Understanding spatially unresolved measurements of molecular line emission

Context. Observations of molecular emission lines are commonly used to derive the physical properties of cold molecular gas clouds. In external galaxies, these measurements suffer from limited spatial resolution, typically averaging over several to tens parsecs of a complex position-position-velocity distribution of emission. Aims. We aim to quantify the variability in the basic parameters (peak brightness, line width) of spatially unresolved (>20 pc) line profiles that can be attributed to beam-averaging. We focus on the commonly observed low-J transitions of CO isotopologues, HCN, ++ HNC,HCO ,CS,SOandN2H . Methods. We generate a sample of 1000 toy molecular cloud observations by resampling high resolution (<0.05 pc) multi-line Galac- tic observations of the Orion B molecular cloud. In the construction of our toy clouds, we impose a range of density and velocity fields, characterized by their statistics and power spectra. These high resolution molecular cloud observations are then averaged to single unresolved spectra. We examine the resulting distribution of line profile parameters, and probe for potential correlations between line profile parameters and the underlying sub-beam density and velocity fields. Results. We find that unresolved line profiles parameters can vary significantly because of the sub-beam distribution of the emission. Emission lines that tend to be excited at higher densities show the most variability, up to a factor two for N2H+ (J = 1 → 0). Overall the variability of an emission line profile is correlated to the emission line’s beam filling factor. As the spectral index of the velocity field increases, unresolved emission lines profiles increasingly diverge from a Gaussian shape. Conclusions. Line profile parameters exhibit non-negligible variability solely due to the sub-beam position-position-velocity distri- bution of the emission. This variability may exceed calibration and noise related uncertainties.

研究背景：分子发射谱线观测通常被用于推导冷分子气体云的物理属性。在河外星系中，这类观测受限于有限的空间分辨率，通常会对发射的复杂位置-位置-速度分布进行数秒差距至数十秒差距尺度的平均。

研究目的：本研究旨在量化可归因于束平均（beam-averaging）效应的、空间未分辨（spatially unresolved，>20 pc）谱线轮廓的基础参数（峰值亮度、谱线宽度）的变化程度。我们聚焦于一氧化碳同位素体、HCN、HNC、HCO+、CS、SO以及N2H+的常见低J跃迁（low-J transitions）。

研究方法：我们通过重采样猎户座B分子云的高分辨率（<0.05 pc）多谱线银河观测数据，生成了包含1000个理想化分子云观测样本的数据集。在构建理想化云团时，我们引入了一系列以统计特征和功率谱表征的密度场与速度场。随后将这些高分辨率分子云观测数据平均为单条空间未分辨光谱。我们分析了所得谱线轮廓参数的分布，并探究了谱线轮廓参数与束内潜在密度场、速度场之间的潜在相关性。

研究结果：我们发现，由于发射的束内分布差异，空间未分辨谱线轮廓的参数会发生显著变化。倾向于在更高密度下被激发的发射谱线表现出最大的变化程度，其中N2H+（J=1→0）的变化幅度可达两倍。总体而言，发射谱线轮廓的变化程度与该谱线的束填充因子（beam filling factor）相关。随着速度场的谱指数增大，空间未分辨发射谱线轮廓与高斯分布轮廓的偏差愈发显著。

结论：仅由发射的束内位置-位置-速度分布所导致的谱线轮廓参数变化不可忽视，这类变化甚至可能超过定标与噪声相关的不确定度。