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Yes! The energy they give off have an equivalent mass, and this mass is lost to the star. This follows from (a) the equivalence between mass and energy, and (b) conservation of mass. As an example, our Sun, which gives off tremendous amounts of light, loses 4 million tonnes a second, just through the light that leaves the Sun - that is, apart from any solar wind.

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Q: Do stars lose mass while they give off energy?
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