PAH Emission Spectra and Band Ratios for Arbitrary Radiation Fields with the Single Photon Approximation

TL;DR

This work introduces the single photon approximation (SPA) to compute PAH emission spectra in arbitrary radiation fields by expressing spectra as a linear combination of basis spectra from individual photon absorptions. By constructing basis spectra p̃_{λ_em}(λ_abs) and scaling them to any input radiation field, the SPA reproduces multi-photon heating results to about 10% accuracy in the 3–20 μm range for U≲100, enabling rapid exploration of PAH band ratios as functions of grain size and radiation-field hardness. The study reveals a strong dependence of the 3.3 μm/11.2 μm ratio on radiation-field hardness and shows substantial a–λ_abs degeneracies in several key PAH band ratios. The framework, validated against established models and released with public software and basis spectra, offers a practical tool for JWST-era PAH analyses and radiative-transfer modeling, while clarifying the regime where the SPA remains reliable.

Abstract

We present a new method for generating emission spectra from polycyclic aromatic hydrocarbons (PAHs) in arbitrary radiation fields. We utilize the single-photon limit for PAH heating and emission to treat individual photon absorptions as independent events. This allows the construction of a set of single-photon emission "basis spectra" that can be scaled to produce an output emission spectrum given any input heating spectrum. We find that this method produces agreement with PAH emission spectra computed accounting for multi-photon effects to within $\simeq10\%$ in the $3-20~{\rm μm}$ wavelength range for radiation fields with intensity $U<100$. We use this framework to explore the dependence of PAH band ratios on the radiation field spectrum across grain sizes, finding in particular a strong dependence of the 3.3 to $11.2~μ$m band ratio on radiation field hardness. A Python-based tool and a set of basis spectra that can be used to generate these emission spectra are made publicly available.

Figures (7)

• Figure 1: (Left) temperature evolution of a $5~\textup{\AA}$ ionized PAH as it radiates the energy absorbed from individual photons ranging from far-UV to mid-IR wavelengths. (Right) the resulting emission spectra, $\tilde{p}_{\lambda_{\rm em}}(\lambda_{\rm abs})$, which we adopt as our basis spectra.
• Figure 2: The size- and ionization-integrated spectra for PAHs in the mMMP radiation field, normalized by $U$. We use the standard size distribution and ionization function defined in Draine2021. The black dotted line shows the SPA spectrum, which has no $U$-dependence after normalization. The solid colored lines show models from Draine2021, with line color indicating the value of $U$. The bottom panel shows the Draine2021 and SPA spectra for each $U$ normalized by $U p_{\lambda,1}$, where $p_{\lambda,1}$ is the $U=1$ spectrum.
• Figure 3: Same as Figure \ref{['fig:size_integrated_spectrum']}, but for individual grains. In the left and right panels we show results for $a=5.0~\textup{\AA}$ and $15.0~\textup{\AA}$ ionized PAHs, respectively.
• Figure 4: Fractional residuals between single-grain spectra generated using the SPA ($p_{\lambda}^{\rm SPA}$) and from Draine2021 ($p_{\lambda}^{\rm D21}$) for grains heated by the mMMP radiation field with $U=1$. The sharp features are caused by interpolation effects near the peaks of the PAH emission features in the Draine2021 spectra whereas the rise toward long wavelengths for the 5 Å PAH originates from our SPA calculations neglecting discretization effects in the lowest energy states.
• Figure 5: (Left) ten radiation field models from Draine2021, all with $U=100$. (Right) The resulting emission spectra, integrated over the standard size distribution and ionization function. Dotted lines show the SPA models and solid lines show the Draine2021 models. Note that some spectra are not readily distinguishable from each other on this scale. The bottom right panel shows the Draine2021 and SPA spectra normalized by $100\, p_{\lambda,1}$, where $p_{\lambda,1}$ is the $U=1$ spectrum.