Once everything had been plotted out, this is the map of the galactic center they were able to produce. It showed that stars were hurtling around in very fast and tight orbits. But what Ghez was interested in was what they were circling around.
If there is a black hole, there is a further prediction you can make about what these stars are gonna do. They are gonna move around the black hole on very short periods. In another words, you are gonna be able to see them move on more than just straight lines as part of their travel around the black hole. These stars are gonna move around the black hole because of the gravity just like planets move around the sun.
There is only one thing that has the shear force of gravity to compel such huge stars to veer round on such tight trajectories.
So what we see is that indeed you can, you see these stars were vibrant. In fact, in these images you can actually tell where the black hole was. The black hole was at the center of the focus of these orbits.