Hyperfine Group Ratio: A Recipe for Deriving Kinetic Temperature from Ammonia Inversion Lines

Abstract

Although ammonia is a widely used interstellar thermometer, the estimation of its rotational and kinetic temperatures can be affected by the blended Hyperfine Components (HFCs). We developed a new recipe, referred to as the HyperFine Group Ratio (HFGR), which utilizes only direct observables, namely the intensity ratios between the grouped HFCs. As tested on the model spectra, the empirical formulae in HFGR can derive the rotational temperature ($T_{\mathrm{rot}}$) from the HFC group ratios in an unambiguous manner. We compared HFGR with two other classical methods, intensity ratio and hyperfine fitting, based on both simulated spectra and real data. HFGR has three major improvements. First, HFGR does not require modeling the HFC or fitting the line profiles, thus is more robust against the effect of HFC blending. Second, the simulation-enabled empirical formulae are much faster than fitting the spectra over the parameter space, so the computer time and human time can be both largely saved. Third, the statistical uncertainty of the temperature $\Delta T_{\mathrm{rot}}$ as a function of the signal-to-noise ratio (SNR) is a natural product of the HFGR recipe. The internal error of HFGR is $\Delta T_{\mathrm{rot}}\le 0.5$ K over a broad parameter space of rotational temperature (10 to 60 K), line width (0.3 to 4 km/s), and optical depth (0 to 5). When there is a spectral noise, HFGR can also maintain a reasonable uncertainty level at $\Delta T_{\mathrm{rot}}\le 1.0$ K (1 $\sigma$) when SNR > 4.

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