Modelling CH$_3$OH masers: Sobolev approximation and accelerated lambda iteration method

TL;DR

This paper compares the accuracy of the Sobolev approximation and the accelerated lambda iteration method in modeling CH$_3$OH masers, highlighting conditions under which each technique is effective.

Contribution

It introduces a simple one-dimensional model for CH$_3$OH masers and evaluates the applicability of LVG and ALI methods for calculating molecular level populations.

Findings

LVG approximation is accurate for large maser regions

ALI method provides precise results regardless of size

Large velocity gradient conditions are crucial for LVG validity

Abstract

A simple one-dimensional model of CH$_3$OH maser is considered. Two techniques are used for the calculation of molecule level populations: the accelerated lambda iteration (ALI) method and the large velocity gradient (LVG), or Sobolev, approximation. The LVG approximation gives accurate results provided that the characteristic dimensions of the medium are larger than 5-10 lengths of the resonance region. We presume that this condition can be satisfied only for the largest observed maser spot distributions. Factors controlling the pumping of class I and class II methanol masers are considered.