Low Frequency Carbon Radio Recombination Lines I: Calculations of Departure Coefficients

TL;DR

This paper calculates departure coefficients for high quantum number carbon radio recombination lines, incorporating updated atomic physics and dielectronic recombination effects, to aid future low-frequency radio observations.

Contribution

It introduces improved calculations of departure coefficients for carbon recombination lines, including dielectronic recombination and updated collision rates, advancing the modeling of these lines.

Findings

Results agree with previous hydrogenic approximations.

Including dielectronic recombination causes notable differences.

Updated atomic data improve the accuracy of level population models.

Abstract

In the first paper of this series, we study the level population problem of recombining carbon ions. We focus our study on high quantum numbers anticipating observations of Carbon Radio Recombination Lines to be carried out by the LOw Frequency ARray (LOFAR). We solve the level population equation including angular momentum levels with updated collision rates up to high principal quantum numbers. We derive departure coefficients by solving the level population equation in the hydrogenic approximation and including low temperature dielectronic recombination effects. Our results in the hydrogenic approximation agree well with those of previous works. When comparing our results including dielectronic recombination we find differences which we ascribe to updates in the atomic physics (e.g., collision rates) and to the approximate solution method of the statistical equilibrium equations adopted in previous studies. A comparison with observations is discussed in an accompanying article, as radiative transfer effects need to be considered.