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There are lots of different types of stars, all in various stages of the star life cycle. Our sun is a star, classified as a medium, yellow star, somewhere in the middle of it's life cycle. Depending on the star type and it's location in the life cycle, you may get any of the three spectrum types you mentioned. Emission, because they certainly emit radiation that can be measured. Absorption, because, they certainly radiate energy, whether by wave or by particle, that may be absorbed by materials here on Earth. Continuous, at least for the time being, meaning the energy radiation isn't going to end anytime soon. Our sun is only a medium, yellow star, which puts it squarely in the middle of the stars in terms of fuel consumption. It is currently forecast to last another ten million years. So for the time being, it will continue to radiate energy of all types to us, making it a continuous spectrum.
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