Tracing Interstellar Heating: An ALCHEMI Measurement of the HCN Isomers in NGC 253

We analyze HCN and HNC emission in the nearby starburst galaxy NGC 253 to investigate its effectiveness in tracing heating processes associated with star formation. This study uses multiple HCN and HNC rotational transitions observed using ALMA via the ALCHEMI Large Program. To understand the conditions and associated heating mechanisms within NGC 253's dense gas, we employ Bayesian nested sampling techniques applied to chemical and radiative transfer models which are constrained using our HCN and HNC measurements. We find that the volume density $n_{\text{H}_{2}}$ and cosmic ray ionization rate (CRIR) $\zeta$ are enhanced by about an order of magnitude in the galaxy's central regions as compared to those further from the nucleus. In NGC 253's central GMCs, where observed HCN/HNC abundance ratios are lowest, $n \sim 10^{5.5}$ cm$^{-3}$ and $\zeta \sim 10^{-12}$ s$^{-1}$ (greater than $10^4$ times the average Galactic rate). We find a positive correlation in the association of both density and CRIR with the number of star formation-related heating sources (supernova remnants, HII regions, and super hot cores) located in each GMC, as well as a correlation between CRIRs and supernova rates. Additionally, we see an anticorrelation between the HCN/HNC ratio and CRIR, indicating that this ratio will be lower in regions where $\zeta$ is higher. Though previous studies suggested HCN and HNC may reveal strong mechanical heating processes in NGC 253's CMZ, we find cosmic ray heating dominates the heating budget, and mechanical heating does not play a significant role in the HCN and HNC chemistry.