Hyperfine group ratio: a recipe for deriving kinetic temperature from the 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 have 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 the HFGR can derive the rotational temperature (Trot) from the HFC group ratios in an unambiguous manner. We compared the HFGR with two other classical methods, intensity ratio and hyperfine fitting, based on both simulated spectra and real data. The HFGR has three major improvements. First, it does not require modelling the HFC or fitting the line profiles, so it 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 both computer time and human time can be saved. Third, the statistical uncertainty of the temperature ΔTrot as a function of the signal-to-noise ratio (S/N) is a natural product of the HFGR recipe. The internal error of the HFGR is ΔTrot ≤ 0.5 K over a broad parameter space of rotational temperature (10–60 K), linewidth (0.3–4 km s−1) and optical depth (0–5). When there is spectral noise, the HFGR can also maintain a reasonable uncertainty level at ΔTrot ≤ 1.0 K when S/N > 4.

The TMRT K band observations towards 26 infrared dark clouds: NH3, CCS, and HC3N

“…We use the newly developed hyperfine group ratio (HFGR) [35,36] method, which utilizes the integrated intensities of hyperfine groups to derive T rot and T k . Relying solely on observed line-intensity-ratios and completely circumventing hyperfine-fitting, HFGR is impervious to the coupling between linewidth and opacity, thus more robust and accurate for a wider range of parameters than all traditional methods.…”

“…Relying solely on observed line-intensity-ratios and completely circumventing hyperfine-fitting, HFGR is impervious to the coupling between linewidth and opacity, thus more robust and accurate for a wider range of parameters than all traditional methods. A key product of the HFGR is the statistical uncertainties of the fitted temperatures based on the signal-to-noise ratio of the observed spectra [36]. The temperatures of the regions range between 10 and 18 K.…”

Cyanopolyyne line survey towards high-mass star-forming regions with TMRT

“…Here, T rot was taken from the rotational temperature of NH 3 , which could be obtained from the NH 3 inversion lines and was widely used as a good tracer of temperature in the molecular clouds (Tafalla et al 2004;Mangum & Shirley 2015;Wang et al 2020). Notably, NH 3 and cyanopolyynes may come from different regions in the clumps and therefore lead to error in calculations of the column density of cyanopolyynes.…”

The TMRT K Band Observations towards 26 Infrared Dark Clouds: NH$_{3}$, CCS, and HC$_{3}$N

“…We use the newly developed hyperfine group ratio (HFGR) [35,36] method, which utilizes the integrated intensities of hyperfine groups to derive 𝑇 𝑟 𝑜𝑡 and 𝑇 𝑘 . Relying solely on observed line-intensity-ratios and completely circumventing hyperfine-fitting, HFGR is impervious to the coupling between linewidth and opacity, thus more robust and accurate for a wider range of parameters than all traditional methods.…”

“…Relying solely on observed line-intensity-ratios and completely circumventing hyperfine-fitting, HFGR is impervious to the coupling between linewidth and opacity, thus more robust and accurate for a wider range of parameters than all traditional methods. A key product of the HFGR is the statistical uncertainties of the fitted temperatures based on the signal-to-noise ratio of the observed spectra [36]. The temperatures of the regions range between 10 K and 18 K. Figure 1 compares the dust temperatures from the Herschel Far-Infrared observations [24] with gas temperatures from this K Band NH 3 survey.…”