Testing the Physical Parameter Constraining Power of HCN and HNC with Neural Networks

TL;DR

This work evaluates how well HCN and HNC transitions constrain molecular gas conditions in the NGC-253 CMZ, using ALMA/ALCHEMI data and a forward model that combines UCLCHEM chemistry, a neural-network surrogate, and RADEX radiative transfer within a Bayesian nested-sampling framework. By testing numerous subsets of the eight measured transitions, the authors quantify how transition count, energy range, and species mixing affect recovery of $T_K$, $n_{H_2}$, $\zeta$, $N_{H_2}$, and $\eta_{ff}$ across three representative regions, including a low-SNR case. They find that single transitions perform poorly, while combinations spanning low and high $E_u$ from both species—especially including HCN/HNC $1-0$ and higher-$J$ lines—more reliably reproduce the full-transition control results; CRIR in particular requires multi-species constraints across the energy ladder. The study provides practical guidance for designing molecular-line observations to diagnose gas conditions in starburst environments and demonstrates a scalable inference framework that can be extended to other galaxies and chemical networks.

Abstract

We quantify the utility of HCN and HNC to characterize gas conditions in the nearby starburst galaxy NGC 253. We use measurements from the Atacama Large Millimeter/Submillimeter Array (ALMA) Large Program ALCHEMI: the ALMA Comprehensive High-resolution Molecular Inventory. Using different subsets of the eight total HCN and HNC transitions measured by ALCHEMI, we test the number and combinations of transitions necessary for constraining the temperature, H$_2$ volume and column densities, cosmic-ray ionization rate, and beam-filling factor in three representative regions within NGC 253. We use these combinations of HCN and HNC transitions to constrain chemical and radiative transfer models and infer the gas conditions using a Bayesian nested sampling algorithm combined with neural network models for increased efficiency. By comparing the shapes of the resulting posterior distributions, as well as the medians and uncertainties for each gas parameter, from each test case to what we obtain with the full set of eight transitions (the control), we quantify how well each test reproduces the control. We find that multiple transitions each of both molecules are required to obtain a median parameter value within a factor of 2 of the control with an uncertainty less than 2-3 times that of the control. We also find that transition combinations that feature a range of upper-state energies are most effective. We show that single transitions, such as HCN J = 1-0 or 3-2, are among the worst-performing combinations and result in parameter values up to an order of magnitude different than the control.

Figures (21)

• Figure 1: Map of NGC 253 HCN 1--0 integrated emission with S/N $> 3$ overlaid with the regions analyzed in Behrens2024. The three regions analyzed in this paper are highlighted in purple. The circle in the bottom left corner indicates the size of the 1. $^{\prime\prime}6$ ($\sim$27 pc) ALCHEMI beam. The orange cross indicates the location of the galaxy's kinematic center Turner1985.
• Figure 2: Bayesian inference results for the controls of the high-$n$-$\zeta$ region (top left) and for the synthetic region where the synthetic data SNR = 3 (top right) and SNR = 5 (bottom).
• Figure 3: Normalized least-squares residuals for each transition combination listed in Table \ref{['tab:mol_combos']}, where residual values close to zero indicate better agreement between the test and control distributions. The solid gray lines represent the median residual value across all parameters for the low-$n$-$\zeta$ region, and the dashed gray lines represent the first and third quartiles.
• Figure 4: Same as in Figures \ref{['fig:reg26_resids']} and \ref{['fig:reg51_resids']} but for the high-$n$-$\zeta$ region.
• Figure 5: Same as in Figure \ref{['fig:reg26_resids']} but for the low-SNR region.