Optics of Porous Dust in Protoplanetary Disks, Debris Disks, and Comets Aigen Li1, Fangzhou Liu2, You Zhou3 1. University of Missouri 2. Hunan Normal University 3. Hunan University of Finance & Economics Huaibei 2019 July 17

Contents (1) Dust in protoplanetary disks around young stars (2) Dust in debris disks around main-sequence (MS) Stars (3) Dust in cometary nuclei and comae (4) Optical properties of porous dust

Protoplanetary disks around young stars (1) Interstellar grains  coagulational growth in cold, dense molecular clouds and protoplanetary dust disks  creating dust with fluffy, inhomogeneous structures  formation of planetary systems (Weidenschilling & Cuzzi 1993). (2) Grain growth: the first step in the process of planet formation. (3) Protoplanetary disks around T Tauri stars and Herbig Ae/Be stars: the extent to which their dust grains have grown beyond the submicron sizes characteristic of the interstellar medium?

Protoplanetary disks around young stars (4)  Finding evidence for grain growth in protoplanetary disks (i) broadband photometry from mid-IR to mm wavelengths (i.e., spectral energy distribution = SED) (ii) scattered light imaging in the visible or near-IR  Optics of porous dust!

Debris Disks/“Vega-type” Disks around Main-Sequence Stars 

Debris disks: a signpost for the existence of extrasolar planetary systems! Density variations in debris disks (cavities, clumps, warps, rings etc)  the presence of planets; β Pictoris

“Vega-type” Disks: Debris Disks! Primordial or 2nd generational? Radiation pressure  dust expulsion; Poynting-Robertson drag  dust spiraling in; Rad-Prs, P-R drag timescale « stellar age  2nd generational!  Require replenishment!  Li & Lunine 2003

Dust Sources for Debris Disks Collisional grinding down of asteroidal bodies; Evaporation of cometary bodies;

IDPs and Cometary Dust IDP Interplanetary Dust Particles of cometary origin: fluffy structure, density 2 g/cm3  porosity P=Vvacuum/Vtot ~ 0.4 (Brownlee 2003); Cometary nuclei: density 0.5 g/cm3  P ~ 0.9 (Rickman 2003; Whipple 1999) for cometary dust; IDP

Porosity: P=Vvacuum/Vtot

To model the scattered starlight, IR thermal emission, grain dynamics in protoplanetary disks, debris disks, comets Optics of Porous Dust Associate Prof. LIU Fangzhou @Hunan Normal University Assistant Prof. ZHOU You @Hunan Univ. Fin. & Eco.

Aggregation Models for Porous Dust BAM (Ballistic Aggregation with Migration) A particle moves in a straight line until it sticks to other ones, and a stuck particle can slide to stick to more particles. The more neighbors a particle sticks to, the lower the porosity. BA only requires each particle to stick to one particle. BAM1 requires each particle to stick to two adjacent particles. BAM2 requires each particle to stick to three adjacent particles. (Shen & Draine 2008) DLA (Diffusion Limited Aggregation) A particle moves randomly until it sticks to another particle according to a certain sticking probability. The lower the sticking probability, the more compact the aggregated cluster. DLCA (Diffusion Limited Cluster Aggregation) Both BAM and DLA have a stationary core particle, and other particles stick to the core or the stuck particles, forming a stationary cluster. DLCA has no core, that is, the aggregated clusters also move randomly and can aggregate into larger clusters.

Comparison of Aggregation Models Large sticking probability  “open” cluster particles enter the inner gaps after collisions  smaller porosity Small sticking probability “compact” cluster  particles move outwards  larger porosity Liu, Li & Zhou 2019 BAM DLA DLCA Advantage Wide porosity range Continuous porosity High porosity Disadvantage Discrete porosity Narrow porosity range

Comparison of Aggregation Models BAM2 cluster DLA cluster (Pstick=0.0004) The facts that DLCA which seems to be closer to the true aggregating process of dust grains has the highest porosity and DLA also requires a very low sticking probability to get low porosity imply that dust grains with low porosity may be rare if only Brownian motion is considered. DLCA cluster (Pstick=0.0002)

Optics of Dust

Individual Partciles: single radii Uniform radii (r=0.1 μm) Uniform radii (r=0.05 μm) Composition: Carbon (red), Silicate (green) Vcarbon:Vsilicate=1 Rabc=1 μm Porosity=0.8 aeff=0.5848 μm

Individual Partciles: Power-Law Size Distribution Composition: Carbon (red), Silicate (green) Vcarbon:Vsilicate=1 Rabc=1 μm Porosity=0.8 aeff=0.5848 μm dn/dr ~ r-3.5 (0.06<r<0.25 μm)

Uniform Particle Radii vs Particle Radii in Power-Law carbon + silicate (no water ice)

Uniform Particle Radii vs Power-Law Particle Radii Uniform radii (r=0.02 μm) Power-law distrib. radii (0.005 < r < 0.25 μm) Composition: Carbon (red), Silicate (green) Vcarbon:Vsilicate:Vice=0.5:0.5 Rabc=1 μm Porosity=0.8 aeff=0.5848 μm In Computing…

With ice Uniform Particle Radii vs Particle Radii in Power-Law Uniform radii (r=0.1 μm) Random radii (0.06 < r < 0.25 μm) Composition: Carbon (red), Silicate (green), Ice (yellow) Vcarbon:Vsilicate:Vice=0.28:0.28:0.44 Rabc=1 μm Porosity=0.8 aeff=0.5848 μm With ice

Uniform Particle Radii vs Particle Radii in Power-Law With water ice

Ice as individual particles or coats

Conclusion: The optical properties of porous dust are only related to the composition, aeff and porosity, but not to the size distribution of the individual particles that make up the porous dust grains.  We can use a small number of particles with a large uniform radius to derive the scattering properties of porous dust grains, provided the required porosity can be obtained by aggregating these particles.

Ice as individual particles vs ice as coats ice as coats on silicate, carbon grains Uniform particle radius (r=0.1 μm) Composition: Carbon (red), Silicate (green), Ice (yellow) Vcarbon:Vsilicate:Vice=0.28:0.28:0.44 Rabc=1 μm Porosity=0.8 aeff=0.5848 μm

Separate Ice Particles VS Ice Coat Uniform particle radius

Separate Ice Particles vs Ice Coat Random particle radii in power law (r-3.5, 0.06 < r< 0.25 μm) Composition: Carbon (red), Silicate (green), Ice (yellow) Vcarbon:Vsilicate:Vice=0.28:0.28:0.44 Rabc=1 μm Porosity=0.8 aeff=0.5848 μm

Separate Ice Particles vs Ice Coat Random particle radii in power law

Conclusion: The optical properties of separate ice particles and ice coat are basically the same. So we can simply model water ice with separate particles.

Aigen Li （University of Missouri） Coloring the Dusty Universe：from the Solar System to Exoplanetary Disks to Active Galactic Nuclei and the Intergalactic Medium Aigen Li （University of Missouri） 2018年7月28日星际物理与化学（昆明2018）

Red coloration of Solar system objects as an analog for debris disks? Li 2018 Measured spectral reflectance of several solar system small bodies (Pholus: Centaur object; Iapetus: Saturn satellite; Hektor, Odysseus, Euphrosyne: Trojan asteroids; Himalia: Jupiter satellite; Borrelly: Jupiter-family comet). Taken from Dalle Ore et al. (2011).

HR 4796A AU Mic Red AU Mic HD32297 Gray Blue