A planetary nebula can be identified by the following two characteristics:
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Central star remnant - Planetary nebulae typically have a hot, central star that is the remnant of the original star that shed its outer layers.
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Diffuse edges - Planetary nebulae often show a diffuse appearance at their edges due to the expansion of the gas and dust that forms the nebula.
So, the correct answers are central star remnant and diffuse edges.