An analytic formalism to describe the $N_{\rm eff}(\rm H)$-$n_{\rm H}$ relationship in molecular clouds
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| Format: | Preprint |
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2025
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| author | Gaches, Brandt A. L. |
| author_facet | Gaches, Brandt A. L. |
| contents | Context. Astrochemical modeling requires, as input, the effective column density of gas (or extinction) that attenuates an external, isotropic, far-ultraviolet radiation field. In three-dimensional simulations, this can be calculated through ray-tracing schemes, while in 0D chemical models it is often treated as a free parameter. Aims. We aim to produce an analytic, physically motivated formalism to predict the average relationship between the effective hydrogen-nuclei column density, $N_{\rm eff}({\rm H})$, and the local hydrogen-nuclei number density, $n_{\rm H}$. Methods. We construct an analytic model utilizing characteristic length scales that connects the turbulence-dominated regime and the gravitational-dominated regime at high-density. Results. The model well-reproduces a previous analytic fit to simulation results and is consistent with the high-density power-law indices, e.g., $N_{\rm eff}(H) \propto n^γ$, of $γ\approx 0.4 - 0.5$ found in previous numerical simulations utilizing ray-tracing. Conclusions. We present an analytic model relating the average effective column density, $N_{\rm eff}$, to the local number density, $n_{\rm H}$, which reproduces the behaviors found in three-dimensional simulations. The analytic model can be utilized as a sub-grid prescription for shielded molecular gas or in astrochemical models for a physically motivated estimation of the attenuating column density. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An analytic formalism to describe the $N_{\rm eff}(\rm H)$-$n_{\rm H}$ relationship in molecular clouds Gaches, Brandt A. L. Astrophysics of Galaxies Context. Astrochemical modeling requires, as input, the effective column density of gas (or extinction) that attenuates an external, isotropic, far-ultraviolet radiation field. In three-dimensional simulations, this can be calculated through ray-tracing schemes, while in 0D chemical models it is often treated as a free parameter. Aims. We aim to produce an analytic, physically motivated formalism to predict the average relationship between the effective hydrogen-nuclei column density, $N_{\rm eff}({\rm H})$, and the local hydrogen-nuclei number density, $n_{\rm H}$. Methods. We construct an analytic model utilizing characteristic length scales that connects the turbulence-dominated regime and the gravitational-dominated regime at high-density. Results. The model well-reproduces a previous analytic fit to simulation results and is consistent with the high-density power-law indices, e.g., $N_{\rm eff}(H) \propto n^γ$, of $γ\approx 0.4 - 0.5$ found in previous numerical simulations utilizing ray-tracing. Conclusions. We present an analytic model relating the average effective column density, $N_{\rm eff}$, to the local number density, $n_{\rm H}$, which reproduces the behaviors found in three-dimensional simulations. The analytic model can be utilized as a sub-grid prescription for shielded molecular gas or in astrochemical models for a physically motivated estimation of the attenuating column density. |
| title | An analytic formalism to describe the $N_{\rm eff}(\rm H)$-$n_{\rm H}$ relationship in molecular clouds |
| topic | Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2507.16931 |