Planet Formation via Core Accretion
Planet Migration
PHY 688, Lecture 32
Apr 20, 2009
Outline
• Course administration
– final presentations reminder
• see me for presentation preview 1 week before talk: Apr 27–29 talks
– class re-scheduling reminder
• no class Apr 24, Fri (Astro2010 Town Hall meeting at Columbia U)
– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm
– recommended seminar today (1pm in ESS 450):
• “The Youngest Planets and Spots’ Tricks” (Lisa Prato, Lowell
Observatory)
• Review of previous lecture
– formation of planets: gravitational instability
• Formation of planets through core accretion
• Planet migration in circumstellar disks
Apr 22, 2009
PHY 688, Lecture 32
2
Previously in PHY 688…
Apr 22, 2009
PHY 688, Lecture 32
3
Turbulent Compression of
Low-Mass Prestellar Cores
•
•
•
•
supernovae-driven
turbulence
very high
compression due to
interacting shocks
brown dwarfs form
from most overdense shockcompressed regions
BD formation
efficiency depends
strongly on
turbulence (i.e.,
Mach number MS)
Apr 22, 2009
PHY 688, Lecture 32
(Padoan & Nordlund 2004)
4
Disk Fragmentation through
Gravitational Instability
•
isolated relaxed disks
– require high mass (>10% of host star mass), rapid cooling, and rapid loss of angular
momentum
– however, expected to have high opacity due to high surface density: radiative cooling likely
inefficient
– possible mitigating factors:
• sublimation of disk material decreases opacity of surface layer, leading to more efficient radiative
cooling (but mot important only for T > 200–2000 K)
• convection within disk (but considerable numerical complexities)
•
unrelaxed disks
–
–
–
–
•
around intermediate- to high-mass (>5 MSun) prestellar cores
these are massive disks that fragment before relaxing to equilibrium
accrete lumpy material that seeds fragmentation
quickly form lower-mass stars
interacting disks
– interaction with another disk or naked star
– typical disk diameters ≥300 AU, whereas mean interstellar spacing in clusters is ~3000 AU
– interactions expected to be frequent
Apr 22, 2009
PHY 688, Lecture 32
5
Other Scenarios for BD Formation: I.
Ejection of Protostellar Embryos
Apr 22, 2009
PHY 688, Lecture 32
6
Other Scenarios for BD Formation: II.
Photoevaporation of Pre-existing Cores
• a pre-existing core of
standard (~1 MSun) mass is
exposed to photo-ionizing
radiation
– e.g., within an H II region
created by a hot O star
– e.g., evaporationg gaseous
globules (EGGs) in M16
• inefficient: need massive
pre-stellar core to form a
single BD
• can not explain BDs in
star-forming regions
without hot O stars
Apr 22, 2009
PHY 688, Lecture 32
– e.g., Taurus
7
Planets Form In Disks
Orion protoplanetary disks
β Pictoris debris disk
HST/WFPC2
500 AU
25"
(Kalas & Jewitt 1996)
1" = 400 AU
O’Dell & Wien (1994)
Bok globules in IC 2944
HST/WFPC2
1´ = 0.5 pc
Apr 22, 2009
Beckwith (1996)
PHY 688, Lecture 32
8
Reipurth et al. (1997)
Disk Dispersal Timescale
• signature of warm
dust in disks disappears after ~5 Myr
• no stars older than
~10 Myr are known
to have disks with
>1 MJup of gas mass
Apr 22, 2009
PHY 688, Lecture 32
(Haisch et al. 2001)
9
Planet Formation through
Gravitational Instability
• can occur in any region that becomes sufficiently cool or develops
high enough surface density
• can produce
–
–
–
–
local and global spiral waves
self-gravitating turbulence
mass and angular momentum transport through long-range torques
fragmentation into clumps and subtructure (given extreme cooling)
• potential to form giant planets
• a.k.a., “disk instability” theory for planet formation
• cooling is on disk dynamical time scale (days–years)
– planets form very fast: ~1000 yr!
Apr 22, 2009
PHY 688, Lecture 32
10
Gravitational Instability: Criteria
• Toomre Q stability parameter
– cs: sound speed
– κ: epicyclic frequency, at which a fluid element
oscillates when perturbed from circular motion
c s"
Q=
#G$
• for a Keplerian disk, κ ~ Ω (angular rotation rate)
– Σ: surface density
!
• condition for disk instability: Q < 1
– disk is unstable against perturbations due to selfgravity
– spiral arms form
• condition for fragmentation: tcool < 3/Ω
– planets can form before mass is transferred away from
instability region via viscous torques
Apr 22, 2009
PHY 688, Lecture 32
(Mejia et al. 2005)
11
Gravitational Instability:
Problematic Issues
• cooling time scale:
– debate over efficiency of
radiative/convective cooling
• disk mass
– requires high disk masses: ~10% host star’s
– observations point to ~1% disk masses
– minimum-mass solar nebula: ~0.01MSun
• possible in outskirts of (massive) disks
– > 50–100 AU
– GQ Lup B, AB Pic B may have formed
through gravitational instability
Apr 22, 2009
PHY 688, Lecture 32
(Chauvin et al. 2004) 12
Outline
• Course administration
– final presentations reminder
• see me for presentation preview 1 week before talk: Apr 27–29 talks
– class re-scheduling reminder
• no class Apr 24, Fri (Astro2010 Town Hall meeting at Columbia U)
– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm
– recommended seminar (today, 1pm in ESS 450):
• “The Youngest Planets and Spots’ Tricks” (Lisa Prato, Lowell
Observatory)
• Review of previous lecture
– formation of planets: gravitational instability
• Formation of planets through core accretion
• Planet migration in circumstellar disks
Apr 22, 2009
PHY 688, Lecture 32
13
The Classical Planet Formation
Model: Core Accretion
•
Safronov (1969)
–
terrestrial planet formation
•
•
i.e., ≤1 MEarth at <1.5 AU
three-step scenario for rocky
planets / giant planet cores
Mp, Rp – planet mass, radius
ρs
– volume mass density of swarm of
planetesimals
Σ
– surface density of planetesimals
v
– velocity of average planetesimal
relative to planet
ve
– escape speed from planet’s surface
Ω
– orbital angular velocity of planet
Fg
– gravitational focusing term
a
– planet semi-major axis
1. ~1 µm dust grains undergo sticky
collisions to form ~1 km rocky
planetesimals
* $ v '22. larger planetesimals gravitational- dM p
= "R p2 # sv,1+ & e ) / = "R p2 01Fg
ly accrete smaller planetesimals
dt
+ %v(.
3. rocky planet / core growth stops
$ M p '1 3
once planet’s “feeding zone” is
(Hill sphere radius)
depleted of smaller planetesimals R H = a&% 3M )(
•
•
feeding zone half-width ~ 4–5RH
*
Earth formation: 30–100 Myr
Apr 22, 2009
PHY
! 688, Lecture 32
14
Problems with the Classical Model
a–3/2 (Kepler’s
• Ω∝
3rd law)
• Σ ∝ r–3/2 (for an optically
thick protoplanetary disk)
• Jupiter’s core forms in
50–500 Myr
– no gas left in disk by then to
form envelope
• Neptune requires >5 Gyr to
form
Apr 22, 2009
Mp, Rp – planet mass, radius
ρs
– volume mass density of swarm of
planetesimals
Σ
– surface density of planetesimals
v
– velocity of average planetesimal
relative to planet
ve
– escape speed from planet’s surface
Ω
– orbital angular velocity of planet
Fg
– gravitational focusing term
a
– planet semi-major axis
* $ v '2dM p
= "R p2 # sv,1+ & e ) / = "R p2 01Fg
dt
+ %v(.
$ M p '1 3
R H = a&
)
3M
%
*(
PHY
! 688, Lecture 32
(Hill sphere radius)
15
Modifications to CA Model
•
runaway growth of planetesimals
– energy equipartition
– numerical simulations show most of mass remains
in small planetesimals during stage 2.
dM p
" M4 3
dt
• their random velocities v remain comparable to their
own escape velocities (i.e., small)
dM
2*
$
'
v
p
= "R p2 # sv,1+ & e ) / = "R p2 01Fg
dt
+ %v(.
– Fg up to ~104
• Safronov (1969) assumed the opposite
•
followed by oligarchic growth
!
– supply of much smaller planetesimals exhausted
– slower growth by infrequent accretion!of
comparably-sized planetesimals
– starts with 10–6–10–5 MEarth oligarch planetesimals
•
•
growth continues until reaching isolation mass
Jupiter’s (~10 MEarth) core forms in ~1 Myr,
Neptune’s in ~10–30 Myr
Apr 22, 2009
PHY 688, Lecture 32
!
dM p
" M2 3
dt
16
Runaway + Oligarchic Growth
snow line (2.5 AU)
•
•
length of runaway
growth stage depends
on orbital time scale
during oligarchic
growth stage planet
cores grow above
isolation mass
(dashed line)
– snow line: orbital
distance beyond
which water ice
does not sublimate
•
simulation includes
effects of
fragmentation during
collisions and
accretion of
planetesimals
Apr 22, 2009
PHY 688, Lecture 32
(Chambers 2008)
17
Rocky Core Growth Front
• growth time increases with distance from star
• growth front moves outward
– partially destructive collisions between planetesimals generate
copious amounts of dust
• inner regions reach isolation mass
• size of inner region grows with time
– dust from planetesimal collisions is further ground-down and
smallest grains are blown out through radiation pressure
• i.e.: annulus of growth moving outward
Apr 22, 2009
PHY 688, Lecture 32
18
Rocky Core Growth Front: Simulation
• simulation time
scale: 1 Gyr
Apr 22, 2009
PHY 688, Lecture 32
(Kenyon & Bromley 2004) 19
Such Debris Rings Are Now Observed!
Schneider et al. (1999)
HR 4796A
(A0V; ~10 Myr)
AU Microscopii
et al.688,
(2004);
et al. (2004); Metchev et al. (2005) 20
Apr 22, 2009 Schneider et al. (1999); KristPHY
LectureArdila
32
Forming Gas Giants after the
Accretion of a Rocky Core
• proto-planetary disk is rich in gas
– initially, gas : dust ~ 100 : 1
– gas is gravitationally accreted along with planetesimals
• runaway gas accretion occurs when
Mgas > Mcore ~ 10 MEarth
• growth continues until a gap is opened in the disk
– planet feeding zone is now empty of both
planetesimals and gas
Apr 22, 2009
PHY 688, Lecture 32
21
Forming Gas Giants after the
Accretion of a Rocky Core
Apr 22, 2009
PHY 688, Lecture 32
(Pollack et al. 1996) 22
Opening of Gaps in Protoplanetary Disks
• occurs when planet
Hill radius RH ~
disk scale height H
• the existence of
such disk gaps is
also supported by
observational
evidence
Apr 22, 2009
PHY 688, Lecture 32
(Armitage 2005) 23
Core Accretion vs.
Gravitational Instability
•
CA can explain 10–15 MEarth cores of giant planets
– GI favors smaller (≤ 5 MEarth) cores, formed through sedimentation of solids once
planet is formed
– experimental data on Jupiter’s core are not inconsistent with a core mass of 0 MEarth
•
CA can explain observed trend for higher-metallicity stars to more frequently
host planets
– high metallicity facilitates initial grain formation
•
CA is the universally accepted scenario for terrestrial planet formation
– dual formation mechanisms possible, with Jupiter formed via GI
•
•
Neptune’s formation still potentially problematic for CA
Planet migration: a major problem for CA
Apr 22, 2009
PHY 688, Lecture 32
24
Outline
• Course administration
– final presentations reminder
• see me for presentation preview 1 week before talk: Apr 27–29 talks
– class re-scheduling reminder
• no class Apr 24, Fri (Astro2010 Town Hall meeting at Columbia U)
– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm
– recommended seminar today (1pm in ESS 450):
• “The Youngest Planets and Spots’ Tricks” (Lisa Prato, Lowell
Observatory)
• Review of previous lecture
– formation of planets: gravitational instability
• Formation of planets through core accretion
• Planet migration in circumstellar disks
Apr 22, 2009
PHY 688, Lecture 32
25
Evidence for Planet Migration
• semi-major axis
distribution of radial
velocity planets
Apr 22, 2009
PHY 688, Lecture 32
(Marcy et al. 2008)
26
Type I vs. Type II Migration
• Type I
– planet core mass is insufficient to open a gap
– inward drift speed: vI ∝ –MpΣr2
• Type II
– planet opens gap when RH/H ~ 1
– planet radial motion is ~locked to that of the disk
– inward drift speed: vII ∝ –(Md/Mp)(3υ/2r)
• υ = αcs2/Ω : turbulent viscosity, α = 10–3–10–2
Apr 22, 2009
PHY 688, Lecture 32
27
How Does Planet Migration End?
• planet swallowed by host star
• or planet stops at inner edge of dust / gas disk
Apr 22, 2009
PHY 688, Lecture 32
(Romanova & Lovelace 2006) 28
Formation of Jupiter: Effect of Migration
• solar system
giant planets
can form
even faster
• no conflict
with short
(~10 Myr)
gas disk
time scale
Apr 22, 2009
PHY 688, Lecture 32
29
Rocky Cores: Effect of Migration
• type I
migration
quickly
removes
innermost
rocky cores!
• survival of
terrestrial
planets is now
a problem
– swallowed
by the star
Apr 22, 2009
PHY 688, Lecture 32
(Chambers 2008)
30