Bias‐free Measurement of Giant Molecular Cloud Properties

(abridged) We review methods for measuring the sizes, line widths, andluminosities of giant molecular clouds (GMCs) in molecular-line data cubes withlow resolution and sensitivity. We find that moment methods are robust andsensitive -- making full use of both position and intensity information -- andwe recommend a standard method to measure the position angle, major and minoraxis sizes, line width, and luminosity using moment methods. Withoutcorrections for the effects of beam convolution and sensitivity to GMCproperties, the resulting properties may be severely biased. This isparticularly true for extragalactic observations, where resolution andsensitivity effects often bias measured values by 40% or more. We correct forfinite spatial and spectral resolutions with a simple deconvolution and wecorrect for sensitivity biases by extrapolating properties of a GMC to those wewould expect to measure with perfect sensitivity. The resulting method recoversthe properties of a GMC to within 10% over a large range of resolutions andsensitivities, provided the clouds are marginally resolved with a peaksignal-to-noise ratio greater than 10. We note that interferometerssystematically underestimate cloud properties, particularly the flux from acloud. The degree of bias depends on the sensitivity of the observations andthe (u,v) coverage of the observations. In the Appendix to the paper we presenta conservative, new decomposition algorithm for identifying GMCs inmolecular-line observations. This algorithm treats the data in physical ratherthan observational units, does not produce spurious clouds in the presence ofnoise, and is sensitive to a range of morphologies. As a result, the output ofthis decomposition should be directly comparable among disparate data sets.