Adam Frank,

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Disk-Planet Interactions with a short Numerical
Prelude

• Adam Frank,
• University of Rochester
• Department of Physics and Astronomy

Collaborators Alice Quillen E Blackman, P.
Varniere, L. Hartmann (CfA) J. Bjorkman (Toledo)
HR 4796A image G. Schneider etal.
OSU Colloquium Feb, 2004
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Table of Contents

• Numerical Methods development at U of Rochester
  The AstroBEAR AMR Code
• Planet Searches a brief review
• Planet Disk Interactions Basic Physics
• Making Gaps
• Seeing Gaps
• Seeing Spiral Waves
• The Hole Problem CoKuTau/4

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AstroBEAR MHD Adaptive Mesh Refinement

• Adaptive Mesh Refinement high resolution only
  where needed
• Block AMR Retain grids upon refinement
• Berger Collella
• Built on BEARCLAW formalism
• (Boundry Embedded AMR Conservation Law Package)
• BEARCLAW developed by Sorin Mitran UNC
• CLAWPACK developed by Randy LeVeque (UWash)

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AstroBEAR features

• Computations in 2D, 2.5D, and 3D
• access to all features without coding or
  recompilation
• Set of different Riemann solvers
• full non-linear hydrodynamic
• linearized Roe
• linearized (arithmetic average) MHD
• Generic implicit 4-th order accurate source term
  routine
• suited for arbitrary systems of source term ODEs
• Modular structure for user-supplied applications
• Variety of provided initial conditions
• shocks and blast waves (tabulated and defined
  via Mach number)
• arbitrary density distributions user-specified
  and random
• disk wind outflows with user-specified
  properties
• jets
• accretion disks

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AstroBEAR features

• Built-in physics modules
• radiative cooling via cooling curve
• radiation driving via Thomson scattering
• central gravity

• Current AstroBEAR development
• Full ionization dynamics and photoionization
• MHD
• Radiation driving via Sobolev approximation
  (e.g. radiatively driven disk outflows)
• Current BEARCLAW development
• MPI and OpenMP based parallelization with
  full load balancing
• Fast Multipole Method for elliptic equations
• Embedded boundaries for complicated flow
  geomtries

BEARCLAW website http//www.amath.unc.e
du/Faculty/mitran/bearclaw.html AstroBEAR results
website http//pas.rochester.edu/wma
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Jets as Hypersonic Radiative Bullets YSOs
Orion KL
HH 47 Bowshock Patrick Hartigan (Rice University)
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Jets as Hypersonic Radiative Bullets PNe
Calabash Nebula Hubble Flow! V a R
CRL 618
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Hypersonic Radiative Bullets LBVs

• Strings in h Carinae
• High length to width ratio
• Hubble flow along string

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Mach 10 radiatively cooled bullet ambient density
103 cc-1, clump density 105 cc-1, tcool/thydro
2.510-2
AMR grid generation in the system
Synthetic observation (shown is the logarithm of
the total projected emissivity)
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Extremely strongly cooled systems
Mach 20 radiatively cooled bullet, ambient
density 102 cc-1, clump density 104 cc-1,
tcool/thydro 2.810-3
Mach 20 radiatively cooled bullet, ambient
density 103 cc-1, clump density 105 cc-1,
tcool/thydro 2.810-5
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h Carinae Strings Bullets - Correct Length
Ratios and Kinematics
Synthetic Image
V vs Z
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Extra-Solar Planets

• Many Worlds debate
• Millennia old question.
• 1600 - Bruno burnt at stake for answering yes.
• 100 planets found so far.

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Planets and Planet Searches
Radial velocity searches
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Planets and Planet Searches
Planetary Transits

• This technique measures the radius, identifying
  these as gas giants hot Jupiters
• Confusion with eclipsing binaries!

HD 209458b
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Extra-solar Solar Systems We are the Weirdoes.
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Diversity of Planetary Systems Demand for
Orbital Migration

• Two major classes of orbital migration models
• Planet gas disk interactions
• Planet planetesimal interactions

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Planet-Disk interactions

• Current planet search techniques biased to inner
  parts of solar systems.
• Planet migration scenarios require planet-disk
  interactions.
• By understanding planet disk interactions we can
  try to understand planet/disk formation and
  evolution and possibly account for the DIVERSITY
  of planetary systems.
• We can also search for planets in the outer parts
  of solar systems. Complimentary to other planet
  search techniques.

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Physics of Planet-Disk interactions Gaps

• Planets drive density waves into gaseous or/and
  planetesimal disks
• (Goldreich Tremaine 1978,79, Lin Papaloizou
  1979, Ward 1997)
• Because density waves carry angular momentum,
  which is dissipated, they govern the way planets
  open a gap.

T Torque Density Sm Tm
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Gaps Driven at Resonances
Takeuchi et al 1996
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Spiral Density Waves
2-armed spiral structure driven at the Inner
Lindblad Resonance by an exterior planet
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Condition to open a Gap

• Angular momentum carried by the spiral density
  waves pushes gas away from the planet.
• Viscosity resulting in accretion fills the gap
• When torque from spiral density waves exceeds
  that from viscosity, a gap is opened.

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Gaps Physics Previous WorkLin, Papaloizou,
Bryden, Nelson, Kley

• Determine Gap Opening Condition.
• q Mp/M gt 40/R
• Show modifications to surface density profiles.
• Link gaps and migration physics
• Type I (low Mp, No Gap)
• Type II (high Mp, Gap)

Nelson et al 2002
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What Was Missed.Varniere, Quillen Frank 2004

• Condition for Gap Width Wrong.
• No link between gap and planet properties.
• Physics of maintaining gap edge not explicated

Gap Width
Reynolds Number
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Constraints on planet masses from disk edges
New Results
2d Hydro simulations of a planet opening a gap in
a gaseous accretion disk.
Varniere, Quillen Frank 2004
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1. Depths of gaps are strongly dependent on planet
   mass and viscosity
2. Widths are weakly dependent on both

Gap Width
Log Depth
Planet mass
Planet mass
3. Slopes of disk edges depend strongly on planet
mass and viscosity
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Model for Sharp Disk Edges
Disk edges balance inward diffusion and outward
mass flux via spiral density waves driven by the
planet.

• Model accounts for
• The weak dependence of edge location on planet
  mass and viscosity
• The strong dependence of slope on both quantities
• The form of the dependence Mp2/?

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Detecting Gaps SEDs and Direct Images
Varniere et al 2004
Rice et al. 2003 proposed that the slope of the
inner edge of the disk, required a 1 Jupiter
mass planet to maintain it. The Models shown
represent different disks with different edge
slopes
Spectral Energy Distribution of GM Aurigae (Rice
et al. MNRAS 2003)
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Detection of Bright Disk Edges

• Use hydro models as input to Monte Carlo Rad
  Transfer Models (Bjrokman, Wood, Whitney)
• Allow disk to flare via stellar rad heating
• RESULT Gap edge heated via stellar illumination
  -gt Bright Annulus

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Detection of Gap-Modified SEDs

• Unlike Hole gaps simply reprocess stellar
  radiation
• Deficiet at one wavelength leads to excess at
  another
• Gaps can be detected but confusion possible.

Disk with Gap Disk without Gap
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Disk Edges and Planet Formation

• The location of the disk edge for Jupiter mass
  planets is a function of viscosity. For our
  simulations between 1.3 and 1.7 rp
• As accretion continues gas piles up just
  outside the edge.
• Its tempting to consider sequential planet
  formation .. aSaturn/aJupiter 1.8 set by
  viscosity and planet mass.

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Surface Density Structure
Quillen et al 2004c

• Disk Morphology tells us about
• Disk properties
• Evolution of the outer parts of planetary systems

HST/STIS, HD 100546 Grady et al. (2001)
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Both stellar flybys and external planets can
produce spiral structure, however external
perturbers truncate disks
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HD 141569Spiral structure driven by close
passage of the binary HD 141569B,C
Quillen, Varniere, Minchev, Frank 2004
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Case Studies
Submillimeter imaging

• HD 100546, probably a flyby. Flybys do not
  truncate the disk. Extremely unlikely in field.
• HD 141569A. Binary companion. Disk strongly
  truncated and perturbed on each passage.
• Beta Pic. Another flyby. Warp excited (Kalas et
  al. 2001).
• Vega, Epsilon Eridani. Outer eccentric planets
  required to explain dust distribution.

HD 100546
Optical scattered light
Beta Pictorus
HD 141569A
Credits, ESO, Wilner, Grady, Clampin, HST
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The Role of Birth Cluster Environment

• Outer regions of large disks often show evidence
  of perturbations from other stars flybys, or
  companion binaries.
• Close or fast flybys effectively scatter a
  fraction of the disk. The disk is not truncated.
• It is possible to excite the eccentricity of a
  single planet and leave most of the disk
  unperturbed.
• Natural explanations for the morphologies of
  Epsilon Eridanis, Beta Pics and Vegas disk.
• An example of a recent occurrence HD 100546.
• Flybys at 100AU or less are very unlikely in the
  field, however they can be important in forming
  stellar clusters.
• We might predict that the properties of
  young disks will depend on environment.

Cluster MonR2 Guttermuth, Peterson, Pipher,
Forrest, Megeath. SIRTF young cluster project
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In Summary

• We will also learn about the properties of gas
  and planetesimals of these systems
• Disk edges are sensitive to the planets that
  maintain them. Disk edges are illuminated.
  Their shape determines the morphology of
  scattered light images and should affects
  spectral energy distributions.
• We primarily probe young systems, so we learn
  about the evolution and formation of planetary
  systems.
• Dynamics is RICH
• Outer parts of solar systems have revealed
  surprises just as inner ones did! Eccentric
  planets, perturbations by stars.

• The structure of dust, gas and planetesimals,
  more easily detectable than planets, let us
  constrain planetary properties in the outer parts
  of extra-solar planetary systems.
• Resonances allow small perturbations by low mass
  planets to become important! Planets can be
  treated like dark matter.
• Dust distributions are sensitive to planet orbit
  properties. Future observations will
  discriminate between and test models.

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Prospects for the Future

• SMA now operating 0.1 resolution in
  submillimeter. This is 10AU for an object at
  100pc.
• ALMA coming on line in 2010. Ground broken
  this year. 0.01 in submillimeter. This is 1AU
  for an object at 100pc.
• JWST 0.1 resolution in mid-infrared.
• Spitzer Space Telescope detection sensitivity
  in IR improves by a factor 100. Firehose of
  data now happening
• Other miscellany AO, interferometers, new
  coronagraphs and other space projects such as
  TPF, Kepler.

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Condition to open a Gap

• Angular momentum carried by the spiral density
  waves pushes gas away from the planet.
• Viscosity resulting in accretion fills the gap
• When torque from spiral density waves exceeds
  that from viscosity, a gap is opened.

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Driving Spiral Density waves

• Spiral density waves are driven at Lindblad
  resonances.
• Torque driven depends on the strength of the mth
  Fourier component of the
  gravitational potential of the planet.