Hyperfine Group Ratio: A Recipe for Deriving Kinetic Temperature from
  Ammonia Inversion Lines
  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 ($T_{\rm
rot}$) 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 $\Delta
T_{\rm rot}$ as a function of the signal-to-noise ratio (SNR) is a natural
product of the HFGR recipe. The internal error of HFGR is $\Delta T_{\rm
rot}\leq0.5$ 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
$\Delta T_{\rm rot}\leq 1.0$ K (1 $\sigma$) when SNR > 4.
