An Empirical Planetesimal Belt Radius–Stellar Luminosity Relation

Abstract

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 , following R ∝ L 0.19 with a low intrinsic scatter of ∼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 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 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 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.

Population synthesis of exocometary gas around A stars

“…Let's assume that CO is released at a constant rate Σ + CO , parametrized as a Gaussian centred on r belt = 100 au (belt mid radius) and with FWHM ∆r belt = 50 au. These are arbitrary choices, but overall consistent with the observed distribution of planetesimal disc radii and width around high luminosity stars (Matrà et al 2018b). In Figure 1 the resulting evolution of the CO (left panels) and carbon (middle panels) surface densities and total masses (right panels) are shown for different CO mass input rates and values of α: 0.1 and 0.001.…”

“…That study found best-fit parameters A = 5.5 × 10 5 , B = 0.1 and γ = −1.7. We assume the same planetesimal strength relation as before, eccentricities of 0.001 and Γ = 3.1 (the average true to blackbody radius ratio for FGK stars resolved by ALMA, Matrà et al 2018b). Fixing these parameters we have D c = 0.03 km and M mid = 0.16 M ⊕ (vs 0.02 km and 0.5 M ⊕ for A stars), i.e.…”

Extrasolar Kuiper belts

“…For example, a common assumption is that the mass distribution is log-normal, with the non-detections arising from close-in disks that undergo rapid depletion and so are not detectable in the nearby star population, but it could be that the mass distribution is bimodal, with 80% of stars having no disk. Also, more recently a correlation has been found between planetesimal belt radii determined from high resolution imaging of the sub-mm dust emission and the luminosity of the star (Matrà et al 2018a). If this holds up as more disks are resolved, this would suggest a preferential location for the formation of planetesimal belts that could be linked to ice-lines in the protoplanetary disk for example, which would provide an additional constraint on the population models (as well as significant insight into the origin of the belts).…”

The REASONS Survey: Resolved Millimeter Observations of a Large Debris Disk around the Nearby F Star HD 170773

“…The disk instead lies closer to three other potentially outlying early F/late A disks, which are HR 10 1 10 0 10 1 L (L ) 10 1 10 2 R (au) Figure 6. Radius-Luminosity relation that expands upon the one published in Matrà et al (2018a). The black points represent the published millimeter-resolved belt radii and corresponding belt widths, compared to the host star luminosity.…”

“…Understanding why debris disks form at their particular radii from their host stars is key to better understanding the physical mechanisms that create these disks. Matrà et al (2018a) conducted a population study of 26 millimeter-resolved debris disks and found a statistically significant correlation between the host star luminosity and disk radius, which persists when accounting for potential observational biases. Constraining the radii for additional debris disks is the next step to further characterize this radius-luminosity relationship and to further explore other potential correlations.…”