Pawel Artymowicz, University of Toronto at Scarborough

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 theirphilosophy to cosmos, not microcosmos

C.)

Democritusbibliography: 60 vol, none survived

480C.)

Leucippus

THEN: = NOW:Worlds () Planetary systems (terra firma + atmosphere + moons + sun + stars)

matter:- made of the same types cosmic (solar)abundanceatoms and void everywhere- evolving yes- large variety yes - include Earth-like worlds ? NASA's goal

HOW ANCIENT GREEK ATOMISTSdeduced ("invented") other worlds

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]

Plato and Aristotle

Aristotle's work rediscovered and enthusiastically accepted during the 12th century Renaissance at the 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 awaycontains numerous dark clouds

Oph V380 Ori + NGC1999

GMCs contain: dark clouds, cores, Bok globulesGMC mass / solar mass ~ 105

Dark clouds

L57 Barnard 68

UKAFF (UK Astroph. Fluid Facility)

Our tools…parallel supercomputers:dozens to thousands of fast PCsconnected 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 248CPUs inside SunFireV20z workstations)

Matthew Bate(2003), Bate and Benz (2003)SPH, 1.5M particles

starting from turbulentgas cloud

Simulations produce large numbers of Brown Dwarfs

Brown Dwarfs in OphiucusNumerous

Trapezium cluster in Orion

with many Brown Dwarfs

HST/NICMOS

F110W+F160W

5 M_jup planet around a 25 M_jup Brown Dwarf in 2MASS1207

There are rater few such star-bound brown dwarfs (so-called brown dwarf desert) but… the desert isn’t barren:

ESO/VLT AO HST/NICMOS, 1.6um

Primordial diskshave 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, exceptfor 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 conditionsresembling 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 dustcleared out to several AU in 3-10 Myr

This is the timescalefor giant planet formation

0.1 1 100 1000 MyrAge

10

The evolutionary sequenceThe birth of planetary systems

Formation of disks and planets up to T Tau phase

Formation of disks and planets post- T Tau phase

Dusty disksaround 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 disksundergo a metamorphosis

They lose almost all H and He and after a brief period astransitional disks, become low-gas high-dustiness Beta Pictoris systems (Vega systems).

Beta Pictoris

A silhouette disk in Orionstar-forming nebula

Prototype of Vega/beta-Pic systems

Beta Pictoris

11 micron image analysis converting observed fluxto 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 confirmedby the new observations

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 planetsaround 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)

These planets were foundvia Doppler spectroscopyof the host’s starlight.

Precision of measurement:~3 m/s

Hot jupitersRadial migration

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)

~2003

2005

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

Innersolarsystem(samescale)

.

1

2Definition of logitude of pericenter (periapsis) or misalignment angle

In the secular pertubation theory, semi-major axes (energies) are constant (as a result of averaging over time).

Eccentricities and orbit misalignment vary, such asto 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.

Classical celestial mechanics

ecce

ntr

icit

y

Orbit alignment angle

0.8 Gyr integration of 2 planetary orbitswith 7th-8th order Runge-Kutta method

Initial conditionsnot those observed!

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 expectedand observed to be strong, and stabilizes the systemof two nearby, massive planets3. There are no mean motion resonances4. The present state lasted since formation period5. Eccentricities in inverse relation to masses, contrary to normal N-body trend tendency for equipartition.Alternative: a lost most massive planet - very unlikely6. Origin still studied, Lin et al. Developed first modelsinvolving 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 m? (high) e

star-planet interaction a m e?

disk breakup (fragmentation into GGP) a m e? metallicity

X

XXX

X X

Disk-planet interaction:

resonances and wavesin 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 commensurabilityof 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 isthus 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 numberk_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 andthe 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 satisfyWKB 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 Lindbladresonance located along the vertical axis)in azimuthal direction, but graduallyrefracts toward a radial, tightening,wave departing to +infinity radially.

r

k

LR

k = wave vector|k| = 2*pi/wavelength

Refraction of a density wave - why the pre-1993 WKB treatment was inaccurate.The wave is launched (at a Lindbladresonance located along the vertical axis)in azimuthal direction, but refracts moreand more toward a radial, tightening,wave departing to r=+ (radially).

r

k ~ m/r

LR

WKB is OK here, because k_r >> m/r

WKBnot good here, because k_r < m/r

k = (k_r, m/r) components of the vector

k~k_r

H=h=z (diskthickness=verticalscale height)

The reason for torque cutoff and the dominanceof eccentricity damping over excitation

OLR: de/dt > 0ILR: de/dt < 0

Wave (with m arms)

Satellite potential (m-harmonic)

(r-a)/h

--> m(z/r)Ecc

entr

icit

y pu

mpi

ng

Eccentricity in type-Isituation is always strongly damped.

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 thenear-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 gapopened by a jupiter-class exoplanet

----> Superplanets can form

Binary star on circular orbitaccreting from a circumbinary disk through a gap.

Surface density Log(surface density)

An example of modern Godunov (Riemann solver) code:PPM VH1-PA. Mass flows through a wide and deep gap!

AMR PPM (Flash) simulation of a Jupiter in a standard solar nebula. 5 levels/subgrids.(P

epli

nski

an d

Ar t

y mow

icz

2 004

)

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

FLASH-AG FLASH-AP

Comparison of Jupiter in an inviscid disk after t=100P

FLASH-AP

RH2DNIRVANA-GD

PARA-SPH

Jupiter in an inviscid disk t=100P

RODEO

Surface density comparison

Disk-planet interaction:

new strange migrationmode

Migration Type I :embedded in fluid

Migration Type II :more in the open (gap)

Ward(1997) (1986,1993)

time

radius

Viscousevolution

Migration Type I :embedded in fluid

Migration Type III partially open (gap)

Migration Type II :in the open (gap)

Type I-III Migration of protoplanets/exoplanets Disks repel planets:

Type I (no gap) Type II (in a gap)

Currently THE problem is: how not to lose planetary embryos (cores) ?

II

I

M/M_Earth

TimescaleWard (1997)

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 If disks repel

planets: Type I (no gap) Type II (in a gap)

If disks attract planets: Type III

Q’s: Which way do they

migrate? How fast? Can the protoplanets

survive?

II

I

…....III……..

M/M_Earth

Timescale

Variable-resolutionPPM (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 outto x_CR = 0.17 from the planet

disk

disk gap (CR region)

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 IIIof 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 showsradius in the range (0.5-5) a

Full range of azimuthson the vertical axis.

Time in units of initialorbital period.

Are there ANY SURVIVORS of type III migration?!

YES!

Edges or gradients in disks:

Magneticcavities aroundthe 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?

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 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 mobility2. Late formation (including Last Mohican scenario)