An Empirical Planetesimal Belt Radius - Stellar Luminosity Relation

Resolved observations of millimetre-sized dust, tracing larger planetesimals, have pinpointed the location of 26 Edgeworth-Kuiper belt analogs. We report that a belt's distance $R$ to its host star correlates with the star's luminosity $L_{\star}$, following $R\propto L^{0.19}_{\star}$ with a low intrinsic scatter of $\sim$17%. Remarkably, our Edgeworth-Kuiper belt in the Solar System and the two CO snow lines imaged in protoplanetary disks lie close to this $R$-$L_{\star}$ relation, suggestive of an intrinsic relationship between protoplanetary disk structures and belt locations. To test the effect of bias on the relation, we use a Monte Carlo approach and simulate uncorrelated model populations of belts. We find that observational bias could produce the slope and intercept of the $R$-$L_{\star}$ relation, but is unable to reproduce its low scatter. We then repeat the simulation taking into account the collisional evolution of belts, following the steady state model that fits the belt population as observed through infrared excesses. This significantly improves the fit by lowering the scatter of the simulated $R$-$L_{\star}$ relation; however, this scatter remains only marginally consistent with the one observed. The inability of observational bias and collisional evolution alone to reproduce the tight relationship between belt radius and stellar luminosity could indicate that planetesimal belts form at preferential locations within protoplanetary disks. The similar trend for CO snow line locations would then indicate that the formation of planetesimals and/or planets in the outer regions of planetary systems is linked to the volatility of their building blocks, as postulated by planet formation models.