Analytical Methods for Measuring the Parameters of Interstellar Gas Using the Data of Methanol Observations

Abstract

We analyze methanol excitation in the absence of external radiation and consider LTE methods for probing interstellar gas. We show that rotation diagrams correctly estimate the gas kinetic temperature only if they are built from lines with the upper levels located in the same K-ladders, such as the J_0-J_{-1}E lines at 157~GHz, the J_1-J_0E lines at 165~GHz or the J_2-J_1E lines at 25~GHz. The gas density should be no less than 10^7~cm^{-3}. Rotation diagrams built from lines with different K values of the upper levels (2_K-1_K at 96~GHz, 3_K-2_K at 145~GHz, or 5_K-4_K at 241~GHz) significantly underestimate the temperature but allow a density estimation. In addition, the diagrams based on the 2_K-1_K lines make possible methanol column density estimates within a factor of about 2--5. We suggest that rotation diagrams should be used in the following manner. First, one should build two rotation diagrams, one from the lines at 96, 145, or 241~GHz, and another from the lines at 157, 165, or 25~GHz. The former diagram is used to estimate the gas density. If the density is about 10^7~cm^{-3} or higher, the latter diagram reproduces the temperature fairly well. If the density is around 10^6~cm^{-3}, the temperature obtained from the latter diagram should be multiplied by a factor of 1.5--2. If the density is about 10^5~cm^{-3} or lower, then the latter diagram yields a temperature that is lower than the kinetic temperature by a factor of three or larger and should be used only as a lower limit on the kinetic temperature. Errors of methanol column density determined from the integrated intensity of a single line may be larger than an order of magnitude even when the gas temperature is well-known. However, if the J_0-(J-1)_0E lines, as well as the J_1-(J-1)_1A^{+} or A^{-} lines are used, the relative error of the column density proves to be no larger than several units.