The Debris Disk of Vega: A Steady-State Collisional Cascade, Naturally

Abstract

The archetypical debris disk around Vega has been observed intensively over the past 25 years. It has been argued that the resulting photometric data and images may be in contradiction with a standard, steady-state collisional scenario of the disk evolution. In particular, the emission in the mid-infrared (mid-IR) appears to be in excess of what is expected from a "Kuiper belt" at ∼100 AU, which is evident in the submillimeter images and inferred from the majority of photometric points. Here we re-address the question of whether or not the Vega disk observations are compatible with a continuous dust production through a collisional cascade. Instead of seeking a size and spatial distribution of dust that provide the best fit to observations, our approach involves physical modeling of the debris disk "from the sources." We assume that dust is maintained by a belt of parent planetesimals, and employ our collisional and radiative transfer codes to consistently model the size and radial distribution of the disk material and then thermal emission of dust. In doing so, we vary a broad set of parameters, including the stellar properties, the exact location, extension, and dynamical excitation of the planetesimal belt, chemical composition of solids, and the collisional prescription. We are able to reproduce the spectral energy distribution in the entire wavelength range from the near-IR to millimeter, as well as the mid-IR and submillimeter radial brightness profiles of the Vega disk. Thus, our results suggest that the Vega disk observations are not in contradiction with a steady-state collisional dust production, and we put important constraints on the disk parameters and physical processes that sustain it. The total disk mass in 100 km-sized bodies is estimated to be ∼10 Earth masses. Provided that collisional cascade has been operating over much of the Vega age of ∼350 Myr, the disk must have lost a few Earth masses of solids during that time. We also demonstrate that using an intermediate luminosity of the star between the pole and the equator, as derived from its fast rotation, is required to reproduce the debris disk observations. Finally, we show that including cratering collisions into the model is mandatory.

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

“…Such a radial profile that rises outward with a sharp outer edge contrasts with those derived for the archetypal disks Vega (Su et al 2005;Krivov et al 2006;Müller et al 2010;Sibthorpe et al 2010) and β Pictoris (Golimowski et al 2006;Thébault & Wu 2008;Krivov et al 2009;Vandenbussche et al 2010). In these disks, the derived geometrical optical thickness typically falls off with a moderate r −1.5 relationship beyond the peak value, i.e.…”

“…The mass depends on the assumed initial size distribution. For collisional equilibrium, κ = −3.0, we would have M(s < 100 km) = 100 Earth masses, a value that is in-between the ones inferred for, e.g., A110, page 12 of 15 Vega (Müller et al 2010) and q 1 Eridani (Augereau et al, in prep.). For κ = −4.0, there would be only M(s < 100 km) = 0.7 Earth masses.…”

“…Following the strategy outlined in Müller et al (2010), we start from a first-guess setup based on the roughly known belt location (Krist et al 2010;Marshall et al 2011). After computation of the resulting SED and the radial profiles, we manually alter the most important (and least constrained) disk parameters and re-run the model until we reach a point from where no further significant improvements can be achieved that way.…”

Herschelobservations of the debris disc around HIP 92043

“…7, having subtracted the 70 µm-attributable component, overplotted with the expected thermal emission from fiducial discs of equal-sized grains with different optical properties, placed at a distance of 130 AU from an F6 V star. A comparison clearly demonstrates that grains smaller than a few tens of micrometres -those that are expected from collisional models (Krivov et al 2006;Thébault & Augereau 2007;Müller et al 2010;Löhne et al 2012) -yield emission that is too warm to be consistent with the observed fluxes. A rough agreement with the observations can only be achieved for larger grains ( > ∼ 1 mm), and only if they have low absorption at optical wavelengths (e.g.…”

The cold origin of the warm dust aroundε Eridani

“…The resulting brightness profiles were convolved with the instrumental PSF (see Sect. 2 in Müller et al 2010, for the algorithm used) and compared them with observed profiles.…”