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In recent years, a number of eccentric debris belts have been observed inextrasolar systems. The most common explanation for their shape is the presenceof a nearby eccentric planetary companion. The gravitational perturbation fromsuch a companion would induce periodic eccentricity variations on theplanetesimals in the belt, with a range of precession frequencies. The overallexpected shape is an eccentric belt with a finite minimum width. However,several observed eccentric debris discs have been found to exhibit a narrowerwidth than the theoretical expectation. In this paper, we study two mechanismsthat can produce this small width: (i) the protoplanetary disc can interactwith the planet and/or the planetesimals, slowly driving the eccentricity ofthe former and damping the eccentricities of the latter; (ii) the companionplanet could have gained its eccentricity stochastically, through planet-planetscatterings. We show that under appropriate conditions, both of these scenariosoffer a plausible way to reduce the minimum width of an eccentric belt exteriorto a perturbing planet. However, the effects of protoplanetary discs arediminished at large separations (a > 10 au) due to the scarcity of gas and thelimited disc lifetime. These findings suggest that one can use the shape andwidth of debris discs to shed light on the evolution of extrasolar systems,constraining the protoplanetary disc properties and the prevalence ofplanet-planet scatterings. Further observations of debris-harbouring systemscould confirm whether thin debris belts are a common occurrence, or the resultsof rare initial conditions or evolutionary processes.

Eccentric debris belts reveal the dynamical history of the companion exoplanet