The quasars have very large redshifts, indicating by the Hubble law that they are at great distances. The fact that they are visible at such distances implies that they emit enormous amounts of energy and are certainly not stars.
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For reference in discussing the distances and redshifts of quasars, this table relates these quantities to look-back times.
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These absorption systems are unrelated to the quasar itself. The only role of the quasar is to provide the background illumination that generates the absorption lines in more nearby clouds of gas.