Forming terrestrial planets & impacts

Transcription

1 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

2 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

3 1. Terrestrial planet formation

4 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 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 (red), GJ 581 (blue), HD (green) and HD (magenta) The 15 planetary systems with at least three known planets as of May 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.

5 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 ( 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.

6 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.

7 Stages of terrestrial planet formation Simulation setting 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) Outcome 4 terrestrial planets with masses between 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 energy equipartition

8 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.

9 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 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.

10 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: ~ kg mass of water (0.001): ~ kg mass of comet: ~ kg 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 impacts of comets on Earth... sea water: D/H = 1/6410 comets: D/H = 1/3240 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.

11 2. Giant impacts

12 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.

13 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.

14 2.1 Collision physics

15 Collision physics 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: 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 Some useful quantities: 1) Collision timescale τ coll = 2(R tar + R imp ) v imp v esc v imp 2R tot v esc v esc v imp 1 Gρ v esc v imp τ dyn Collisions for which vimp h >> v vesc >> are v strength are strength dominated dominated while those while for which those vimp vesc are said to be in the gravity regime. 1/2 1/2 2GM ρ R 2) Escape velocity and sound speed v esc = 400 R 3g/cm 3 1km cm/s Compare this with the typical values for the sound speed in silicates: 3 km/s. The escape velocity becomes comparable to sound speed for rocky bodies with R=750 km. For vimp<cs : acoustic waves. For vimp>>cs: strong shock waves, strong heating. the typical values for the sound speed in silicates

16 3) Accretion efficiency Collision physics II ξ = M lr M tar M imp wh where Mlr: mass of the largest remnant Mtar: Mass of the target Mimp: mass of the impactor If the impactor is accreted perfectly, this quantity is 1, if no mass is accreted or lost, zero, and for target erosion it is <0. 4) Catastrophic disruption threshold Specific incoming kinetic energy Q. The catastrophic disruption threshold is defined by i.e. it is this Q where the largest remnant is half the original target mass. Note that the largest remnant can either be an intact fragment or a gravitationally re-accumulated rubble pile.

17 Catastrophic disruption threshold Note: -resistance to disruption is decreasing in the strength regime. More faults in larger bodies. gravity regime -gravity makes bodies increasingly difficult to destroy. strength regime -objects in the size range 100m to 1km are the weakest of all. -beyond 1 km, all remnants are gravitational aggregates. -impact geometry can change the threshold by a factor 4 to 8. increasing impact angle (0,30,45,60,75) v imp M imp Benz & Asphaug θ graz impact angle: θ=0 : face on impact θ=90 : grazing impact θ A M tar

18 Collision regimes Reufer 2011 icy bodies = M imp /M targ head on 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.

19 2.2 The formation of the moon

20 Characteristics of the Earth-Moon system Observed characteristics of the Earth-Moon system are: 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 LEarth=Moon=3.5 x g cm 2 /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. The Moon is highly depleted in volatile (As, Sb, Ge, Pb, Au...) and enriched in refractory elements. Its bulk composition is otherwise very similar to the Earth's mantle. In particular, oxygen isotopes are identical to within measurement errors... It is conventional to express variations in abundances of the isotopes in terms of isotopic ratios, relative to an standard, called SMOW (standard mean ocean water): Oxygen isotopes d 18 O ¼ d 17 O ¼ ð 18 O= 16 OÞ sample ð 18 O= ;000 OÞ SMOW ð 17 O= 16 OÞ sample ð 17 O= ;000 OÞ SMOW Pahlevan & Stevenson 2007

21 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! 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 why capture a body with only a small iron core? 2) 2)Co-accretion: Co-accretion:Simultaneous Simultaneousformation formation 3) Binary formation/co-accretion: together at the same time! unfeasible...!dynamically dynamicallyformed unfeasible... how to explain the chemical differences dynamically 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!

22 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.

23 The impact Red, yellow: mantel Dark & light blue: iron

24 The impact Red, yellow: mantel Dark & light blue: iron

25 Moon formation phases Stevenson )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 10 3 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.

26 Cold disk evolution Results found by N-body simulation: 2.9 days -Disk cools and spreads -Moons grow just outside RRoche~4 Earth radii. The roche distance is the radius where a (fluid) body cannot withstand any more the differential gravitational pull of the the other body. 8.8 days -Large moons sweep up the smaller ones. 29 days Formation time ~ 1 year. 290 days Kokubo et al 2000 The newly formed moon was 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.

27 2.3 More imprints of giant impacts

28 Anomalous density of Mercury Mercury's mean uncompressed density is of order 5.3 g/cm 3 compared to the one of the Earth which is close to 4.3 g/cm 3. 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.

29 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.

30 Questions?