Gas Flows in Binary Systems Pawel Artymowicz U
Gas Flows in Binary Systems Pawel Artymowicz U of Toronto I. How they can help characterize binaries II. How they supersede the Lindblad torques and generate fast migration mode (type III) III. How do we model them? Preliminary results : evolution of m, a, & e MSF workshop May 2007
SPH, Artymowicz & Lubow 1996 Efficient flows found (~ unperturbed disk d. M/dt) mu = 0. 3, e = 0. 1 binary
1 3 2 4
mu = 0. 44, e = 0. 5 binary apoastron periastron
Time variability of photometry and spectra. . . Diagnostic tool for observed binaries (cf. Mathew et al, 1990 s)
part II. Migration type III does it apply to stars?
Up to mid-1990 s, disk-satellite interaction was understood as resonant / tidal interaction (Lindblad resonances --> waves, wakes etc. Easily identifiable) Afterwards, Corotational Torques began to displace LRs. . . These are torques connected with the librating U-turn orbits (horseshoe orbits) within the secondary’s gravitational realm, called CR zone (+- 2. 5 times Roche lobe radius for planets). No spectacular waves, unless the flow hits a shock near the secondary.
Inner and Outer Lindblad resonances in an SPH disk with a jupiter
DISK-PLANET interaction and migration, including outward migration It used to be just type I and II. . . now we study a new mode of migration: type III. This is a nonperturbative, nonlinear mode of migration
Migration Type I, II, and III Underlying fig. from: Protostars and Planets IV (2000) cf. Papaloizou et al in Protostars and Planets V (2007) (years) type III Time-scale ?
Variable-resolution PPM (Piecewise Parabolic Method) [Artymowicz 1999] Jupiter-mass planet, fixed orbit a=1, e=0. White oval = Roche lobe, radius r_L= 0. 07 Corotational region out to x_CR = 0. 17 from the planet disk gap (CR region) disk
Simulation of a Jupiter-class planet in a constant surface density disk with soundspeed = 0. 05 times Keplerian speed. PPM = Piecewise Parabolic Method Artymowicz (2000), resolution 400 x 400 Although this is clearly a type-II situation (gap opens), the migration rate is NOT that of the standard type-II, which is the viscous accretion speed of the nebula.
Consider a one-sided disk (inner disk only). The rapid inward migration is OPPOSITE to the expectation based on shepherding (Lindblad resonances). Like in the well-known problem of “sinking satellites” (small satellite galaxies merging with the target disk galaxies), Corotational torques cause rapid inward sinking. (Gas is trasferred from orbits inside the perturber to the outside. To conserve angular momentum, satellite moves in. )
Now consider the opposite case of an inner hole in the disk. Unlike in the shepherding case, the planet rapidly migrates outwards. Here, the situation is an inward-outward reflection of the sinking satellite problem. Disk gas traveling on hairpin (half-horeseshoe) orbits fills the inner void and moves the planet out rapidly (type III outward migration). Lindblad resonances produce spiral waves and try to move the planet in, but lose with CR torques.
Outward migration type III of a Jupiter Inviscid disk with an inner clearing & peak density of 3 x MMSN Variable-resolution, adaptive grid (following the planet). Lagrangian PPM. Horizontal axis shows radius in the range (0. 5 -5) a Full range of azimuths on the vertical axis. Time in units of initial orbital period.
AMR PPM (FLASH). Jupiter simulation by Peplinski and Artymowicz (in prep. ). Red color marks the fluid initially surrounding the planet’s orbit.
Variable-resolution PPM (Piecewise Parabolic Method) [Artymowicz 1999] Jupiter-mass planet, fixed orbit a=1, e=0. White oval = Roche lobe, radius r. L= 0. 07 Corotational region out to x. CR = 0. 17 from the planet disk gap (CR region) disk
Guiding center trajectories in the Hill problem Unit of length = Hill sphere Unit of da/dt = Hill sphere radius per dynamical time Animation: Eduardo Delgado-Donate
azimuth Variable-resolution PPM (Piecewise Parabolic Method) 1. Gas surface density, accentuating LR-born waves (surf) 2. Vortensity, showing gas flow (rip-tide) 0. 1 Jupiter mass planet in a z/r=0. 05 gas nebula Horizontal tick mark = 0. 1 a Corotational region out to x. CR = 0. 08 a away from the planet 0. 8 1 radius 1. 2 1. 4
Saturn-mass protoplanet in a solar nebula disk (1. 5 times the Minimum Nebula, PPM, Artymowicz 2003) Azimuthal angle (0 -360 deg) Type III outward migration Condition for FAST migration: disk mass in CR region ~ planet mass. Notice a carrot-shaped bubble of “vacuum” behind the planet. Consisting of material trapped in librating orbits, it produces 1 2 CR torques smaller than the matrial radius in front of the planet. The net CR torque powers fast migration. 3
Migration type III, neglecting LRs & viscous disk flow independent of planet mass, e. g. , in MMSN at a= 5 AU, the type-III time-scale = 48 Porb
Peplinski and Artymowicz (MNRAS, 2006, in prep. ) AMR code FLASH adaptive multigrid, PPM, Cartesian coordinates local resolution up to 0. 0003 a = 0. 0015 AU = 225000 km = 3 Jupiter radii NUMERICAL CONVERGENCE when gas given higher temperature near the planet - results not sensitive to gravitational softening length - and resolution
1 Disk gap 2 Smooth initial disk As theorized - no significant dependence on mass: 4 jupiter masses 1 jupiter mass Radius (a) 0 50 100 P time
1 Disk gap 2 Smooth initial disk As theorized - no significant dependence on mass: 4 jupiter masses 1 jupiter mass Radius (a) 0 50 100 P time
ALL TORQUES RESTORED (LRs, viscous) Outward migr. Inward migr.
Mass deficit Global migration reverses at the outer boundary Migration rate
n n n SURVIVAL OF PMS BINARIES extremely old dynamical age: period = days ==> up to 1 e 9 orbits How to explain their existence ? Standard (LR) theory predicts merger.
Summary of type-III migration n n n n New type, sometimes extremely rapid (timescale < 1000 years). CRs >> LRs Direction depends on prior history, not just on disk properties. Supersedes a much slower, standard type-II migration in disks more massive than planets Conjecture: modifies or replaces type-I migration Very sensitive to disk density (or vortensity) gradients. Migration stops on disk features (rings, edges and/or substantial density gradients. ) Such edges seem natural (dead zone boundaries, magnetospheric inner disk cavities, formation -caused radial disk structure) Offers possibility of survival of giant planets at intermediate distances (0. 1 - 1 AU), . . . and of terrestrial planets during the passage of a giant planet on its way to the star. If type I superseded by type III then these conclusions apply to cores as well, not only giant protoplanets.
Migration: type 0 type II & IIb Interaction: Gas drag + Radiation press. Resonant excitation of waves (LR) Timescale of migration: from ~1 e 2 yr to disk lifetime (up to 1 e 7 yr) > 1 e 4 yr Tidal excitation of waves (LR) > 1 e 5 yr type III Corotational flows (CR) > 1 e 2 - 1 e 3 yr N-body Gravity > 1 e 5 yr (? ) Not for stars
III+IV. Modeling of gas flows and preliminary results
AMRA
PPM = Piecewise Paraboli Method (Woodward and Colella) A Godunov-type code Solves Riemann shock tube problem on each cell interface Alternates x and y sweeps bin 11
MNRAS (2006)
Code comparison project: EU RTN, Stockholm
Surface density jupiter vortex L 4
Mass ratio = 0. 050 (e. g. , star+BD), eccentricity e=0, then e=0. 2 (two simulations) Bin 08+12
Disk similar to min. mass solar nebula ~AU scale ________ 1 st simulation: (2: 3 mass ratio) mu = 0. 4 init. e=0 a increases (CRs!) e slowly increases ________ 2 nd simulation: (1: 4 mass ratio) mu = 0. 2 init. e=0. 3 a decreases e ~stable ________ bin 10
z/r = 0. 05 z/r = 0. 1 Same binary: mass parameter = 0. 050 (like sun + 50 Jup. ) Different mass flow & distribution, as a function of disk temperature Bin 08+13
e=0 e = 0. 2 Same binary: mass parameter = 0. 050 (like sun + 50 Jup. ) Different mass flow & distribution, as a function of binary eccentricity Bin 08+12
RESULTS on mass flow through the gap mass ratio flow __________________ star+star binary - efficient star+BD - less efficient/inefficient star planet - usually efficient __________________ flow splitting: mostly onto primary if disk hot or binary eccentric mass equalization still there, but not as often as once thought
RESULTS on migration (da/dt) mass ratio a __________________ star+star binary - grows/stabilizes star+BD - decreases star planet - either grows or decreases __________________ This may explain the existence of spectroscopic PMS binaries
RESULTS on eccentricity mass ratio e __________________ star+star binary - ends at intermediate value (0. 2 -0. 3? ) star+BD - low during migration, later excited? star planet - same as BDs __________________ Much more work needed. Complicated, because a, m, and e interdependent (can’t be found separately)
Additional material:
Small softening 600 x 600 300 x 300 600 x 600 Large softening 300 x 300
PROBLEM: PPM (Lagrangian w/remap) based on VH-1, on different grids & implementation may cause SPURIOUS ARTIFICIAL INSTABILITIES, as can ANY OTHER KNOWN HI-RES HYDROCODE ! Small softening of gravity relative to Roche lobe a - Viscosity Low-order interpolation of forces on polar grid Large softening of gravity relative to the Roche lobe High-order interpolation of forces on polar grid
Some conclusions from hydrodynamical simulations of PMS binaries with disks: 1. Gaps are not empty (around satellites, planets, stars) 2. Corotational torques somehow help the binaries survive the Lindblad-torque mandated merger 3. Flow is not stationary even if e=0 4. Eccentricity induces a strong time-variability of flow, in phase with orbit, and possibly longer modulations 5. Flow/shocks/companions should be observable
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