An analytic formalism to describe the $N_{\mathrm{eff}}(\mathrm{H})$-$n_{\mathrm{H}}$ relationship in molecular clouds

Abstract

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, $N_{\mathrm{eff}}(\mathrm{H})$, and the local hydrogen-nuclei number density, $n_{\mathrm{H}}$. 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., $N_{\mathrm{eff}}(H)\propto n^{\gamma }$, of $\gamma \approx 0.4-0.5$ found in previous numerical simulations utilizing ray-tracing. Conclusions. We present an analytic model relating the average effective column density, $N_{\mathrm{eff}}$, to the local number density, $n_{\mathrm{H}}$, 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.

Accepted to A&A. 4 pages and 3 figures in the main body, 2 pages and 4 figures in the appendix. GitHub repository with demonstration here: https://github.com/AstroBrandt/AnalyticNeffnH

References in corpus (10)

• Simulating the formation of molecular clouds. I. Slow formation by gravitational collapse from static initial conditions
• A parsec-scale Galactic 3D dust map out to 1.25 kpc from the Sun
• On the Three-Dimensional Structure of Local Molecular Clouds
• Metallicity dependence of the H/H${}_2$ and C${}^{+}$/C/CO distributions in a resolved self-regulating interstellar medium
• Photodissociation Region Diagnostics Across Galactic Environments
• PDFchem: A new fast method to determine ISM properties and infer environmental parameters using probability distributions
• The impact of cosmic-ray attenuation on the carbon cycle emission in molecular clouds
• Radiation transport methods in star formation simulations
• Bird's eye view of molecular clouds in the Milky Way: II. Cloud kinematics from sub-pc to kpc scales
• 3D structure of the Milky Way out to 10 kpc from the Sun. Catalogue of large molecular clouds in the Galactic Plane

Cited by in corpus (1)

• The impact of attenuation on cosmic-ray chemistry: I. Abundances and chemical calibrators in molecular clouds