Download Disk-planet interaction

PSCD01 - 11 Oct. 2005
UTSC
Understanding of extrasolar and solar planetary
systems through theory of their formation
Introdroducing extrasolar systems
Protoplanetary disks
Disk-planet interaction: resonances and torques,
numerical calculations, mass buildup, migration of
planets
Dusty disks in young planetary systems
Origin of structure in dusty disks
Already the Ancient...
…had a good theory of
star and planet formation
Some of the earliest recorded physics
was very far-sighted &
essentially correct!
Predicted: evolution (formation/decay), role of
disks, and diversity of “worlds”=planets.
Atomists (Ionian materialists) devoted 50% of their
philosophy to cosmos, not microcosmos
HOW ANCIENT
GREEK ATOMISTS
deduced ("invented")
other worlds
480C.)
Leucippus
C.)
Democritus
bibliography: 60 vol, none survived
THEN:
Worlds ()
=
NOW:
Planetary systems
(terra firma + atmosphere +
moons + sun + stars)
matter:
- made of the same types
atoms and void everywhere
- evolving
- large variety
- include Earth-like worlds
cosmic (solar)abundance
yes
yes
? NASA's goal
From: Diogenes Laertius,  (3rd cn. A.D.), IX.31
“The worlds come into being as follows: many bodies of all sorts and shapes move
from the infinite into a great void; they come together there and produce a single
whirl, in which, colliding with one another and revolving in all manner of ways, they
begin to separate like to like.”
Leucippus
(Solar nebula of Kant & Laplace A.D. 1755-1776? Accretion disk?)
“There are innumerable worlds which differ in size.
In some worlds there is no Sun and Moon, in others they are larger than in our world,
and in others more numerous. (...) in some parts they are arising, in others failing.
They are destroyed by collision with one another. There are some worlds devoid of
living creatures or plants or any moisture.”
Democritus
(Planets predicted: around pulsars, binary stars, close to stars?)
There are infinite worlds both like and unlike this world of ours. For the atoms
being infinite in number (...) there nowhere exists an obstacle to the infinite number
od worlds.
Epicurus (341-270 B.C.)
(...) it follows that
there cannot be more worlds than one.
Aristotle [On the Heavens]
Aristotle's work rediscovered and enthusiastically
accepted during the 12th century Renaissance at the
Plato and Aristotle new universities (Paris, Oxford)
e.g., Roger Bacon (1214-1292) cites the impossibility of
vacuum between the hypothetical multiple worlds.
Thomas Aquinas (1225-1274) also accepts Aristotle's
arguments about impossibility of other worlds, despite
a growing controversy within Church.
Obviously, a very ancient and
worthy quest…
…as well as controversial
OTHER WORLDS: the pendulum starts swinging
Franciscans: God can create other worlds.
Idea of Earth's uniqueness censored under the threat of
excommunication :
In 1277 bishop of Paris, Etienne Tempier, officially condemns 219 passages from
Aristotle taught at universities, among others that "the First Cause cannot make
many worlds".
Many supporters of other worlds, e.g., William of Ockham (ca.1280-1347).
Mikolaj Kopernik's heliocentric system (1543) seen as supporting other worlds.
Giordano Bruno: infinite number of inhabited terrestrial planets. Burned at
stake 1600 by Holy Roman Inquisition (though not predominantly for that!).
William of Vorilong (ca. 1450) thought that it is "not fitting" for Christ to go to
another world to die again. And there is no mention of other worlds in Scriptures.
Johannes Kepler (1571-1630) did not believe that stars are distant suns or that
they may have planets.
And so on, until the end of 20th century came...
Kant-Laplace nebula ~ primitive solar nebula ~ accretion disk
~ protoplanetary disk ~ T Tauri disk
R. Descartes (1595-1650) - vortices of matter
-> planets
I. Kant (1755) - nebular hypothesis
(recently revived by: Cameron et al, Boss)
P.S. de Laplace (1796) - version with rings
Stars and Brown Dwarfs
…form in stellar
nurseries from/with
protostellar disks
 Oph
Giant Molecular Cloud, 160 pc away
contains numerous dark clouds

GMCs contain: dark clouds, cores, Bok globules
GMC mass / solar mass ~ 105
 Oph
V380 Ori + NGC1999

Dark clouds
L57
Barnard 68
UKAFF
(UK Astroph. Fluid Facility)
Our tools…
parallel supercomputers:
dozens to thousands of fast PCs
connected by a very fast network
UTSC: SunGrid cluster, ~200 cpus
ANTARES/FIREANT
Stockholm
Observatory
20 cpu (Athlons)
mini-supercomputer
(upgraded in 2004
with 18 Opteron 248
CPUs inside SunFire
V20z workstations)
Matthew Bate
(2003),
Bate and Benz (2003)
SPH, 1.5M particles
starting from turbulent
gas cloud
Simulations produce large numbers of Brown
Dwarfs
Numerous
Brown Dwarfs in Ophiucus
Trapezium
cluster in Orion
with many
Brown Dwarfs
HST/NICMOS
F110W+F160W
There are rater few such star-bound brown dwarfs
(so-called brown dwarf desert) but… the desert isn’t barren:
5 M_jup planet around a 25 M_jup Brown Dwarf in 2MASS1207
ESO/VLT AO
HST/NICMOS, 1.6um
Primordial disks
have many names:
protostellar disks
T Tau disks
proplyds
protoplanetary disks
solar nebulae
Protoplanetary disks =
= protostellar disks = solar nebulae
Young protoplanetary disks (proplyds)
are rather bland in appearance
No gaps or fine detail seen in the density, except
for rather sharp edges <== photoevaporation
Photoevaporation is like boiling off gas by striking
the hydrogen atoms with UV photons, kicking
electrons and ions, and raising local kT to conditions
resembling HII regions.
Photoevaporation only works in regions where
gravitational binding energy is less than kT:
outer parts of cloud complexes, far-away disk regions
gravitational binding = grav.potential well’s depth =
-GM(r)/r
(for spherical systems)
Percentage of optically thick “outer disks” (at ~3 AU)
From: M. Mayers,
S. Beckwith et al.
Conclusion:
Major fraction of dust
cleared out to several
AU in 3-10 Myr
This is the timescale
for giant planet
formation
0.1
1
10
100
1000 Myr
Age
The evolutionary sequence
The birth of planetary systems
Formation of disks and planets up to T Tau phase
Formation of disks and planets post- T Tau phase
Dusty disks
around main-sequence
stars
1. Transitional
2. Debris disks
3. Zodiacal light
Infrared excess stars (Vega phenomenon)
Source: P. Kalas
At the age of 1-10 Myr the primordial solar nebulae =
protoplanetary disks = T Tau accretion disks
undergo a metamorphosis
A silhouette disk in Orion
star-forming nebula
Beta Pictoris
They lose almost all H and He and after a brief period as
transitional disks, become low-gas high-dustiness
Beta Pictoris systems (Vega systems).
Prototype of Vega/beta-Pic systems
Beta Pictoris
11 micron image analysis
converting observed flux
to dust area
(Lagage & Pantin 1994)
B Pic b(?) sky?
Chemical basis for universality of exoplanets:
cosmic composition (Z=0.02 = abundance of heavy elem.)
cooling sequence: olivines, pyroxenes dominant, then H2O
Hubble Space Telescope/ NICMOS infrared camera
HD 141569A is a Herbig emission star
>2 x solar mass, >10 x solar luminosity,
Emission lines of H are double, because they
come from a rotating inner gas disk.
CO gas has also been found at r = 90 AU.
Observations by Hubble Space Telescope
(NICMOS near-IR camera).
Age ~ 5 Myr
transitional disk
HD 14169A disk (HST observations), gap confirmed
by the new observations
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Gas-dust coupling?
Planetary
perturbations?
Dust avalanches?
HD 141569A: Spiral structure
detected by (Clampin et al. 2003)
Advanced Camera for Surveys
onboard Hubble Space Telescope
Radial-velocity planets
around normal stars
-450: Extrasolar systems predicted (Leukippos, Demokritos). Formation in disks
-325 Disproved by Aristoteles
1983: First dusty disks in exoplanetary systems discovered by IRAS
1992: First exoplanets found around a millisecond pulsar (Wolszczan & Dale)
1995: Radial Velocity Planets were found around normal, nearby stars,
via the Doppler spectroscopy of the host starlight,
starting with Mayor & Queloz, continuing wth Marcy & Butler, et al.
Orbital radii + masses of the extrasolar planets (picture from 2003)
Radial migration
Hot jupiters
These planets were found
via Doppler spectroscopy
of the host’s starlight.
Precision of measurement:
~3 m/s
Like us?
NOT REALLY
Masset and Papaloizou (2000); Peale, Lee (2002)
Some pairs of exoplanets may be caught in a 2:1 resonance
Marcy and Butler (2003)
2005
~2003
From Terquem & Papaloizou (2005)
Mass histogram
semi-major
axis distr.
M sin I vs. a
Eccentricity of exoplanets vs. a and m sini
Metallicity of the star
The case of Upsilon And examined:
Stable or unstable? Resonant? How, why?...
Upsilon Andromedae two outer giant planets
have STRONG interactions
Inner
solar
system
(same
scale)
Definition of logitude of pericenter
(periapsis) or misalignment angle
.
2

1
Classical celestial mechanics
In the secular pertubation theory, semi-major axes
(energies) are constant (as a result of averaging over time).
Eccentricities and orbit misalignment vary, such as
to conserve the angular momentum and energy of the
system.
We will show sets of thin theoretical curves for (e2, dw).
[There are corresponding (e3, dw) curves, as well.]
Thick lines are numerically computed full N-body
trajectories.
0.8 Gyr integration of 2 planetary orbits
with 7th-8th order Runge-Kutta method
Initial conditions
not those
observed!
Orbit alignment angle
Upsilon And: The case of very good alignment of periapses:
orbital elements practically unchanged for 2.18 Gyr
N-body (planet-planet) or disk-planet interaction?
Conclusions from modeling Ups And
1. Secular perturbation theory and numerical
calculations spanning 2 Gyr do agree.
2. The apsidal “resonance” (co-evolution) is expected
and observed to be strong, and stabilizes the system
of two nearby, massive planets
3. There are no mean motion resonances
4. The present state lasted since formation period
5. Eccentricities in inverse relation to masses,
contrary to normal N-body trend tendency for equipartition.
Alternative: a lost most massive planet - very unlikely
6. Origin still studied, Lin et al. Developed first models
involving time-dependent axisymmetric disk potential
Diversity of exoplanetary systems likely a result of:
disk-planet interaction
a
m?
(low-medium) e
planet-planet interaction
a
X
m?
(high) e
star-planet interaction
disk breakup
(fragmentation into GGP)
a
m
X
X
e?
a
m
X
X
e?
X
metallicity
Disk-planet interaction:
resonances and waves
in disks, orbital
evolution
.
.
SPH (Smoothed Particle Hydrodynamics)
Jupiter in a solar nebula (z/r=0.02) launches waves at LRs.
The two views are (left) Cartesian, and (right) polar coordinates.
Inner and Outer Lindblad resonances in an SPH disk with a jupiter
Illustration of nominal positions of Lindblad resonances (obtained
by WKB approximation. The nominal positions coincide with the mean motion
resonances of the type m:(m+-1) in celestial mechanics, which doesn’t include
pressure.) Nominal radii converge toward the planet’s semi-major axis at high
azimuthal numbers m, causing problems with torque calculation (infinities!).
On the other hand, the pressure-shifted positions are the effective LR
positions, shown by the green arrows. They yield finite total LR torque.
Wave excitation at Lindblad resonances (roughly speaking,
places in disk in mean motion resonance, or commensurability
of periods, with the perturbing planet) is the basis of the
calculation of torques (and energy transfer) between the
perturber and the disk. Finding precise locations of LRs is
thus a prerequisite for computing the orbital evolution of a
satellite or planet interacting with a disk.
LR locations can be found by setting radial wave number
k_r = 0 in dispersion relation of small-amplitude, m-armed,
waves in a disk.
[Wave vector has radial component k_r and azimuthal
component k_theta = m/r]
This location corresponds to a boundary between the wavy and
the evanescent regions of a disk. Radial wavelength, 2*pi/k_r,
becomes formally infinite at LR.
LR locations are found from setting k_r = 0 in dispersion
relation, which in a Keplerian disk reads (using W for
Omega, the angular speed of disk material):
W^2 - m^2 (W - W_p)^2 + c^2 (k_r^2 + m^2/r^2) = 0
where W_p is the pattern speed of waves, e.g. equal to the
orbital frequency of the planet if it’s orbit is circular.
In the pre-1993 theories, it was assumed that waves satisfy
WKB relationship k_r>>m/r, and so the m^2/r^2 term was
neglected, which resulted in the following condition for W
(or W_LR):
W_LR = W_p m/(m+-1)
(the + sign for OLR, - for ILR).
But can we neglect the azimuthal component of the wave vector?
WIND
k

Refraction of a density wave in a
differentially rotating disk
The wave is launched (at a Lindblad
resonance located along the vertical axis)
in azimuthal direction, but gradually
refracts toward a radial, tightening,
wave departing to +infinity radially.
k = wave vector
|k| = 2*pi/wavelength
k
LR
r

WKB
not good
here, because
k_r < m/r
k~k_r
Refraction of a density wave why the pre-1993 WKB treatment
was inaccurate.
The wave is launched (at a Lindblad
resonance located along the vertical axis)
in azimuthal direction, but refracts more
and more toward a radial, tightening,
wave departing to r=+  (radially).
k = (k_r, m/r) components of the vector
k ~ m/r
LR
WKB is OK here,
because k_r >> m/r
r
The reason for torque cutoff and the dominance
of eccentricity damping over excitation
(r-a)/h
Satellite potential (mharmonic)
Wave (with m arms)
OLR: de/dt > 0
ILR: de/dt < 0
H=h=z (disk
thickness=vertical
scale height)
Eccentricity in type-I
situation is always
strongly damped.
--> m(z/r)
Conclusion about eccentricity:
As long as there is some gas in the corotational region
(say, +- 20% of orbital radius of a jupiter),
eccentricity is strongly damped.
Only if and when the gap becomes so wide that the
near-lying LRs are eliminated, eccentricity is excited.
(==> planets larger than 10 m_jup were predicted to
be on eccentric orbits (Artymowicz 1992).
In practice, this may account for intermediate-e exoplanets.
For extremely high e’s we need N-body explanation:
perturbations by stars, or other planets.
Disk-planet interaction:
numerics
Mass flows through the gap
opened by a jupiter-class exoplanet
----> Superplanets can form
An example of modern Godunov (Riemann solver) code:
PPM VH1-PA. Mass flows through a wide and deep gap!
Surface density
Log(surface density)
Binary star on circular orbit
accreting from a circumbinary disk through a gap.
AMR PPM (Flash) simulation of a Jupiter in a standard solar nebula. 5 levels/subgrids.
What does the permeability of gaps teach us about
our own Jupiter:
- Jupiter was potentially able to grow to 5-10 m_j, if left
accreting from a standard solar nebula for ~1 Myr
- the most likely reason why it didn’t:
the nebula was already disappearing and not enough mass
was available.
Numerical Troubles:
resolution
grav. softening
and zones where torques are ignored
self-gravity of gas (neglected)
gas heating (and other effects)
the usual troubles: boundary conditions, instabilities, unexplained
crashes,
the unusual troubles: extreme vortex production and/or variability of
flow in some codes
===> Comparison or Test Problem
mini-workshop May 2004 in Stockholm (EU Network on Planet Origins)
paper to be submitted Very Soon
(www.astro.su.se/groups/comparison/)
AMRA
FARGO
Comparison of Jupiter in an inviscid disk after t=100P
FLASH-AG
FLASH-AP
FLASH-AP
RH2D
NIRVANA-GD
Jupiter in an inviscid disk t=100P
PARA-SPH
RODEO
Surface density comparison
Disk-planet interaction:
new strange migration
mode
Migration Type I :
embedded in fluid
Migration Type II :
more in the open (gap)
Ward(1997)
(1986,1993)
Viscous
evolution
radius
Migration Type I :
embedded in fluid
Migration Type II :
in the open (gap)
Migration Type III
partially open (gap)
Type I-III Migration of protoplanets/exoplanets
Timescale

Ward (1997)

I

II
M/M_Earth

Disks repel planets:
Type I (no gap)
Type II (in a gap)
Currently THE
problem is:
how not to lose
planetary embryos
(cores) ?
A gap-opening body in a disk:
Saturn rings, Keeler gap region (width =35 km)
This new 7-km satellite of Saturn was announced 11 May 2005.
To Saturn
Type I-III Migration of protoplanets/exoplanets
Timescale



If disks repel
planets:
Type I (no gap)
Type II (in a gap)
I
II





M/M_Earth
If disks attract
planets: Type III
Q’s:
Which way do they
migrate?
How fast?
Can the protoplanets
survive?
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
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.
Are there ANY SURVIVORS
of type III migration?!
YES!
Edges or gradients in disks:
Magnetic
cavities around
the star
Dead zones
Unsolved problem of the Last Mohican scenario of
planet survival in the solar system:
Can the terrestial zone survive a passage of a giant
planet?
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
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N-body simulations, N~1000 (Edgar & Artymowicz 2004)
A quiet disk of sub-Earth mass bodies reacts to the rapid
passage of a much larger protoplanet (migration speed =
input parameter).
Results show increase of velocity dispersion/inclinations
and limited reshuffling of material in the terrestrial zone.
Migration type III too fast to trap bodies in mean-motion
resonances and push them toward the star
Evidence of the passage can be obliterated by gas drag on
the time scale << Myr ---> passage of a pre-jupiter
planet(s) not exluded dynamically.
Summary of type-III migration
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

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
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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
Very sensitive to disk density 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.
1. Early dispersal of the primordial nebula ==> no material, no mobility
2. Late formation (including Last Mohican scenario)