Sculpting Circumstellar Disks Feb 2008 Alice Quillen University of Rochester

Motivations Planet detection via disk/planet interaction – Complimentary to radial velocity and transit detection methods Rosy future – ground and space platforms Testable – via predictions for forthcoming observations. New dynamical regimes and scenarios compared to old solar system Evolution of planets, planetesimals and disks Collaborators: Peter Faber, Richard Edgar, Peggy Varniere, Jaehong Park, Allesandro Morbidelli, Alex Moore

All extrasolar planets discovered by radial velocity (blue dots), transit (red) and microlensing (yellow) to 31 August Also shows detection limits of forthcoming space- and ground-based instruments. Discovery space for planet detections based on disk/planet interactions Discovery Space

Dynamical Regimes for Circumstellar Disks with central clearings Young gas rich Myr old accretion disks – “transitional disks” e.g., CoKuTau/4. Planet is massive enough to open a gap (spiral density waves). Hydrodynamics is appropriate for modeling.

Dynamical Regimes– continued 2. Old dusty diffuse debris disks – dust collision timescale is very long; e.g., Zodiacal cloud. Collisionless dynamics with radiation pressure, PR force, resonant trapping and removal of particles in corotation region 3.Intermediate opacity dusty disks – dust collision timescale is in regime orbital periods; e.g., Fomalhaut, AU Mic Debris disks, planetary migration, rapid change is planetary architecture, planetary growth

This Talk: Planets in accretion disks – The transition disks Planets in Debris disks with clearings – Fomalhaut Embryos in Debris disks without clearings – AU Mic Number of giant planets in old systems What mass objects are required to account for the observed clearings, what masses are ruled out?

Fomalhaut’s eccentric ring steep edge profile h z /r ~ eccentric e=0.11 semi-major axis a=133AU collision timescale =1000 orbits based on measured opacity at 24 microns age 200 Myr orbital period 1000yr

Free and forced eccentricity radii give you eccentricity If free eccentricity is zero then the object has the same eccentricity as the forced one e forced e free

Pericenter glow model Collisions cause orbits to be near closed ones. This implies the free eccentricities in the ring are small. The eccentricity of the ring is then the same as the forced eccentricity We require the edge of the disk to be truncated by the planet  We consider models where eccentricity of ring and ring edge are both caused by the planet. Contrast with precessing ring models.

Disk dynamical boundaries For spiral density waves to be driven into a disk (work by Espresate and Lissauer) Collision time must be shorter than libration time  Spiral density waves are not efficiently driven by a planet into Fomalhaut’s disk A different dynamical boundary is required We consider accounting for the disk edge with the chaotic zone near corotation where there is a large change in dynamics We require the removal timescale in the zone to exceed the collisional timescale.

Chaotic zone boundary and removal within What mass planet will clear out objects inside the chaos zone fast enough that collisions will not fill it in? M p > Neptune Saturn size Neptune size collisionless lifetime

Chaotic zone boundaries for particles with zero free eccentricity Hamiltonian at a first order mean motion resonance corotation regular resonance secular terms

Dynamics at low free eccentricity Expand about the fixed point (the zero free eccentricity orbit) For particle eccentricity equal to the forced eccentricity and low free eccentricity, the corotation resonance cancels  recover the 2/7 law, chaotic zone same width goes to zero near the planet same as for zero eccentricity planet

Dynamics at low free eccentricity is similar to that at low eccentricity near a planet in a circular orbit No difference in chaotic zone width, particle lifetimes, disk edge velocity dispersion low e compared to low e free planet mass width of chaotic zone different eccentricity points

Velocity dispersion in the disk edge and an upper limit on Planet mass Distance to disk edge set by width of chaos zone Last resonance that doesn’t overlap the corotation zone affects velocity dispersion in the disk edge M p < Saturn

cleared out by perturbations from the planet M p > Neptune nearly closed orbits due to collisions eccentricity of ring equal to that of the planet Assume that the edge of the ring is the boundary of the chaotic zone. Planet can’t be too massive otherwise the edge of the ring would thicken  M p < Saturn

First Predictions for a planet just interior to Fomalhaut’s eccentric ring Neptune < M p < Saturn Semi-major axis 120 AU (16’’ from star) location predicted using chaotic zone as boundary Eccentricity e p ~0.1, same as ring Longitude of periastron same as the ring

The Role of Collisions Dominik & Decin 03 and Wyatt 05 emphasized that for most debris disks the collision timescale is shorter than the PR drag timescale Collision timescale related to observables

The numerical problem Between collisions particle is only under the force of gravity (and < radiation pressure, PR force, etc) Collision timescale is many orbits for the regime of debris disks orbits.

Numerical approaches Particles receive velocity perturbations at random times and with random sizes independent of particle distribution (Espresante & Lissauer) Particles receive velocity perturbations but dependent on particle distribution (Melita & Woolfson 98) Collisions are computed when two particles approach each other (Charnoz et al. 01) Collisions are computed when two particles are in the same grid cell – only elastic collisions considered (Lithwick & Chiang 06)

A Simple Numerical Approach Perturbations independent of particle distribution: Espresante set the v r to zero during collisions. Energy damped to circular orbits, angular momentum conservation. However diffusion is not possible. We adopt Diffusion allowed but angular momentum is not conserved! Particles approaching the planet and are too far away are removed and regenerated Most computation time spent resolving disk edge

Parameters of 2D simulations

Morphology of collisional disks near planets Featureless for low mass planets, high collision rates and velocity dispersions Particles removed at resonances in cold, diffuse disks near massive planets angle radius

Profile shapes chaotic zone boundary 1.5 μ 2/7

Rescaled by distance to chaotic zone boundary Chaotic zone probably has a role in setting a length scale but does not completely determine the profile shape

Diffusive approximations

Density decrement Log of ratio of density near planet to that outside chaotic zone edge Scales with powers of simulation parameters as expected from exponential model Unfortunately this does not predict a simple form for t remove decrement for different planet masses as a function of dispersion

Using the numerical measured fit To truncate a disk a planet must have mass above (here related to observables) Observables can lead to planet mass estimates, motivation for better imaging leading to better estimates for the disk opacity and thickness N c =10 -3 α=0.001 Log Planet mass Log Velocity dispersion N c =10 -2

Application to Fomalhaut Upper mass limit confirmed by lack of resonance clumps Lower mass limit extended unless the velocity dispersion at the disk edge set by planet Velocity dispersion close to threshold for collisions to be destructive Log Velocity dispersion Log Planet mass Quillen 2006, MNRAS, 372, L14 Quillen & Faber 2006, MNRAS, 373, 1245 Quillen 2007, MNRAS

Constraints on Planetary Embryos in Debris Disks AU Mic JHKL Fitzgerald, Kalas, & Graham Thickness tells us the velocity dispersion in dust This effects efficiency of collisional cascade resulting in dust production Thickness increased by gravitational stirring by massive bodies in the disk h/r<0.02

The size distribution and collision cascade Figure from Wyatt & Dent 2002 set by age of system scaling from dust opacity constrained by gravitational stirring observed

The top of the cascade related to observables, however exponents not precisely known

Gravitational stirring

Comparing size distribution at top of collision cascade to that required by gravitational stirring >10objects gravitation stirring top of cascade Hill sphere limit size distribution might be flatter than 3.5 – more mass in high end  runaway growth? > 10objects

Comparison between 3 disks with resolved vertical structure 10 7 yr 10 8 yr

Debris Disk Clearing Spitzer spectroscopic observations show that dusty disks are consistent with one temperature, hence empty within a particular radius Assume that dust and planetesimals must be removed via orbital instability caused by planets

Disk Clearing by Planets Log10 time(yr) Faber & Quillen 07 μ=10 -7 μ=10 -3 Simple relationship between spacing, clearing time and planet mass Invert this to find the spacing, using age of star to set the stability time. Stable planetary system and unstable planetesimal ones.

How many planets? Between dust radius and ice line ~ 4 Neptune’s required ~a Jupiter mass in planets is required to explain clearings in all debris disk systems Spacing and number is not very sensitive to the assumed planet mass It is possible to have a lot more stable mass in planets in the system if they are more massive Would be interesting to extend to relaxing and scattering planetary systems….

Transition Disks 1-3 Myr old stars with disks with central clearings, silicate emission features, discovered in young cluster surveys Challenges to explain: Accreting vs non Dust wall Clearing times Statistics Dust properties 4 AU 10 AU CoKuTau/4 D’Alessio et al. 05 Wavelength μm

Transition disks 5-15% of disks in clusters 1-5Myr old as found from surveys (e.g., Muzerolle et al.) 50% of them are still accreting at low rates 50% have hot fainter, optically thin inner dust disks mm observations in 2 cases have resolved clearings (Wilner’s collaboration)

SED modeling Dust edge in most cases dominated by small amorphous grains Density contrasts clearing/edge in dust and gas are likely large Light reradiated in wall sets dust wall thickness. Consistent with temperature predicted via radiative transfer A denser disk edge  increased flux at longer wavelengths However in some cases large outer disk mass is required from far infrared fluxes Examples of disks without massive outer disks (CoKuTau4) and with (DMTau)

Models for Disks with Clearings 2. Planet formation, gap opening followed by clearing (Quillen, Varniere) -- more versatile than photo-ionization models but also more complex Problems: Failure to predict dust density contrast Predictions:Planet masses required to hold up disk edges, and clearing timescales, detectable edge structure 1. Photo-ionization models (Clarke, Alexander) Problems: -- clearings around brown dwarfs, e.g., L316, Muzerolle et al. -- dense transition disks Predictions: Hole size with time and stellar UV luminosity, clearing when disk accretion drops below a wind outflow rate

Differentiating between models Photo-ionization alone cannot explain all objects, because some have high disk masses Najita et al 07 and Alexander et al. 07 from Najita et al 07, + are transition disks

Vertical motions in the disk edge v z in units of Mach number (radius) azimuthal angle density slice

Minimum Gap Opening Planet In an Accretion Disk Edgar et al. 07 radiation accretion, optically thick Gapless disks lack planets

Minimum Gap Opening Planet Mass in an Accretion Disk Planet trap? Smaller planets can open gaps in self- shadowed disks

Summary Quantitative ties between observations, mass, eccentricity and semi-major axis of planets residing in disks In gapless disks planets can be ruled out – but we find preliminary evidence for embryos and runaway growth The total mass in planets in most systems is likely to be high, at least a Jupiter mass Better understanding of collisional regime More numerical and theoretical work inspired by these preliminary crude numerical studies Exciting future in theory, numerics and observations