Which feature signifies to astronomers that a distant star is part of a planetary system

a) The star periodically dims.

A star is the body of gas in which nuclear fusion of gases like helium and hydrogen  takes place due to this reason the star glows or dim. Star gets the ability to generate light because of this nuclear fusion which  cannot be observed in planets although the process of generation of star and planet is the same.  In distantly located star under observation, it's luminosity ( the property of  emitting lighting) is controlled by size of the star, the larger the size of the star it will have greater surface area the more profound will be the nuclear fusion in it and more light will be emitted. Second factor is the gaseous interaction of gases in and around the star and their temperature which causes the change in the light which has to pass through a layer of these gases. Therefore,  the distant star observed will show light fluctuations.