A rotational line CO cooling rate prescription for AGB outflows

TL;DR

This work tackles accurate CO rotational cooling in 3D NLTE simulations of AGB outflows, where radiative cooling strongly shapes thermal balance. Using 3D SPH wind models and Magritte NLTE transfer, the authors compute $\Lambda$ self-consistently and compare against ISM-based prescriptions, finding large errors when those prescriptions are applied outside their intended regimes. They introduce a new polynomial fit in $\log$-space that expresses $\log_{10}\Lambda$ as a function of $\log_{10}T$, $\log_{10}n_{\mathrm{H}_2}$, $\log_{10}(n_{\mathrm{CO}}/n_{\mathrm{H}_2})$, and $\log_{10}(n_{\mathrm{CO}}/|\nabla\cdot\mathbf{v}|)$ with final configuration $N=[3,4,1,2]$, achieving $\sigma_{fit}=0.034$ dex across the parameter space. The study also quantifies uncertainties via covariance analysis and examines perturbative sensitivities, showing distinct scaling in low- vs high-density regimes and the growing importance of the velocity gradient in the optically thick regime. Overall, the new prescription enables more reliable thermodynamics in AGB wind simulations and highlights the limitations of ISM-based cooling rates for such environments.

Abstract

Asymptotic Giant Branch (AGB) stars significantly contribute to the chemical composition of the universe. In their outflows, complex chemistry takes place, which critically depends on the local temperature. Therefore, if we want to accurately model the AGB environment, we need accurate cooling rates. The CO molecule is abundant in AGB outflows, and has a dipole moment, which enables it to cool through emission from its rotational transitions. We therefore expect it to significantly contribute to cooling in this environment, even at low temperatures ($10$ K $\leqslant T\leqslant 3000$ K). Currently, CO cooling rates are available for ISM-like conditions, which encompasses a different parameter regime, with generally lower densities and velocity gradients, compared to AGB winds. Therefore, these ISM cooling rates might not be applicable to the AGB regime. In this paper, we compute CO cooling rates for hydrodynamics simulations of AGB outflows. To evaluate the net cooling rate, we calculate the energy level distribution of CO self-consistently, using the non Local Thermodynamical Equilibrium (NLTE) line radiative transfer code Magritte. We verify whether already existing CO cooling rate prescriptions for the interstellar medium (ISM) are applicable for this regime. We noticed minor differences between these prescriptions and our calculated cooling rates in general. However, when used far outside their originally intended parameter regimes, significant differences occur. Therefore, we propose a new CO cooling rate prescription for the AGB environment and we study how the computed cooling rate varies depending on input parameters.

Figures (33)

• Figure 1: Distribution of our model points, compared to the parameter ranges in which the Neufeld and Omukai prescriptions are valid. A significant fraction of our data points lie outside the ranges covered by neufeld_radiative_1993 and omukai_low-metallicity_2010.
• Figure 2: Distribution of our model points, compared to the parameter range (box) in which the Whitworth prescription is valid. Most of our data points lie outside the range covered by whitworth_simple_2018.
• Figure 3: Contour plots of the cooling rate versus the CO density, smoothed using a Gaussian kernel. The solid line contains $99\%$ of the data points. The dotted line denotes the outer contour where data is present. Bottom: contour plot of the relative differences between the fits and our computed cooling rate.
• Figure 4: Contour plots of the cooling rate versus the temperature, smoothed using a Gaussian kernel. The solid line contains $99\%$ of the data points. The dotted line denotes the outer contour where data is present. The vertical arrow lines denote the temperature bounds for which the literature fit functions are defined. Bottom: contour plot of the relative differences between the fits and our computed cooling rate.
• Figure 5: Contour plots of the cooling rate versus the velocity divergence, smoothed using a Gaussian kernel. The solid line contains $99\%$ of the data points. The dotted line denotes the outer contour where data is present. Bottom: contour plot of the relative differences between the fits and our computed cooling rate.