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| Star Birth and the Main Sequence |
1. It depends on the average particle mass because the more massive the particle the slower it moves (for a given energy) and the less effective it is in generating pressure to counteract gravity. In the Jeans formula, the cube of the particle mass appears in the denominator, so the critical density is lowered (favoring collapse) if the average particle mass is increased. This is as we would expect from our interpretation.
2. Protostars and the lowest mass stars are expected to be convective through their entire volume because of the opacities at their comparatively low temperatures. If they are fully convective, we can safely assume that the resulting mixing makes the surface abundances representative of the interior abundance of an element.
3. Because of the large disparity of stellar lifetimes as a function of mass. The hottest stars have lifetimes of millions of years, which is essentially instantaneous on the 15 billion year or so timescale for the age of the Universe, but the coolest stars have main sequence lifetimes far longer than the present age of the Universe.
4. The molecular clouds are so cold because of dust reflecting light and radiative cooling from molecules inside that almost all the hydrogen is in molecular form (diatomic hydrogen molecules); the spin flip transition is in atomic hydrogen, which is found in low abundance at such low temperatures. As a result, cold molecular clouds are often mapped using the RF emission of trace molecules such as carbon monoxide, which does give a strong radio signal under these conditions.