Determining Electron Temperature and Density in a H ii Region Using the Relative Strengths of Hydrogen Radio Recombination Lines

We have introduced a new method of estimating the electron temperature and density of H II regions by using single-dish observations. In this method, multiple hydrogen radio recombination lines of different bands are computed under the assumption of low optical depth. We use evolutionary hydrodynamical models of H II regions to model hydrogen recombination line emission from a variety of H II regions and assess the reliability of the method. According to the simulated results, the error of the estimated temperature is commonly <13%, and that of the estimated density is <25% for a <1% uncertainty of the observed line fluxes. A reasonable estimated value of electron density can be achieved if the uncertainty of the line fluxes is lower than 3%. In addition, the estimated values are more representative of the properties in the relatively high density region if the gas density gradient is present in the H II region. Our method can be independent of the radio continuum observations. But the accuracy will be improved if a line-to-continuum ratio at millimeter wavelengths is added to the estimation. Our method provides a way to measure the temperature and density in ionized regions without interferometers.