An nl-model with a full radiative transfer treatment for level populations of hydrogen atoms in a spherically symmetric H II region

¹ Research Center for Astronomical Computing, Zhejiang Laboratory, Hangzhou 311100, PR China
² School of Physical Science and Technology, Guangxi University, Nanning 530004, PR China
³ Department of Astronomy, University of Science and Technology of China, Hefei 230026, PR China

^★ Corresponding authors: zhufy@zhejianglab.com; junzhiwang@gxu.edu.cn; donghui.quan@zhejianglab.com

Received: 11 April 2025
Accepted: 9 July 2025

Abstract

Context. The radiation field consisting of hydrogen recombination lines and continuum emission might significantly affect the hydrogen-level populations in ultra- and hypercompact (U/HC) H II regions. The escape probability approximation was used to estimate the effect of the radiation field in previous models for calculating hydrogen-level populations. The reliability of this approximation has not been systematically studied, however.

Aims. We investigate the appropriate ranges of previous models with the escape probability approximation and without the effects of the radiation field. We create a new model for simulating the integrated characteristics and the spatially resolved diagnostics of the hydrogen recombination lines throughout H II regions.

Methods. We developed a new nl model with a full radiative transfer treatment of the radiation field causd by hydrogen recombination lines and continuum emission to calculate the hydrogen-level populations and hydrogen recombination lines. We then compared the level populations and the corresponding hydrogen recombination line intensities simulated by the new model and previous models.

Results. We studied the applicability and the valid parameter ranges of previous models. Radiation fields exhibit negligible effects on the level populations in classical and UC H II regions. With the modified escape probability, the model with the escape probability approximation is suitable for most HC H II regions. The improved new model performs better in the HC H II region with an extremely high emission measure. To address the high computational costs inherent in numerical models, we trained a precise machine-learning model to enable a rapid estimation of hydrogen-level populations and the associated hydrogen recombination lines.