Download L11 Terrestrial planet formation and Impacts

Lecture 11
Forming
terrestrial
planets
&
impacts
Lecture Universität Heidelberg WS 11/12
Dr. C. Mordasini
Based partially on script of Prof. W. Benz
Mentor Prof. T. Henning
Lecture 11 overview
1. Terrestrial planet formation
2. Giant impacts
2.1 Collision physics
2.2 Formation of the Moon
2.3 More imprints of giant impacts
1. Terrestrial planet
formation
Final stages
•While the gas disk is present, without migration, growth is stalled in the inner system at the
isolation mass. The oligarchs have masses of 0.01 - 0.1 MEarth.
•Once the damping influence of the gas disk (or a sufficiently massive planetesimal disk) is
gone, eccentricities grow, and growth from Miso to final masses by giant impacts starts.
This means that terrestrial planets are thought to form after the giant planets.
•The evolution continues until a long time stable configuration is reached (sufficient mutual
distances in terms of mutual Hill spheres). This leads to Titus-Bode like configurations,
which are also observed in extrasolar planetary systems (Lovis et al 2010).
Semi-major axes as a function of planet
number for the inner solar system
(black), HD 40307 (red), GJ 581 (blue),
HD 69830 (green) and HD 10180
(magenta)
The 15 planetary systems with at least three
known planets as of May 2010. The
numbers give the minimal distance between
adjacent planets expressed in mutual Hill
radii. Planet sizes are proportional to log (m
sin i). Some systems are in mean motion
resonances.
Constraints in the Solar System
Constraints (for the solar system):
• the orbits, in particular the small eccentricities (Earth: 0.03)
• the masses, in particular Mars’ small mass (one would in principle expect that mass
increases with semimajor distance). Likely, this is an imprint of the important role of Jupiter.
• the formation time of Earth from Hf/W isotope dating (50-100 Myr).
• the bulk structure of the asteroid belt (no big bodies).
• Earth’ relatively large water content (mass fraction 10-3) assuming that it was delivered in
the form of water-rich primitive asteroidal material.
• the influence of Jupiter & Saturn.
Method: N body simulation.
As the number of bodies is becoming smaller, statistical methods are no longer needed and
the motion of the individual planetary embryos can be explicitly integrated. Note that even
though the number is relatively small, this is still a very computer intensive task since the
integration has to be performed over many millions of years which represents a large number
of orbits.
Simulation of the inner Solar System
Time evolution of 1885 embryos with Jupiter at 5.2 AU present from t=0. MMSN surface density.
- lasts of order 200 Myr
- considerable mixing
- delivery of water
- giant collisions
Raymond, Quinn & Lunine 2006
The color of each particle represents its water content, and the dark inner circle represents the relative
size of its iron core.
Stages of terrestrial planet formation
Simulation setting
•97 0.01-0.1 MEarth oligarchs
and small planetesimals
•Jupiter and Saturn in 3:2 MMR
•dotsize prop. to M1/3
Excitation at MMRs
Diffusion
Substantial radial mixing
S.N. Raymond et al. / Icarus 203 (2009) 644–662
Outcome
•4 terrestrial planets with
masses between 0.6-1.8 MEarth
•M, Tform, eccentricity and water
content ok.
•But Mars too massive, and 3
additional bodies. A too big
Mars is a generic problem.
Giant planets? Fig. 3. Snapshots in time from a simulation with Jupiter and Saturn in 3:2 mean motion resonance (JSRES). The size of each body is proportional to its
Low
eccentricity,
water
Butredmars
too(5%large
Addit.
bodies
on the x axis). The color of each
body corresponds
to its water
contentrich
by mass, from
(dry) to blue
water). Jupiter
is shown
as the large b
When where? scale
shown.
Growth faster close-in;
Grand tack model?
Raymond et al. 2009
energy equipartition
Mixing during formation
During the late stages planets grow through the collisions of bodies of relatively eccentric orbits.
These orbits are the results of the gravitational interactions between the bodies and such
eccentricities are required in order to allow for further collisions.
In the following figure taken from a paper by Chambers and Wetherill (1999) the fraction of the
final mass of the planets in different radial bins (0-1 AU, 1-2 AU, 2-3 AU) is plotted as a function of
the initial radius of the embryos.
From this figure, it is evident that there is considerable radial mixing occurring as a results of the
dynamics of the embryos. The simple concept of a feeding zone, ie. a relatively narrow zone from
which a planet emerges is not correct. Rather, a planet is made of material originating from almost the
entire inner solar system even though there is a tendency to accrete more from the region where the
embryo is initially located.
Water of Earth
Inherent to the question of mixing during planetary formation is the question of the origin of water
on the terrestrial planets. This question can be addressed by following the planetesimals originally
located inside/outside the ice line and see in which planet they eventually get incorporated.
In the following figure to the left the results of such a numerical experiment by Raymond et al.
2003 is being displayed. The ice line being initially located between 2 and 3 AU, the planetesimals
inside this limit are water poor while those located outside water rich. After 200 Myr of collisional
evolution a few large water rich bodies have survived.
Statistics carried out over a number of simulations show the results on the figure to the
right. Some model planets have an Earth like water content, while some other planets
have orders of magnitude the water content of the Earth, so-called water worlds.
Water of Earth II
An important question regarding the Earth is the problem of the origin of its water. This question is
important since it is often believed that water is key to the emergence of life.
Water can originated from three different sources: 1) as a part of the volatiles accreted by the Earth
during its formation and later out-gassed, 2) it can be brought in later in form of collisions involving
water rich bodies (comets essentially) and 3) a combination of both sources above. Assuming it all
comes from comets, the following statistics apply:
mass of the Earth:
~ 1024 kg
mass of water (0.001):~ 1021 kg
mass of comet:
~ 1014 kg
107 impacts of comets on Earth...
sea water: D/H = 1/6410
However, we know that not all water on Earth can
come from comets. This fact comes from the
comparison between the D/H ratio in a number of
well studied comets and in Earth's ocean water.
The D/H ratio is lower in Earth's sea water than in comets.
Since evolutionary effects would favor the loss of H compared
to D (D is heavier and hence more difficult to loose), this
difference is thought to be primordial. Hence, the sea water
on Earth cannot be entirely cometary water (at least not from
Oort cloud comets).
In this context, it is interesting to compare the terrestrial D/H
ratio to the one of other objects in the Solar System. One
realizes that the Earth's ratio is neither cometary nor equal to
the protosolar ratio.
comets: D/H = 1/3240
2. Giant impacts
Giant impacts
The late stages of the collisional accretion of planets involves collisions between bodies of
almost planetary sizes with bodies not that much smaller. These so-called giant impacts
which involve enormous amounts of energy have been invoked to explain a number of
particularities of solar system bodies:
- the existence of the Earth's Moon
- the anomalous density of Mercury
- the tilt of Uranus' rotation axis
- the existence of Chiron (Pluto's moon).
It is the last giant impact that leaves traces. For extrasolar planetary systems, it has been
suggested that the high luminosity of post-impact planets could make them (relatively) easily
detectable objects. For solid planets, one would for example expect a characteristic spectral
signature of vaporized rocks. For giant planets, a higher luminosity could result.
Collision history
The plot shows for a accretion simulation in the inner solar system the collision history for the
three largest bodies (final masses of ~2, 0.5 and 0.4 Mearth).
largest body 3rd largest body 5th largest body
giant impacts
Note
-Giant impacts occur at all stages
of growth.
-Giant impacts are the major steps
in planetary growth.
2.1 Collision physics
Collisions are at the heart of planet formation. In fact, planets grow as a result
of collisions...
We need a mapping between initial conditions and collision output:
Collisions are at the heart of planet formation. In fact, planets grow as result of collisions. We
therefore need a mapping between initial conditions and collision output:
Collision physics
Initial conditions:
- size of bodies
- internal structure
- chemical composition
- relative velocity
- impact geometry
Collision output:
- mass distribution of fragments
- composition of fragments
- relative velocity of fragments
- spin rate of fragments
Collisions and planetary growth
Collisions
and
planetary
growth
Some useful quantities:
Some useful quantities:
2(Rtar + Rimp )
vesc 2Rtot
vesc 1
vesc
√
τcoll =
≈
≈
≈
vimp
vimp vesc
vimp Gρ
vimp
2(Rtar + Rimp )
vesc 2Rtot
vesc 1
vesc
√
τcoll
≈
≈ dominated
≈whileτthose
Collision timescale
1)1)collision
timescale:
dyn
Collisions
for=whichvvimp
imp >> vescvare strength
v
v
v
Gρ
imp
esc
imp
imp
Some useful1)quantities:
collision timescale:
for
which
v
imp ! vesc (or larger) are said to be in the gravity regime.
Collisions forfor
which
vimp >>
arevesc
strength
dominated
while thosewhile
for which
vimp ≈ vesc are
Collisions
which
vimpvesc
>>
are strength
dominated
those
saidwhich
to be invthe !
gravity
regime.
for
v
imp
esc (or larger) are said to be in the gravity regime.
2) escape velocity and sound speed:
�
�−1/2
�
�1/2
2GM
ρ
R
v
=
≈
400
cm/s
2)2)escape
andsound
sound
speed:esc
Escape velocity
velocity and
speed
3
1km
�1/23 g/cm
�
�−1/2 R �
2GM
ρ
R
Compare this with
the typical
values
for
the
sound
speed
in
silicates:
3 km/s.
escape
Compare
this
with
the
typical
values
for
the
sound
speed
in silicates:
vesc =
≈ 400
cm/sThe
3
R
1km
3 comparable
g/cm
velocity becomes
comparable
to sound
speed
for rocky
bodies with
R=750
km.
For for
km/s.
The escape
velocity
becomes
to
sound
speed
vimp<cs : acoustic
waves.
vimp>>c
shock
waves,speed
strongin
heating.
s: strong
Compare
thisrocky
with
the For
typical
values
for
the sound
silicates: 3
bodies
with:
R=750
km
3
km/s. The escape velocity becomes comparable to sound speed for
km/s. The escape velocity becomes
comparable
to sound speed for
rocky bodies with:
R=750 km
rocky bodies with: R=750 km
M −M
Collision physics II
3) Accretion efficiency
3) accretion efficiency: ξ =
Mlr − Mtar
3) accretion efficiency: ξ =
Mimp
lr
tar
Mimp
0≤ξ
0≤ξ≤1
where Mlr: mass of the largest remnant
≤ 1 Mtar: Mass of the target
Mimp: mass of the impactor
where
M
lr: mass of the largest remnant
If the impactor is accreted perfectly, this quantity is 1, if no mass is accreted or lost, zero, and
Mtar: Mass of the target
for target erosion it is <0.
4) catastrophic disruption threshold Q∗R
Mimp: mass of the impactor
4) Catastrophic disruption threshold
specific incoming kinetic energy:
Specific incoming kinetic energy Q.
2
0.5 µ vimp
QR =
Mtar + Mimp
Mlr (QD ) = 0.5 Mtar
catastrophicdisruption
disruption threshold
is defined
by: by
The the
catastrophic
threshold
is defined
∗
i.e. it is this Q where the largest remnant is half the
original target mass.
note that the largest remnant can be either
an intact
fragment
or largest
a gravitationally
Note
that the
remnantre-can either be an
accumulated
rubble pile....
intact fragment
or a gravitationally re-accumulated
rubble pile.
Catastrophic
threshold
Catastrophicdisruption
disruption threshold
Note:
-resistance to disruption is decreasing in
the strength regime. More faults in larger
Note:
bodies.
gravity regime
strength regime
increasing impact angle (0,30,45,60,75)
- resistance to disruption is decreasing
$)"15&3 4*.*-"34*;&% $0--*4*0/4 " 1"3".&5&
-gravity
makes bodies
increasingly
in the strength
regime
difficult to destroy.
- gravity makes bodies increasingly
-objects
thedestroy
size range 100m to 1km
difficultin to
are the weakest of all.
- object in the size range 100m-10km
-beyond
km, all remnants
are the 1weakest
of all are
gravitational aggregates.
- beyond 1km, all remnants are
-impact
geometry
can change the
gravitational
aggregates
threshold by a factor 4 to 8.
- impact geometry can change
threshold by a factor 4-8.vimp
Mimp
Benz & Asphaug
θgraz
impact angle:
θ=0˚ : face on impact
θ=90˚: grazing impact
θA
Mtar
JOWBSJBODF PO UIF ĕSTU PSEFS 8IFO UIF JNQBDU WF
UJNF UP UIF DPMMJTJPOBM UJNF tcol = (Rimp + Rtarg
*O PUIFS XPSET " DPMMJTJPO BU B HJWFO
JNQBDU WFMP
icy bodies
GPS B DFSUBJO NBTT SBUJPO γ = Mimp /Mtarg IBT UI
BOE 1.0M⊕ BTTVNJOH UIF CPEJFT IBWF JO CPUI DBTF
DPNQSFTTJCJMJUZ DBO CF OFHMFDUFE
ćF DPMMJTJPOBM UJNFTDBMF JT BO FTUJNBUF PO IPX
UISPVHI UIF UBSHFU BOE JT HJWFO CZ
Collision regimes
Reufer 2011
τcoll
head on
2(Rimp + Rtarg )
vesc 2Rto
=
∼
vimp
vimp vesc
grazing
Note:
-Low speed collision lead to accretion, independent of the angle of impact.
-High speed, head on collisions are destructive.
-At an impact angle larger than 60 degrees, with vimp> 1.1 vesc, so called hit and run collisions
occur. No accretion or erosion occurs.
Important for n-body simulations: often not perfect sticking, but hit and run.
2.2 The formation
of the moon
R. N. Clayton
University of Chicago, IL, USA
Characteristics of the Earth-Moon system
1.06.1 INTRODUCTION
1.06.2 ISOTOPIC ABUNDANCES IN THE SUN AND SOLAR NEBULA
1.06.2.1 Isotopes of Light Elements in the Sun
1.06.2.2 Oxygen Isotopic Composition of the Solar Nebula
1.06.2.2.1 Primitive nebular materials
1.06.2.2.2 Sources of oxygen isotopic heterogeneity in the solar nebula
1.06.3 OXYGEN ISOTOPES IN CHONDRITES
1.06.3.1 Thermal Metamorphism of Chondrites
1.06.3.1.1 Ordinary chondrites
1.06.3.1.2 CO chondrites
1.06.3.1.3 CM and CI chondrites
1.06.4 OXYGEN ISOTOPES IN ACHONDRITES
1.06.4.1 Differentiated (Evolved) Achondrites
1.06.4.2 Undifferentiated (Primitive) Achondrites
Earth=Moon
1.06.5 SUMMARY AND CONCLUSIONS
REFERENCES
Observed characteristics of the Earth-Moon system are:
129
131
131
131
132
134
135
137
137
138
138
138
138
140
140
141
•Mass of satellite large compared to mass of planet (1/81). This is the largest mass ratio
satellite-to-planet in the solar system.
•Angular momentum of the system is in the Moon's orbit not in the planet's rotation as it is
the case e.g. for Jupiter with a spin period of just ~10 hours. The angular momentum of the
Earth-Moon system is large and about L
=3.5 x 1041 g cm2/s.
•Moon has only a very small iron core (~ 3-5% by mass). This is a factor ~5-10 smaller than
for Earth, Mars or Venus.
is highly depleted in volatile (As, Sb, Ge, Pb, Au...) and enriched in refractory
•The Moon1.06.1
INTRODUCTION
meteoritic data. Figure 1 shows schematically
elements. Its bulk composition is otherwise very
similar
to the
Earth's
mantle.
In particular,
the effect
of various
processes
on an
initial
Oxygen isotope abundance variations in
composition at the center of the diagram. Almost
oxygen isotopes
identical
to within
measurement
errors...
meteoritesare
are very
useful in elucidating
chemical
all terrestrial materials lie along a “fractionation”
and physical processes that occurred during the
trend; most meteoritic materials lie near a line of
formation of the solar system (Clayton, 1993). On
“16O addition” (or subtraction).
Earth, the mean abundances of the three stable
The three isotopes of oxygen are produced by
isotopes are 16O: 99.76%, 17O: 0.039%, and 18O:
Oxygen
isotopes
nucleosynthesis of
in stars, but by
different
nuclear
It
is
conventional
to
express
variations
in
abundances
0.202%.
It is conventional to express variations in
processes in different stellar environments. The
abundances
of theofisotopes
in terms
of isotopic
the isotopes
in terms
isotopic
ratios,
relative
to an
principal
isotope, 16O, is a primary isotope
ratios, relative to an arbitrary standard, called
(capable of being produced from hydrogen and
standard, called
SMOW
water):
SMOW (for
standard(standard
mean ocean mean
water), asocean
helium alone), formed in massive stars (.10 solar
follows:
masses), and ejected by supernova explosions. The
! 18 16
"
two rare isotopes are secondary nuclei (produced in
ð O= OÞsample
18
stars from nuclei formed in an earlier generation of
d O ¼ 18 16
2 1 £ 1;000
ð O= OÞSMOW
stars), with 17O coming primarily from low- and
intermediate-mass stars (,8 solar masses), and 18O
! 17 16
"
ð O= OÞsample
coming primarily from high-mass stars (Prantzos
d17 O ¼ 17 16
2 1 £ 1;000
et al., 1996). These differences in type of stellar
ð O= OÞSMOW
source result in large observable variations in
stellar isotopic abundances as functions of age,
The isotopic composition of any sample can then
Pahlevan & Stevenson 2007
size, metallicity, and galactic location (Prantzos
be represented by one point on a “three-isotope
Formation
theories
of the Moon
Formation
theories
Moon formation
theories
Theories:
Theories:
Theories:
1) Fission: formed through rotational instability of a fast spinning Earth.
→ corresponding angular momentum is not observed!
→ why capture a body with only a small iron core?
→ how to explain the chemical differences
→ dynamically unfeasible
1)
Fission:
Rotational
instability
of
the
Earth
1)
Fission:
Rotational
instability
of
the
Earth
2) Capture: captured from a heliocentric to a geocentric orbit
!
too
much
angular
momentum...
!
too
much
angular
momentum...
→ tidal dissipation rate not large enough
2)
2)Co-accretion:
Co-accretion:Simultaneous
Simultaneousformation
formation
3) Binary formation/Co-accretion:
together at the same time
!
unfeasible...
!dynamically
dynamicallyformed
unfeasible...
3)
3)Capture:
Capture:The
TheMoon
Moonisiscaptured
capturedby
by the
the Earth
Earth
4) Giant impact: formed from the debris put into Earth orbit as a result
!lack
of
aadissipation
mechanism...
!lack
of
dissipation
mechanism...
of a giant collision
→ most promising theory so far
→ questions:
4)
4)Giant
Giantimpact:
impact:The
TheMoon
Moonoriginates
originates from
from aa collision
collision
- how!the
massive
waspromising
the Earth attheory
the
timeso
of far...
impact
most
!the
most
promising
theory
so
far...
- how big was the impactor?
- observable signatures?
→ numerical simulations are needed to
determine if this scenario is viable!
Moon forming impacts
Simulations show that the Earth underwent during its formation impacts some of which are
suited to lead to moon formation. In the figures, impacts suffered by the Earth during its late
stages of formation are displayed (Agnor and Canup, 1999).
Impactor mass as a function of time.
Note:
-the mass of impactors can be quite large
(equal or larger than Mars)
Impactor velocity as a function of time.
Note
-relative speeds are of order or larger than
escape speed
Angular momentum involved in the collision
as a function of time
Note
-not all collision involve ang. momentum
comparable to the Earth-Moon ang. mom.
The impact
Red, yellow: mantel
Dark & light blue: iron
The impact
Red, yellow: mantel
Dark & light blue: iron
Moon formation phases
1)The impact
For some impact geometries and mass ratios, the iron
core of the ~Mars sized impactor is mostly
incorporated into the Earth. This explains why the
moon is iron poor. The material not incorporated into
the Earth forms at hot disk. The disk consists of
~40% Earth mantel and ~60% impactor mantel
material.
2) The evolution of the hot disk
Isotopic/chemical evolution. Equilibration and
mixing can occur during the hot phases of the disk
lasting of order few 103 yrs. Proto-Earth and the
proto-lunar disk approach diffusive equilibrium,
reducing any pre-existing differences oxygen
isotope composition.
3) The evolution of the cold disk
Formation of the Moon from accretion from the
disk.
Stevenson 2008
“Cold”
diskevolution
evolution
“Cold”
disk
Results found by N-body simulation:
2.9 days
8.8 days
-Disk cools and spreads
-Moons grow just outside RRoche~4 Earth
radii. The roche distance is the radius where
Note:body cannot withstand any more the
a (fluid)
- disk
cools and
differential
gravitational
pull spread
of the the other
body. - moons grow out RRoche
- larger moons sweep up
the smaller ones
-Large moons sweep up the smaller ones.
29 days
290 days
Kokubo et al 2000
Formation time ~ 1 year.
formation
time:
year
The newly
formed moon
was≃1
much
closer
to Earth. Also the days on Earth were
much shorter. Since then, the moon has
constantly receded from the Earth due to
the action of tides and angular momentum
conservation.
2.3 More imprints of
giant impacts
Anomalous density of Mercury
Mercury's mean uncompressed density is of order 5.3 g/cm3 compared to the one of the
Earth which is close to 4.3 g/cm3. This implies that Mercury must have an iron core
representing of order 70% of the planet's mass (compared to ~30% for the Earth's core).
The earth has a metallic core of order
30 % of its mass
Mercury has a metallic core of
order 70 % of its mass
Theories:
1) Equilibrium condensation: the composition reflects the T at the formation location.
→ difference between condensation temperature of iron and rocks is small..
2) Evaporation of the mantle: the mantle is being evaporated by the sun leaving a core behind
→ are the T high enough and/or the solar wind strong enough to remove 80% of the mantle?
This is testable: the bulk composition of the remaining mantle would show specific signatures.
3) Giant impact: mantle is removed following a giant collision
→ chemical signature?
→ re-accumulation of the ejected mantle which is still on Mercury crossing orbit.
Spin axes
The rotation axis of many planets is severely tilted (Uranus: 98º) and Venus is even a
retrograde rotator. All these characteristics can be explain in terms of giant impacts.
Questions?