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Sculpting Circumstellar Disks Alice Quillen University of Rochester Netherlands April 2007
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
Discovery Space All extrasolar planets discovered by radial velocity (blue dots), transit (red) and microlensing (yellow) to 31 August 2004. Also shows detection limits of forthcoming space- and ground-based instruments. Discovery space for planet detections based on disk/planet interactions
Dynamical Regimes for Circumstellar Disks with central clearings • Young gas rich 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 particle in corotation region 3. Intermediate opacity dusty disks – dust collision timescale is in regime 103-104 orbital periods; e.g., Fomalhaut, AU Mic debris disks
What mass objects are required to account for the observed clearings, what masses are ruled out? 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
CoKuTau/4D’Alessio et al. 05 4 AU 10 AU 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 Wavelength μm
Models for Disks with Clearings 1.Photo-ionizationmodels (Clarke, Alexander) Problems: -- clearings around brown dwarfs, e.g., L316, Muzerolle et al. -- accreting systems such as DM Tau, D’Alessio et al. -- wide gaps such as GM Aur; Calvet et al. Predictions: Hole size with time and stellar UV luminosity 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, 3D structure Predictions: Planet masses required to hold up disk edges, and clearing timescales, detectable edge structure
Minimum Gap Opening Planet In an Accretion Disk radiation accretion, optically thick Gapless disks lack planets Edgar et al. 07
Minimum Gap Opening Planet Mass in an Accretion Disk Smaller planets can open gaps in self- shadowed disks Planet trap?
Prospects with ALMA 5km/s for a planet at 10AU PV plot Edgar’s simulations
Fomalhaut’s eccentric ring • steep edge profile • hz/r ~ 0.013 • 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
efree eforced Free and forced eccentricity radii give you eccentricity If free eccentricity is zero then the object has the same eccentricity as the forced one
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? Mp > Neptune Neptune size Saturnsize collisionless lifetime
Chaotic zone boundaries for particles with zero free eccentricity Hamiltonian at a first order mean motion resonance secular terms regular resonance corotation
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 efree different eccentricity points width of chaotic zone planet mass
Velocity dispersion in the disk edgeand 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 • Mp < Saturn
cleared out by perturbations from the planet Mp> 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 Mp< Saturn
First Predictions for a planet just interior to Fomalhaut’s eccentric ring • Neptune < Mp < Saturn • Semi-major axis 120 AU (16’’ from star) • Eccentricity ep=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 possibly radiation pressure, PR force, etc) • Collision timescale is many orbits for the regime of debris disks 100-10000 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)
Our Numerical Approach Perturbations independent of particle distribution: • Espresate set the vr 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
Morphology of collisional disks near planets radius • Featureless for low mass planets, high collision rates and velocity dispersions • Particles removed at resonances in cold, diffuse disks near massive planets radius angle
Profile shapes chaotic zone boundary 1.5 μ2/7
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
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 nice form for tremove
Using the numerical measured fit Log Planet mass To truncate a disk a planet must have mass above (here related to observables) Nc=10-3 Nc=10-2 α=0.001 Log Velocity dispersion Observables can lead to planet mass estimates, motivation for better imaging leading to better estimates for the disk opacity and thickness
Application to Fomalhaut • Upper mass limit confirmed by lack of resonance clumps • Lower mass extended lower unless the velocity dispersion at the disk edge set by planet • Velocity dispersion close to threshold for collisions to be destructive Log Planet mass Quillen 2006, MNRAS, 372, L14 Quillen & Faber 2006, MNRAS, 373, 1245 Quillen 2007, astro-ph/0701304 Log Velocity dispersion
Constraints on Planetary Embryos in Debris Disks Thin AU Mic JHKL Fitzgerald, Kalas, & Graham h/r<0.02 • Thickness tells us the velocity dispersion in dust • This effects efficiency of collisional cascade resulting in dust production • Thickness from gravitational stirring by massive bodies in the disk
The size distribution and collision cascade observed constrained by gravitational stirring Figure from Wyatt & Dent 2002 set by age of system scaling from dust opacity
Hill sphere limit gravitation stirring top of cascade Comparing size distribution at top of collision cascade to thatrequired by gravitational stirring size distribution might be flatter than 3.5 – more mass in high end runaway growth? >10objects > 10objects
Comparison between 3 disks with resolved vertical structure 107yr 107yr 108yr
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 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. Log10 time(yr) μ=10-7 μ=10-3 Faber & Quillen 07
How many planets? • Between dust radius and ice line ~ 4 Neptune’s required • 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
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