Fomalhaut's debris disc is not dominated by primordial Plutos

TL;DR

The paper tackles the challenge of constraining debris-disc masses and largest-body sizes, which are hidden from direct observation. It develops a dynamical approach tailored to narrow discs like Fomalhaut by combining n-body simulations, analytic theory of disc broadening, and collisional evolution. The key finding is that Fomalhaut's debris disc cannot be dominated by primordial Plutos; such large bodies would have self-stirred and broadened the belt beyond observations unless they formed recently or the mass is carried by much smaller bodies. This work provides independent dynamical support for the idea that bright debris discs are dominated by bodies smaller than Pluto and offers a transferable method for weighing discs in other systems.

Abstract

A key challenge in debris-disc science is that we do not know the masses of debris discs, nor the sizes of the largest debris bodies. This is because modern observations can only detect objects up to centimetre sizes, whilst larger planetesimals, which dominate disc mass, remain hidden. We must therefore use other arguments, such as dynamics, to indirectly infer disc masses and body sizes. This paper presents a new method, applicable to narrow debris discs like Fomalhaut. We argue that such discs cannot be too massive, nor the largest bodies too large, otherwise they would self-scatter and the disc would be much broader than observed. Using n-body dynamics and collisional theory, we demonstrate that the mass of Fomalhaut's disc cannot be dominated by primordial Plutos. Instead, if the mass is dominated by primordial bodies, then they should have radii below $300^{+80}_{-70}$ km ($0.3 \pm 0.1$ RPluto) and above $5^{+20}_{-4}$ km. Such bodies would each have less than 1 per cent the mass of Pluto. Our conclusions are robust to additional physics, including shepherding planets and collisional damping. Our results provide independent, dynamical support for the idea that the masses of bright debris discs are dominated by objects smaller than Pluto.

Figures (8)

• Figure 1: Example setup of an $n$-body simulation. This particular disc has total mass ${1\; {\rm M_\oplus}}$, and comprises 3000 debris bodies, each of radius ${620\; {\rm km}}$ (${0.52 \; {\rm R_{Pluto}}}$). The simulation is shown at time 0, although for these parameters the disc maintains its shape for the whole ${440\; {\rm Myr}}$ age of Fomalhaut. Left: positions of bodies. The star is at the origin, and each brown point is a debris body. The blue ring is the median debris orbit, and the straight blue line shows the pericentre direction of the median orbit. Middle: distances of debris bodies from the median orbit (blue bars). The black line is a Gaussian fit. Right: simulated ${1.3\; {\rm mm}}$ ALMA image of the $n$-body disc. The cross marks the star, and the oval in the bottom left represents the ALMA beam from MacGregor2017.
• Figure 2: Example $n$-body simulation where the disc significantly broadens via self-scattering. This disc has a total mass of ${30\; {\rm M_\oplus}}$, and comprises 1000 debris bodies each of radius ${2200\; {\rm km}}$ (${1.9 \; {\rm R_{Pluto}}}$). This simulation started in a similar configuration to Figure \ref{['fig: simPlotLowMass']}, and is shown after ${160\; {\rm Myr}}$; by this time the disc has almost tripled in width, and is incompatible with observations. Definitions and most axis scales are the same as Figure \ref{['fig: simPlotLowMass']}, although the histogram vertical axis has been rescaled due to the different number of bodies, and the flux on the right panel has a different normalisation. The dotted line on the middle panel shows the initial-disc profile.
• Figure 3: Expected broadening of Fomalhaut's debris disc, as a function of disc mass and the size of the largest debris bodies. Crosses mark $n$-body simulations. The colour scale and contour lines show the interpolated final width of those simulated discs, divided by their initial widths. Discs that are too massive, or made up of bodies that are too large, readily scatter into broader structures (upper-right region). Red blocked areas are unphysical; the total disc mass must be larger than that in observed millimetre dust (left), and one body cannot be more massive than the whole disc (top). The 'Theoretical broadening' line is our prediction, above which a narrow planetesimal disc would significantly widen through self scattering (Equation \ref{['eq: maxMDiscBeforeScatter']}). The 'Damping' area is where realistic collisional damping could cause the disc to narrow (Equation \ref{['eq: minMDiscToDamp']}). Numbers in square brackets denote equations, and the shading around the 'Dust mass' line is the observational uncertainty (Table \ref{['tab: systemPars']}).
• Figure 4: Combined dynamical and collisional constraints on the Fomalhaut debris disc. Red shaded regions are ruled out by physical arguments. The numbers in square brackets denote the corresponding equation numbers. The beige region below Line \ref{['eq: tau0FromM0AndSMax']} is not necessarily excluded, but shows where most of the largest primordial bodies would have collisionally broken up by now. Line \ref{['eq: massIntegral']} is an extrapolation from observed dust; if debris follows the 3-powerlaw size distribution of Lohne2008, then the total disc mass and largest-body size lie along this line. 'Max. PPD' denotes the ${10^3 \; {\rm M_\oplus}}$ maximum mass in solids thought inheritable from protoplanetary discs Krivov2021. The horizontal axis is the disc's initial mass, but for the top $\sim$two-thirds of the plot (radii ${>48\; {\rm km}}$), the initial-disc mass equals the present-day mass, because the largest bodies have not yet started colliding. Shading around lines denotes ${1\sigma}$ uncertainties, propagated from observational uncertainties in Table \ref{['tab: systemPars']}. Note that the vertical-axis scale is larger than Figure \ref{['fig: discMassSMaxAllowedRegions']}.
• Figure 5: Effect of placing a small fraction of a disc's mass in one Pluto-sized object, where the disc's mass is dominated by smaller objects (Equation \ref{['eq: widthRatioOneLargerBody']}). The horizontal axis shows the radii of the non-Pluto objects, and the vertical axis the ratio of the disc width with and without the Pluto. Three disc masses are shown, as labelled. The plot shows that a Pluto-sized object could be hidden in a disc dominated by smaller bodies without significantly broadening the disc, provided that the smaller bodies have radii larger than ${100\; {\rm km}}$ (for a ${10\; {\rm M_\oplus}}$ disc) or ${20\; {\rm km}}$ (for a ${1000\; {\rm M_\oplus}}$ disc). The horizontal dashed line shows a width ratio of 1.5.