What does the shape of a Hot Jupiter's final orbit provide direct clues about?

The mechanics of its dramatic journey or migration

Astronomers study the geometric properties of observed Hot Jupiter orbits to deduce the history of their inward journey. Specifically, the shape of the orbit—its eccentricity—acts as a fingerprint for the relocation mechanism. If the orbit is nearly circular and orderly, this strongly implies the planet experienced the relatively gentle process of disk-driven migration, where the gas disk naturally damped out irregularities. Conversely, if the orbit exhibits high eccentricity, it suggests the planet survived a chaotic gravitational scattering event with another massive body, which imparted a highly elliptical path. Therefore, analyzing whether the final orbit is nearly circular or highly eccentric provides crucial, direct evidence regarding the dynamical forces that governed the planet's path from the cold outer regions to its scorching residence near the star.