The Formation of Planets:
Gravitational Instability
PHY 688, Lecture 31
Apr 20, 2009
Outline
• Course administration
– final presentations reminder
• see me for presentation preview 1 week before talk: Apr 27–29 talks
• see me for paper recommendations 2–3 weeks before talk: May 4–9 talks
– class re-scheduling reminder
• no class Apr 24, Fri (Astro2010 Town Hall meeting in Columbia U)
– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm
• Review of previous lecture
– formation of brown dwarfs: empirical evidence, theory
• Scenarios for brown dwarf formation
• Formation of planets
– observational context
– gravitational instability
– (core accretion)
Apr 20, 2009
PHY 688, Lecture 31
2
Previously in PHY 688…
Apr 20, 2009
PHY 688, Lecture 31
3
Brown Dwarfs Form
Like H-Burning Low-Mass Stars
• statistical properties of brown dwarfs form a continuum
with those of low-mass stars
–
–
–
–
–
homogeneously mixed in star-forming regions
initial mass function (IMF) continuity
continuity in binary properties
disks, accretion, and outflows
rotation and x-rays
• A single formation mechanism is likely responsible for
~0.01–100 MSun “stars”
– upper limit set by radiation pressure
– lower limit set by gas opacity
– possible overlap with planetary mass range (<0.015 MSun)
Apr 20, 2009
PHY 688, Lecture 31
4
From Lecture 6: Star Formation
Occurs in Molecular Clouds
• Jeans mass
– minimum mass / density for
gravitational collapse
$ " 5c s6 '1 2
MJ = &
3 )
% 36G # (
sound speed
$
' 3 $ n '+1 2
cs
* (2MSun )&
+1 ) &
3
+3 )
% 0.2kms ( % 10 cm (
or
" 5c s6
#J ,
36G 3 M J2
• collapse occurs on free-fall
(dynamical) time-scale
!
t ff " #
Apr 20, 2009
PHY 688, Lecture 31
!
( R 2)
32
12
(GM )
& $ )%1 2
" 35min (
%3 +
' g cm *
5
Thermodynamics of Collapse and
Fragmentation
• collapse occurs if M > MJ or ρ > ρJ
• fragmentation occurs if ρJ is locally exceeded
• for a fragment to collapse, it must radiate away PdV
heat efficiently
– medium must be optically thin
– luminosity > heat ⇒ there exists a maximum critical density
ρcrit beyond which the medium becomes optically thick
– i.e., for collapse need ρJ < ρ < ρcrit
• minimum collapsing mass Mmin has ρJ ~ ρcrit at the
opacity limit
Mmin ~ 0.003 MSun ~ 3MJup
Apr 20, 2009
PHY 688, Lecture 31
6
Theories of Gravitational Collapse
and Fragmentation
• 3-D collapse and hierarchical fragmentation
– isothermal collapse of optically thin cloud → ρJ increases → parts of the
cloud start collapsing independently (fragmentation)
– fragmentation continues until heat from collapsing fragments can no longer
be radiated away because of high rate of collapse or high (>1) optical depth:
the opacity limit of fragmentation
• 2-D “one-shot” fragmentation of shock-compressed layers
– star formation occurs where turbulent flows collide → produce a shockcompressed layer or filament → filaments fragment directly into pre-stellar
cores with masses down to opacity limit
• fragmentation of a circumstellar disk
– gravitationally unstable (massive) disk fragments → fragments rapidly cool
and loose angular momentum, thus forming pre-stellar cores
Apr 20, 2009
PHY 688, Lecture 31
7
Matthew Bate, U Exeter
Numerical Simulations of Star Formation
Apr 20, 2009
PHY 688, Lecture 31
8
Outline
• Course administration
– final presentations reminder
• see me for presentation preview 1 week before talk: Apr 27–29 talks
• see me for paper recommendations 2–3 weeks before talk: May 4–9 talks
– class re-scheduling reminder
• no class Apr 24, Fri (Astro2010 Town Hall meeting in Columbia U)
– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm
• Review of previous lecture
– formation of brown dwarfs: empirical evidence, theory
• Scenarios for brown dwarf formation
• Formation of planets
– observational context
– gravitational instability
– (core accretion)
Apr 20, 2009
PHY 688, Lecture 31
9
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 20, 2009
PHY 688, Lecture 31
(Padoan & Nordlund 2004)
10
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
Apr 20, 2009
PHY 688, Lecture 31
11
Fragmentation of an Unrelaxed Disk
(top row)
Apr 20, 2009
PHY 688, Lecture 31
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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 20, 2009
PHY 688, Lecture 31
13
Fragmentation in Interacting Disks
Apr 20, 2009
PHY 688, Lecture 31
14
Other Viable Scenarios: I.
Premature Ejection of Protostellar Embrios
•
•
brown dwarfs are protostellar embrios that are separated from their reservoir of
accretable matter early on
can occur through:
– competitive accretion in proto-clusters
•
•
•
•
accretion histories of embrios vary depending on their position on parent cloud
embrios moving slowly through densest parts of cloud accrete most mass
embrios moving rapidly through diffuse gas accrete least mass → BDs
numerical simulations show that it can reproduce shape of IMF
– ejection of BDs from unstable multiple systems
• 15–25% of all stars are triple systems
• star-formation occurs in subclusters of up to ~20 stars
• non-hierarchical multiple systems eject a (low-mass) member within ~100 crossing times
ejection probability of k-th member of a triple system:
Pk = m"n
k
#m
"n
i
;
n$3
i=1,3
• potential constraints on BD velocity dispersion within young star-forming regions,
presence of disks around BDs, binary separations
Apr 20, 2009
PHY 688, Lecture !
31
15
Other Viable Scenarios: I.
Premature Ejection of Protostellar Embrios
Apr 20, 2009
PHY 688, Lecture 31
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Other Viable Scenarios: 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 20, 2009
PHY 688, Lecture 31
– e.g., Taurus
17
Other Viable Scenarios: II.
Photoevaporation of Pre-existing Cores
Apr 20, 2009
NGC 3603
PHY
688, Lecture
NASA
HST 31
18
Outline
• Course administration
– final presentations reminder
• see me for presentation preview 1 week before talk: Apr 27–29 talks
• see me for paper recommendations 2–3 weeks before talk: May 4–9 talks
– class re-scheduling reminder
• no class Apr 24, Fri (Astro2010 Town Hall meeting in Columbia U)
– two 1.5-hour classes on Apr 27, 29 (Mon, Wed): 10:40–12:00pm
• Review of previous lecture
– formation of brown dwarfs: empirical evidence, theory
• Scenarios for brown dwarf formation
• Formation of planets
– observational context
– gravitational instability
– (core accretion)
Apr 20, 2009
PHY 688, Lecture 31
19
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 20, 2009
Beckwith (1996)
PHY 688, Lecture 31
20
Reipurth et al. (1997)
Disk Dispersal Timescale
• signature of warm
dust in disks
disappears after
~5 Myr
Apr 20, 2009
PHY 688, Lecture 31
(Haisch et al. 2001)
21
Colder Dust + Gas Circumstellar
Disks May Survive Longer
• still, no stars older than
~10 Myr are known to
have disks with >1 MJup
of gas mass
• such short time-scale
used to pose problems
for classical (core
accretion) planet
formation theory
– required >> 100 Myr to
build outer solar-system
giant planets
– to be discussed next time
Apr 20, 2009
PHY 688, Lecture 31
22
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 20, 2009
PHY 688, Lecture 31
23
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 20, 2009
PHY 688, Lecture 31
(Mejia et al. 2005)
24
HL Tau b: Planet Formed through
Disk Instability?
• ~1 Myr-old
star with a gas
disk
• claimed ~6σ
detection
• inferred gas+
dust mass of
~14 MJup
Apr 20, 2009
PHY 688, Lecture 31
(Greaves et al. 2008) 25
Suggested Formation of HL Tau b
through Gravitational Instability
• Greaves et al. (2008) movie
Apr 20, 2009
PHY 688, Lecture 31
26
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 been such
Apr 20, 2009
PHY 688, Lecture 31
(Chauvin et al. 2004) 27