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A Molecular Cloud (or Dense Cloud) is a gas cloud of sufficient size and density that molecules form, particularly Molecular Hydrogen (aka HH or H2). They can be assumed to be cool as compared HI Region or HII Region, as too high a temperature would dissociate all the molecules. Stars are typically formed in molecular clouds, where the lower Temperature leads to a higher density.
They are typically detected by observing the Luminosity of Carbon Monoxide which is assumed to be present in molecular clouds and applying the CO to H2 Factor. Their temperature and density are of interest with respect to Star Formation activity/potential and can be determined from the relative strength of various molecular Spectral Lines.
Their diameter is typically in the 5 to 200 Parsec range. The larger end includes Giant Molecular Clouds which are those on the order of a thousand Solar Masses and above, and can be as much as ten million solar masses.
A Magnetized Molecular Cloud is a cloud with a Magnetic Field. If incoming Electromagnetic Radiation ionizes some of the cloud matter making it conductive, an external magnetic field can interact with the cloud, affecting its behavior, perhaps helping or hindering a collapse leading to star formation. A cloud's magnetism can be inferred from the Zeeman Effect, presumably observed through Zeeman-Doppler Imaging.
There are a number of terms used for particular types of molecular clouds or dense portions of them: