Gas Flows in Binary Systems

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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
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SPH, Artymowicz Lubow 1996
Efficient flows found ( unperturbed disk dM/dt)
mu 0.3, e 0.1 binary
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2
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4
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mu 0.44, e 0.5 binary
apoastron
periastron
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Time variability of photometry and spectra
... Diagnostic tool for observed binaries (cf.
Mathew et al, 1990s)
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part II. Migration
type III does it apply to stars?

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Up to mid-1990s, disk-satellite interaction was
understood as resonant / tidal interaction
(Lindblad resonances --gt 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 secondarys
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.
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Inner and Outer Lindblad resonances in an SPH
disk with a jupiter
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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
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Migration Type I, II, and III
Underlying fig. from Protostars and Planets IV
(2000) cf. Papaloizou et al in Protostars and
Planets V (2007)

?
type III
Time-scale (years)
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Variable-resolution PPM (Piecewise Parabolic
Method) Artymowicz 1999 Jupiter-mass
planet, fixed orbit a1, e0. 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
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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.
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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.)
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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.
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Outward migration type III of a
Jupiter Inviscid disk with an inner clearing
peak density of 3 x MMSN Variable-resolution, ad
aptive 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.
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AMR PPM (FLASH). Jupiter simulation by Peplinski
and Artymowicz (in prep.). Red color marks the
fluid initially surrounding the planets orbit.
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Variable-resolution PPM (Piecewise Parabolic
Method) Artymowicz 1999 Jupiter-mass
planet, fixed orbit a1, e0. White oval
Roche lobe, radius rL 0.07 Corotational region
out to xCR 0.17 from the planet
disk
gap (CR region)
disk
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Guiding center trajectories in the Hill problem
Unit of length Hill sphere Unit of
da/dt Hill sphere radius per dynamical time
AnimationEduardo Delgado-Donate
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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/r0.05 gas nebula Horizontal tick mark 0.1
a Corotational region out to xCR 0.08 a
away from the planet
azimuth
0.8 1 1.2 1.4 radius
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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 CR
torques smaller than the matrial in front of the
planet. The net CR torque powers fast migration.
1
2
3
radius
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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
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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
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As theorized - no significant dependence on mass
4 jupiter masses
Radius (a)
1 jupiter mass
2
Disk gap Smooth initial disk
1
0 50 100 P
time
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As theorized - no significant dependence on mass
4 jupiter masses
Radius (a)
1 jupiter mass
2
Disk gap Smooth initial disk
1
0 50 100 P
time
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ALL TORQUES RESTORED (LRs, viscous)
Outward migr.
Inward migr.
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Mass deficit
Global migration reverses at the outer boundary
Migration rate
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• SURVIVAL OF PMS BINARIES
• extremely old dynamical age
• period days gt up to 1e9 orbits

How to explain their existence ? Standard (LR)
theory predicts merger.
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Summary of type-III migration

• New type, sometimes extremely rapid (timescale
  lt 1000 years). CRs gtgt 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.

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Migration type 0 type I type II
IIb type III N-body
Interaction Gas drag Radiation
press. Resonant excitation of waves (LR) Tidal
excitation of waves (LR) Corotational flows
(CR) Gravity
Timescale of migration from 1e2 yr to disk
lifetime (up to 1e7 yr) gt 1e4 yr gt 1e5 yr gt
1e2 - 1e3 yr gt 1e5 yr (?)
Not for stars
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IIIIV. Modeling of gas
flows and preliminary
results

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AMRA
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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
bin11
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MNRAS (2006)
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Code comparison project EU RTN, Stockholm
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jupiter
vortex
L4
Surface density
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Mass ratio 0.050 (e.g., starBD),
eccentricity e0, then e0.2

(two simulations)
Bin0812
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Disk similar to min. mass solar nebula AU scale
________________ 1st simulation (23 mass
ratio) mu 0.4 init. e0 a increases
(CRs!) e slowly increases ________________ 2nd
simulation (14 mass ratio) mu 0.2 init.
e0.3 a decreases e stable ________________
bin10
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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
Bin0813
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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
Bin0812
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RESULTS on mass flow through the gap mass
ratio flow ____________________
________________ starstar binary -
efficient starBD - 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
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RESULTS on migration (da/dt) mass ratio
a ____________________________________
starstar binary - grows/stabilizes starBD
- decreases star planet
- either grows or decreases _______________
_____________________
This may explain the existence of spectroscopic
PMS binaries
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RESULTS on eccentricity mass ratio
e ____________________________________ star
star binary - ends at intermediate
value (0.2-0.3?) starBD -
low during migration, later excited? star
planet - same as BDs _______________
_____________________
Much more work needed. Complicated, because a,
m, and e interdependent (cant be found
separately)
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Additional material
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300x300
600x600
Small softening
300x300
600x600
Large softening
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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 !
Large softening of gravity relative to the Roche
lobe
Small softening of gravity relative to Roche lobe
a - Viscosity
stable wakes
Unstable wakes
Low-order interpolation of forces on polar grid
High-order interpolation of forces on polar grid
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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 e0 4.
Eccentricity induces a strong
time-variability of flow, in phase with
orbit, and possibly longer modulations 5.
Flow/shocks/companions should be observable