Forecasting Catastrophe: Constraints on the Fomalhaut Main Belt Planetesimal Population from Observed Collisional Remnants

Abstract

Catastrophic planetesimal disruptions offer a unique opportunity to study and characterize large planetesimal populations in exoplanetary systems that are not currently detectable by modern observatories. The unexpected discovery of a second collision event in the Fomalhaut system raises important questions about the planetesimal population and dynamical state inside the Fomalhaut main belt that led to two collisions in 20 years. We present a statistical model developed and applied to the archetypal Fomalhaut system to provide new constraints on the bulk properties of the planetesimals in Fomalhaut's main belt. Utilizing the constraints provided by the spatially resolved Fomalhaut cs1 and cs2 collision events, we retrieve the belt parameters that best reproduce the observed collision rate while remaining consistent with the system's age and dust mass. Our best-fit model suggests a total main belt mass of 200-360 $M_{\oplus}$, with the transition from a collisionally evolved to a primordial planetesimal population occurring at a radius of $115_{-10}^{+30}$ km and a maximum planetesimal radius of $380_{-202}^{+643}$ km. We estimate a catastrophic collision rate of $0.086_{-0.048}^{+0.067}$ collision events per year for planetesimals with radii $\ge$ 100 km in the region interior to the main belt. Our findings show that further observable collisions are likely, motivating continued monitoring of Fomalhaut and other nearby debris disks.

Figures (11)

• Figure 1: Left: A schematic of the Fomalhaut main belt under our model. The blue region indicates the observed main belt, while the red region contains the low surface density, dynamically hot component of the main belt. Right: The fraction of the belt mass in each region of the disk as a function of belt semi-major axis, which is governed by a Gaussian surface density distribution.
• Figure 2: Minimum impactor radius needed to catastrophically disrupt a planetesimal with a radius of 100 km as a function of the relative velocity of the impact.
• Figure 3: The posterior distribution of the emcee chain of the six parameters fit in our model for collisional progenitors with radii $\ge$ 100 km. The model is fit with 50 walkers, 10000 steps, and 1000 burn-in steps. The dashed lines indicate the 16th, 50th, and 84th percentiles, respectively.
• Figure 4: The posterior distribution of the emcee chain of the six parameters fit in our model for collisional progenitors with radii $\ge$ 30 km. The model is fit with 50 walkers, 10000 steps, and 1000 burn-in steps. The dashed lines indicate the 16th, 50th, and 84th percentiles, respectively.
• Figure 5: 1000 posterior draws from the best-fit planetesimal population. The green lines indicate the evolved planetesimal population, where the planetesimals have been collisionally processed and follow a power-law consistent with a collisional cascade. The gray dashed line indicates the point where the the collisional cascade transitions from particles whose cohesion is mainly from material strength to cohesion from self-gravity Pan2005. The model jointly fits the strength and gravity power law indices in $\alpha_{12}$. The black lines indicate the best-fit primordial planetesimal population, which is made up of planetesimals that have individual collision timescales that are longer than the age of the Fomalhaut system. The planetesimal radius where the evolved population transitions to the primordial population is $s_{break}$.