Case A or Case B? The effective recombination coefficient in gas clouds of arbitrary optical thickness

In calculations of the ionization state, one is often forced to choose between the Case A recombination coefficient \(\alpha_{\rm A}\) (sum over recombinations to all hydrogen states) or the Case B recombination coefficient \(\alpha_{\rm B}\) (sum over all hydrogen states except the ground state). I...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2023-05
1. Verfasser: Nebrin, Olof
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In calculations of the ionization state, one is often forced to choose between the Case A recombination coefficient \(\alpha_{\rm A}\) (sum over recombinations to all hydrogen states) or the Case B recombination coefficient \(\alpha_{\rm B}\) (sum over all hydrogen states except the ground state). If the cloud is optically thick to ionizing photons, \(\alpha_{\rm B}\) is usually adopted on the basis of the "on-the-spot" approximation, wherein recombinations to the ground state are ignored because they produce ionizing photons absorbed nearby. In the opposite case of an optically thin cloud, one would expect the Case A recombination coefficient to better describe the effective recombination rate in the cloud. In this paper, I derive an analytical expression for the effective recombination coefficient in a gas cloud of arbitrary optical thickness which transitions from \(\alpha_{\rm A}\) to \(\alpha_{\rm B}\) as the optical thickness increases. The results can be readily implemented in numerical simulations and semi-analytical calculations.
ISSN:2331-8422
DOI:10.48550/arxiv.2305.05764