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Inspired by the question, Are heavy elements equally distributed throughout the Solar System?, with a little further inspiration from this one as well, Star formation analogy, particularly the answer by David Hammen, where he states "... oftentimes needs a little help from an external disturbance such as a passing star or a supernova shock".

Is the formation of a star just about the concentrated accumulation of hydrogen gas and its self ignition, with the assistance of an external disturbance, or does cosmic dust have a role in producing a heavy core that can act as a gravitational attractor drawing in hydrogen gas?

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Dust is usually only about 1% of the mass of the gas in the typical interstellar medium, so no, it doesn't play the role you suggest.

Where it does play a role is in providing infrared emissivity. In order to collapse, a gas cloud must be able to cool. Hydrogen and helium gas is very poor at radiating away energy but molecular gas (things like carbon monoxide) and dust are quite efficient radiators.

Dust also aids in forming molecules in the first place by providing a site for these chemical reactions to take place - i.e. it catalyses molecule formation, which are then able to act as coolants.

Finally, dust can play an important role through its high opacity to UV radiation. This can shield gas from external ionising sources, which would otherwise keep them hot and prevent the initiation of star formation.

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