Self-stirring of debris discs by planetesimals formed by pebble concentration

Abstract

When a protoplanetary disc loses gas, it leaves behind planets and one or more planetesimal belts. The belts get dynamically excited, either by planets ("planet stirring") or by embedded big planetesimals ("self-stirring"). Collisions between planetesimals become destructive and start to produce dust, creating an observable debris disc. Following Kenyon & Bromley (2008), it is often assumed that self-stirring starts to operate as soon as the first ∼ 1000 km-sized embedded "Plutos" have formed. However, state-of-the-art pebble concentration models robustly predict planetesimals between a few km and ∼ 200 km in size to form in protoplanetary discs rapidly, before then slowly growing into Pluto-sized bodies. We show that the timescale, on which these planetesimals excite the disc sufficiently for fragmentation, is shorter than the formation timescale of Plutos. Using an analytic model based on the Ida & Makino (1993) theory, we find the excitation timescale to be T excite ≈ 100 x −1 m M −3/2 a 3 Myr, where x m is the total mass of a protoplanetary disc progenitor in the units of the Minimum-Mass Solar Nebula, a its radius in the units of 100 AU, and M is the stellar mass in solar masses. These results are applied to a set of 23 debris discs that have been well resolved with ALMA or SMA. We find that the majority of these discs are consistent with being self-stirred. However, three large discs around young early-type stars do require planets as stirrers. These are 49 Cet, HD 95086, and HR 8799, of which the latter two are already known to have planets.

VLT/SPHERE Multiwavelength High-contrast Imaging of the HD 115600 Debris Disk: New Constraints on the Dust Geometry and the Presence of Young Giant Planets

“…Alternatively, according to turbulent concentration and gravitational clumping models (Johansen et al 2007;Cuzzi et al 2008) large planetesimals can form directly from the concentration of small pebbles in a protoplanetary disk. Though these models predict very rapid formation of hundred kilometer size bodies even at radii >100 au (Carrera et al 2017), additional time is needed to excite the neighbouring disk sufficiently (Krivov & Booth 2018). According to equation 34 from Krivov & Booth (2018) in this model the stirring of the belt at a time of 15 Myr needs an even lower initial surface density (x m ∼ 0.3) than in the case of the gradual buildup approach.…”

“…Though these models predict very rapid formation of hundred kilometer size bodies even at radii >100 au (Carrera et al 2017), additional time is needed to excite the neighbouring disk sufficiently (Krivov & Booth 2018). According to equation 34 from Krivov & Booth (2018) in this model the stirring of the belt at a time of 15 Myr needs an even lower initial surface density (x m ∼ 0.3) than in the case of the gradual buildup approach. Obviously, the initial surface density could not be arbitrarily large: ac-cording to Mustill & Wyatt (2009), x m > 10 would imply that the self-stirring scenario may not be feasible in the given system raising the suspicion that the dynamical excitation is rather related to a planet.…”

Extrasolar Kuiper belts

“…However, the growth of Pluto-sized objects at 100s of au in the disk takes too long to explain large disks seen around Gyr-old stars. One possibility is that these form directly from the protoplanetary disk (rather than from the collisional growth of smaller planetesimals), or it could be that a massive disk of ∼ 200 km planetesimals can stir itself without the need for larger bodies (Krivov and Booth 2018). If the belts do mark the outer edge of the planetary system then those planets could stir the disk through their gravitational perturbations.…”

The scattered disc of HR 8799

“…As discussed above, formation of scattered discs require planets to be present in the systems. Considering the same sample of discs from Matrà et al (2018), Krivov & Booth (2018) checked which of them do require planets as stirrers to explain the dust production. They found three such discs: HR 8799, HD 95086 and 49 Cet.…”

“…The excitation models of Kenyon & Bromley (2008) need Pluto sized objects to stir the disc, but the formation of these objects at the distance of the cold disc of HR 8799 would take longer than the age of the system. Even assuming smaller objects sufficiently stir the disc, self stirring is still not able to produce destructive collisions in the extended disc (Krivov & Booth 2018). This poses the question of how to explain any sort of destructive collision at these distances.…”