When confronted with such an anomaly in very-well-established theory (that F3 main-sequence stars should not have such dips), the possibility arises that we are seeing the first example of some entirely new and unexpected phenomenon. And this is always exciting to astronomers. Who knows what startling wonders are being pointed at by Tabby’s Star?
So how to proceed? Well, looking at the star when there isn’t a dip going on is unlikely to tell us anything more than the background information that we’ve already worked out. So the only way to advance is to catch Tabby’s Star in the middle of a dip.
What I’d most like to see is a good spectrum of Tabby’s Star at mid-dip. The starlight, spread out into fine gradations of color, should tell us about the nature of whatever is producing the occultations. If the occulter is some sort of a dusty cloud, then the dimming will be greatest for blue light and least for red light, with the relative dimming across the colors being in a known and characteristic pattern. If this dust cloud has gas mixed in, then we should also see characteristic absorption lines at known colors, giving us the composition of the gas, and revealing the origin and nature of the cloud. If the light-blocker is solid, then all of the colors will dim by exactly the same amount. And we might even see some emission lines if there is some sort of stellar activity on the primary star. So all it takes is one good spectrum during a dip, and we’ll know the nature of the occulter.