How hard is dust in debris disks?

TL;DR

This work probes the poorly known tensile strength of debris-disk dust by comparing three $Q_{D}^*$ prescriptions (Reference, Zodi, Fomalhaut) using the ACE collisional code. Across a wide range of sizes and disk radii, the authors show that when $Q_{D}^*$ is sufficiently high, rebound (bouncing) collisions dominate, driving small grains into circular outer orbits and producing outward-increasing brightness profiles that conflict with resolved-disk observations. An analytic limit $Q_{D}^*(s) \lesssim \frac{1}{8} v_K^2(r)$ (near the blowout size) yields $Q_{D}^* \lesssim 10^9{-}10^{10}\ \mathrm{erg}\ \mathrm{g}^{-1}$ for micrometer grains at $\sim100$ AU, constraining how hard debris-dust can be. Despite similar spectral energy distributions across models, the radial brightness profile emerges as the most sensitive diagnostic for dust strength, allowing observed disks to disfavour rebound-dominated, too-hard-dust scenarios.

Abstract

Observational appearance of debris disks is largely controlled by collisional grinding of their dust grains. However, the mechanical strength of dust at sizes in the micrometer to millimeter range is poorly known. Recent studies suggested that dust particles in the Solar system might have a higher critical fragmentation energy $Q_{D}^*$ value than previously anticipated. Another recent study considered the Fomalhaut debris disk and found lower $Q_{D}^*$ values to provide better fits to the data. In order to constrain the mechanical strength of dust, we investigate collisional evolution of debris disks with $Q_{D}^*$ prescriptions differing by $\sim 3$ orders of magnitude. We find that, above a certain threshold $Q_{D}^*$ value, the disk's collisional evolution is dominated by rebounding -- rather than disruptive or cratering -- collisions. Rebounding (a.k.a. bouncing) collisions are those in which both impactors survive, being only slightly eroded and producing fragments that only carry a minor fraction of their mass. We show that disks dominated by rebounding collisions would have brightness profiles increasing outward outside the parent belt. Since such profiles are not observed, this places an upper limit on how hard the debris dust is allowed to be in order not to violate the observations. We derive an approximate analytic expression for this limit: $Q_{D}^* \approx (1/8) v_{K}^2(r)$ for grains close to the radiation pressure blowout size, where $v_{K}$ in the Keplerian circular speed at a distance $r$ from the star. This implies $Q_{D}^* \lesssim 10^{9...10} \,\hbox{erg}\,\hbox{g}^{-1}$ for micrometer-sized grains in typical debris disks. Even though rebounding collisions are not expected to affect debris disk evolution significantly, we emphasize that these collisions are actually much more frequent than disruptive and cratering ones in all debris disks.

Figures (15)

• Figure 1: $Q_\text{D}^*$ models chosen: Reference (blue), Zodi (red), and Fomalhaut (green). These are shown for two typical collisional velocities: $300\,\hbox{m}\,\hbox{s}^{-1}$ (left) and $30\,\hbox{m}\,\hbox{s}^{-1}$ (right). For comparison, the $Q_\text{D}^*$ fit from pokorny-et-al-2024 (pink) as well as the sommer-et-al-2025 constraint at $32\,\text{µm}$ (black dot with the uncertainty bar) are plotted as well. Horizontal black lines mark an approximate disruption threshold, for the respective velocities. Note that the pokorny-et-al-2024 model only describes particles with sizes up to $1\,\hbox{cm}$.
• Figure 2: Schematic of the four possible collisional outcomes, eqs. (\ref{['eq:disrupt']})--(\ref{['eq:stick']}). The "projectile" particle (the less massive of the two colliders, marked with "p" and shown in red), and the "target" one (the more massive one, "t", in blue) collide to produce one or two remnants ("rem" or "rem, p" and "rem, t", each having the color of its progenitor particle) and a cloud of fragments that may originate from both colliders ("frag", shown in black).
• Figure 3: Dust mass evolution for the three runs. Dashed lines depict the original (unscaled) and solid lines the scaled versions of the runs. Only one curve is shown for the Reference run as the scaled and unscaled versions are equivalent here.
• Figure 4: Time evolution of disk brightness in all three runs at $1\,\text{µm}$ (dashed lines) and $1\,\hbox{mm}$ (solid lines).
• Figure 5: Size distribution at $100\,\hbox{au}$ in the three runs in the initial state (thin lines) and at $T=100\,$Myr (thick lines).