaches may yield misleading results, especially under strong non-equilibrium conditions. Here, high resolution rotational spectra of N$_2$(C), OH(A), NH(A) and NO(A), generated in the plasma jet of a DC Ar/N$_2$ microhollow cathode discharge (MHCD), are recorded and their associated rotational temperatures ($T_{\rm rot}$) are cross compared. A detailed experimental analysis and robust fitting of the rotational spectra are performed, achieving a reliable estimation of $T_{\rm Gas}$. The dominant formation mechanisms of these species and their corresponding impact on rotational population distributions are also interrogated. Particularly, our findings indicate that the $T_{\rm rot}$of N$_2$(C) is significantly influenced by energy transfers from argon metastables (Ar$^m$) and spectral interference from NH(A). This makes it unreliable as a thermometric probe in Ar-rich MHCD, unless complex analyses are employed. In contrast, OH(A) rotational population distribution appears to be less sensitive to Ar-induced perturbations across various discharge currents and pressures, providing more straightforward results. For all molecules considered, this study reveals the conditions under which all the measured $T_{\rm rot}$ can be reliably considered to be in equilibrium with $T_{\rm Gas}$. This highlights the importance of crossvalidating multiple thermometric probes and investigating relevant excitation kinetics when measuring $T_{\rm rot}$ in reactive microplasmas.