Low-frequency Carbon Radio Recombination Lines. I. Calculations of Departure Coefficients

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.

Spectroscopy with the Engineering Development Array: cold H+ at 63 MHz towards the Galactic Centre

“…The presence of lowfrequency HRRL and CRRL associated with cold, diffuse gas is consistent with recent models (e.g. Salgado et al 2017a). A possible origin for the RRL emission observed here is the nearby RC cloud, as its promixity, size and the background radiation field create a particularly favorable situation for detection with the EDA.…”

“…This can be understood as the l -changing collision rates are known to primarily affect low to intermediate n values (e.g. Salgado et al 2017a;Hummer & Storey 1987). We are therefore confident that the differences in the l -changing collision rates discussed in the recent literature do not affect the results presented here.…”

Carbon radio recombination lines from gigahertz to megahertz frequencies towards Orion A

“…These models solve the level population equations taking into account deviations from local thermodynamical equilibrium (LTE). The deviation from LTE in the population of carbon atoms is characterized by the factor b n and the effect of stimulated emission by the factor β nn (e.g., Shaver 1975;Salgado et al 2017a). These are known as departure coefficients.…”

“…Another property of CRRLs is that the population of carbon atoms in each energy state is determined by the gas density, temperature, and radiation field, as well as the atomic physics involved (e.g., Shaver 1975;Watson et al 1980;Salgado et al 2017a). Therefore, it is possible to determine the gas physical conditions by observing CRRLs at a range of frequencies and comparing this to the predicted line properties (e.g., Dupree 1974;Payne et al 1989;Roshi & Kantharia 2011;Salgado et al 2017b;Oonk et al 2017;Salas et al 2018).…”

“…The velocity resolution of the 158 µm-[CII] line ob-servations in this study was of ≈ 50 km s −1 , while in the observations of Pabst et al (2019) this is 0.2 km s −1 . Additionally, we use models that describe the level population of carbon atoms including the effect of dielectronic capture (Salgado et al 2017a). Incorporating this effect can change the predicted CRRL intensities by a factor of two (e.g., Wyrowski et al 1997).…”