Long‐Term Collisional Evolution of Debris Disks

Abstract

Infrared surveys indicate that the dust content in debris disks gradually declines with stellar age. We simulated the long-term collisional depletion of debris disks around solar-type (G2 V) stars with our collisional code. The numerical results were supplemented by, and interpreted through, a new analytic model. General scaling rules for the disk evolution are suggested. The timescale of the collisional evolution is inversely proportional to the initial disk mass and scales with radial distance as r 4.3 and with eccentricities of planetesimals as e −2.3 . Further, we show that at actual ages of debris disks between 10 Myr and 10 Gyr, the decay laws of the dust mass and the total disk mass are different. The reason is that the collisional lifetime of planetesimals is size-dependent. At any moment, there exists a transitional size, which separates larger objects that still retain the "primordial" size distribution set in the growth phase from smaller objects whose size distribution is already set by disruptive collisions. The dust mass and its decay rate evolve as that transition affects objects of everlarger sizes. Under standard assumptions, the dust mass, fractional luminosity, and thermal fluxes all decrease as t ξ with ξ = −0.3...−0.4. Specific decay laws of the total disk mass and the dust mass, including the value of ξ, largely depend on a few model parameters, such as the critical fragmentation energy as a function of size, the primordial size distribution of largest planetesimals, as well as the characteristic eccentricity and inclination of their orbits. With standard material prescriptions and a distribution of disk masses and extents, a synthetic population of disks generated with our analytic model agrees quite well with the observed Spitzer/MIPS statistics of 24 and 70 µm fluxes and colors versus age.

Vertical structure of debris discs

“…As an example, a disc with h = 0.04 could harbour embryos as large as a few 100 km. As a matter of fact, we subscribe to the theoretical arguments supporting the presence of large hidden bodies, which are in particular needed to provide the mass reservoir for sustaining the high collisional activity of debris discs (Löhne et al 2008). What we have demonstrated is that direct observational evidence can probably not be easily obtained, since for aspect ratios lower than ∼0.06 there is no direct link between vertical thickness and the dynamical excitation of the system.…”

“…Numerical studies of debris discs fall into two main categories: those investigating the collisional and size distribution evolution of the system are usually statistical particle-in-the-box models, of no or poor spatial resolution and very limited dynamical evolution (e.g., Krivov et al 2006;Thébault & Augereau 2007;Löhne et al 2008), while those studying the dynamics and the formation and evolution of spatial structures are mostly N-body type codes, where size distributions and mutual collisions are usually neglected (see for example Reche et al 2008).…”

Modelling the huge,Herschel-resolved debris ring around HD 207129

“…During the inside-out stirring, different annular regions in a disk brighten up and enter their erosive debris disk phase. Their individual fractional luminosities decay more slowly than 1/t (Dominik & Decin 2003;Wyatt et al 2007;Trilling et al 2008;Löhne et al 2008). However, this decay is even more rapid than the outward migration of the stirring front.…”

Insights into Planet Formation from Debris Disks

“…2), and so a higher collision rate at the collision point and along the anti-collision line expected to start with the shape it tends to in steady state. Both are valid criticisms, but their consequences can be readily accounted for (Löhne et al 2008;Wyatt et al 2011). Furthermore, it is found that the simple prescription given above is usually accurate to within a factor of a few and so is acceptable for many applications.…”

“…However, this is not interpreted as giant impact debris. Rather, this dust is believed to be the product of steady state collisional grinding of planetesimal belts that are analogous to the Kuiper Belt in the Solar System (Wyatt et al 2007b;Löhne et al 2008;Gáspár et al 2013). At the large orbital separations inferred for these belts, collisional lifetimes are long enough that their dust can persist several Gyr above the detection threshold.…”