#### Transcript M p - University of Rochester

Sculpting Circumstellar Disks Alice Quillen University of Rochester Netherlands April 2007 Motivations • Planet detection via disk/planet interactions – Complimentary to radial velocity and transit detection methods • Rosy future – ground and space platforms • Testable models – 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 , also Eric Blackman, Adam Frank, Pasha Hosseinbor, Amanda LaPage Observational Background • Submillimeter imaging Young Clusters: 5--20% of stars surveyed in young clusters are TTauri stars hosting disks with large clearings – Dozen or so now with IRS/Spitzer spectra, more identifiedFomalhau t with Spitzer/IRAC photometry Older Disks and Debris Disks: Optical scattered light • Fraction detected with disks with IR excess depends on age, wavelength surveyed and detection limit. 50—100 now known from Spitzer/MIPS surveys • HD 100546 HR4796A Unexplained structure: edges, clearings, spiral arms, warps, clumps Beta Pictorus HD 141569A Credits, ESO,Schneider Wilner, Grady, Clampin, HST, Kalas Dynamical Regimes for Circumstellar Disks with central clearings 1. 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, drag forces, resonant trapping, removal of orbit crossing particles 3. Intermediate opacity dusty disks – dust collision timescale is in regime 103-104 orbital periods; e.g., Fomalhaut, AU Mic debris disks This Talk i. What mass objects are required to account for the observed clearings, What masses are ruled out? Planets in accretion disks with clearings -- CoKuTau/4 ii. Planets in Debris disks with clearings -- Fomalhaut iii. Embryos in Debris disks without clearings -- AU Mic iv. Total mass in planets in older systems -- Clearing by planetary systems Transition Disks Estimate of minimum planet mass to open a gap requires an estimate of disk viscosity. CoKuTau/4 D’Alessio et al. 05 4 AU 10 AU Wavelength μm Disk viscosity estimate either based on clearing timescale or using study of accretion disks. Mp > 0.1MJ Models for Disks with Clearings 1. Photo-ionization models (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. -- single temperature edges 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 heat from accretion heat from stellar radiation =0.01, M * M Gapless disks lack planets Park et al. 07 in preparation Minimum Gap Opening Planet Mass in an Accretion Disk Different mass stars M M *2 =0.01 Planet trap? Smaller planets can open gaps in selfshadowed disks Hole radii scale with stellar mass (Kim et al. in prep) Retired A stars lack Hot Jupiters? (Johnson et al. 07) Fomalhaut ’s • eccentric steep edge profile h /r ring ~ 0.013 z • 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 Free and forced eccentricity e sin v radii give you eccentricity efree v free eforced v forced e cosv If free eccentricity is zero then the object has the same eccentricity as the forced one v longitude of pericenter Pericenter glow model • Collisions cause orbits to be near closed ones. Small free eccentricities. • The eccentricity of the ring is the same as the forced eccentricity e forced b3/2 2 ( ) 1 e planet b3/ 2 ( ) a ap • We require the edge of the disk to be truncated by the planet ~ 1 ering e forced e 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 N N D and removal within a a t collisionless lifetime removal Neptun e size Saturn size What mass planet will clear out objects inside the chaos zone fast enough that collisions will not fill it in? Chaotic zone boundaries for particles with zero free eccentricity Hamiltonian at a first order mean motion resonance H ( ; , ) a 2 b c d 1/ 21/p 2 cos( - p ) g 0 1/ 2 cos( ) g11/p 2 cos( p ) Poincare variables ~ e2 , only depends on a c regular resonance 5/ 2b3/1 2 4 g 0 2 5/ 4 f 31 d corotation 5/ 2b3/2 2 2 g1 2 5/ 4 f 27 With secular terms only there is a fixed point at p , 1/ 2 secular terms b3/2 2 1/ 2 1 p that is the e free 0 orbit b3/ 2 Dynamics at low free eccentricity Expand about the fixed point (the zero free eccentricity orbit) H ( ; I , ) a 2 b cI same as for zero g I 1/ 2 cos( 0 eccentricity planet goes to zero near the planet ) ( g 01/f 2 g11/p 2 ) cos( p ) 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 Dynamics at low free eccentricity is similar to that at low eccentricity near a planet in a circular orbit width of chaotic zone different eccentricity points 1.5 2/ 7 planet mass No difference in chaotic zone width, particle lifetimes, disk edge velocity dispersion low e compared to low efree Velocity dispersion in the disk edge and an upper limit on Planet mass • Distance to disk edge set by width of chaos zone 2/ 7 da ~ 1.5 • Last resonance that doesn’t overlap the corotation zone affects velocity dispersion in the disk edge • Mp < Saturn ue ~ 3/ 7 cleared out by perturbations from the planet Mp > Neptune 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 nearly closed orbits due to collisions eccentricity of ring equal to that of the planet 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 tcol ~ n 1 where n is normal optical depth The number of collisions per orbit N c ~ 18 n 2r n ~ f IR where f IR is fraction stellar light dr re-emitted in infrared 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 vr 0 v v v • 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 N c collision rate, collisions per particle per orbit - related to optical depth v tangential velocity perturbation size - related to disk thickness planet mass ratio - unknown that we would like to constrain from observations radius Morphology of collisional disks near planets 105 , N c 102 , e 0.02 104 , N c 103 , e 0.01 radius • Featureless for low mass planets, high collision rates and velocity dispersions • Particles removed at resonances in cold, diffuse disks near massive planets angle Profile shapes chaotic zone boundary 1.5 μ2/7 105 104 106 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 Reasonable well fit with the function log10 0.12 0.23log10 6 10 Nc dv 0.1log10 2 0.45log10 10 0.01 Unfortunately this does not predict a nice form for tremove To truncate a disk a planet must have mass above n log10 6 0.43log10 3 5 10 u / vK 1.95 0.07 (here related to observables) Log Planet mass Using the numerical measured fit Log Velocity dispersion Observables can lead to planet mass estimates, motivation for better imaging leading to better estimates for the disk opacity and thickness • Upper mass limit confirmed by lack of resonant structure • Lower mass limit ~ lower than previous estimate unless the velocity dispersion at the disk edge set by planet Log Planet mass Application to Fomalhaut 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 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 Figure from Wyatt & Dent 2002 set by age of system scaling from dust opacity constrained by gravitational stirring Scaling from the dust: 1 q a d ln N N (a ) N d d ln a ad 3 q a (a) d ad (multiply by a 2 ) As tcol ~ 1 13 1 q 3 a u tcol tcol ,d * ad 2QD Set tcol tage and solve for a 2 The top of the cascade Gravitational stirring In sheer dominated regime 2 1 d i ~ s2 s dt i where s s Solve: i (t ) t 4 s mass density ratio M *r 2 ms M* mass ratio Comparing size distribution at top of collision cascade to that required by gravitational stirring size distribution might be flatter than 3.5 – more mass in high end runaway growth? top of cascade Earth Comparison between 3 disks with resolved vertical structure 108yr 107yr 107yr Clearing by Planetary Systems • Assume planet formation leaves behind a population of planetesimals which produce dust via collisions • Central clearings lacking dust imply that all planetesimals have been removed • Planets are close enough that interplanetary space is unstable across the lifetime of the system • ~ 50 known debris disks well fit by single temperature SEDs implying truncated edges (Chen et al. 06) Clearing by Planetary Systems Log10 time(yr) Instability happens at t 1/ 4 ~ 9.5 log10 7 5 10 yr 10 Mp where planets of mass ratio = M* are spaced ri 1 1 ri ~0.5 r N 2 1 ~ max rmin Separation Chambers et al. 96 Faber et al. in preparation Clearing by planetary systems 2 1 ~ N rmax rmin rmin set by ice line rmax set by observed disk temperature Result is we solve for N and find 3-8 planets required of Neptune size for most debris disks. This implies a total minimum mass in planets of about a Saturn mass Summary • Quantitative ties between disk structure and planets residing in disks • Better understanding of collisional regime and its relation to observables • 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 Saturn mass • More numerical and theoretical work inspired by these preliminary crude numerical studies • Exciting future in theory, numerics and observations 5km/s for a planet at 10AU PV plot Prospects with ALMA Edgar’s simulations Diffusive approximations N Nf (r ) D r r tremoval planet dv u2 where D ~ ~ N c tcol n 2 v K 2 Consider various models for removal of particles by the planet f (r ) 1 N (r ) elr f (r ) 1 r N (r ) is an Airy function f (r ) e r N (r ) is a modified Bessel function All have exponential solutions near the planet with inverse scale length 1/ 2 l ~ tremove 2 / 7 N c1/ 2 dv1 and unknown function tremove