Theory of planet formation C. Mordasini

Transcription

1 Theory of planet formation C. Mordasini Kiel, Y. Alibert, W. Benz, K. Dittkrist, H. Klahr Max Planck Institute for Astronomy, Germany University of Berne, Switzerland Observatoire de Besancon, France

2 Content star formation dust & gas dynamics disk evolution collisional growth 1. Constraints on planet formation 2. Dust > Planetesimals 3. Planetesimals > Protoplanets 4. Protoplanets > Terrestrial Planets 5. Protoplanets> Giant planets 6. Planetary population synthesis planetary system

3 1. Observational constraints on planet formation

4 Centuries of solar system studies... remote observations laboratory analysis theoretical modelling in-situ measurements sample returns Benchmark for formation models: detailed constraints

5 Protoplanetary disks Decades of nearby star formation region studies various stages of star formation sizes, masses, radial structure chemical analysis of disks lifetime of disks Initial & boundary conditions

6 Example: The evolution of disks Hernandez et al NGC 2024 Trapezium IC 348 disks disappear in about 5-7 Myr NGC 2362! formation timescale for giant gaseous planets

7 15 years of exoplanet studies planets orbit a large fraction of stars (30% ++ for low mass planets) the planet population is extremely diverse! heavy elements play a role in the formation of at least the giant planets End products

8 The surprise... giant planets cannot form 455 planets... Jupiter Saturn Exoplanets have been found exactly where one did not expect to find them... Neptune Venus Earth Mars Uranus points towards a serious gap in our understanding of planet formation derived from the solar system alone!

9 Planet Formation: stages in presence of gas dust 10 7 years giant planets planetesimals protoplanets giant collisions terrestrial planets migration 10 8 years in absence of gas

10 2. Growth from dust to planetesimals

11 Classical coagulation - solids and gas do not orbit the star at the same speed! gas drag causes dust to drift towards the star! gas drag & turbulence determines the relative collision velocities maximum relative velocities? surface effects!m mm m km x 1000 x 1000 x 1000 strength regime Barrier for classical coagulation gravity regime -Drift barrier (drift timescale only 100 yr for 1 m body at 1 AU) -Fragmentation barrier (typical relative velocities for 1 m bodies lead to destructive collisions)

12 Classical coagulation fdg=1% fdg=3% fdg=1%, vf=10m/s fdg=3%, vf=30m/s Time No fragmentation Brauer et al With fragmentation

13 Alternative: The Goldreich & Ward Instability Dust settles into the midplane into a thin sheet: for sufficiently high dust concentration, could become instable to a self-gravity. (Goldreich & Ward 1973) The turbulent speed of grains must however be low to reach the necessary concentration. Vertical shear between (kepler.) dust disk and (subkepler.) gas above causes KH instabilities: stir up dust: no collapse possible. Conclusion: Turbulence prevents self gravitational formation. from Klahr al. 2008

14 Gravoturbulent planetesimal formation Dust is trapped locally in transient gas vortices in a turbulent disk and eventually becomes gravitationally bound. max(n) Johansen et al Klahr & Johansen t/(2&"!1 0 ) max(n)/n 0 max(! p /! g ) " K # f = M Hill /M Ceres!!!> t Turbulence aided growth might proceed from pebbles directly to intermediate-sized ( km) objects. Sedimentation Self!gravity 10 0!10.0! t/t orb

15 Planetesimals: Evidence for born big? Morbidelli et al The observed size frequency distribution SFD in the asteroid belt cannot be reproduced with planetesimals that grow (and fragment) starting at a small size (left). but with initial sizes between 100 and 1000 km (right).

16 3. From planetesimals to protoplanets

17 Collisional growth Gravity is now the dominant force. Still difficult to study because: - Initial conditions poorly known - how do the first planetesimals form? - large number of planetesimals to follow (no direct N body) - 10 MEarth > 10 8 rocky bodies with R=30 km - long evolution time years are equivalent to 10 7 dynamical times... - highly non-linear with complex feed-back mechanisms - growing bodies play an increasing role in the dynamics - non-trivial physics - shock waves, multi-phase fluid, fracturing, etc. Tackle with different approaches, each with + and - points.

18 Semi-analytical rate equations Rate equations: simplest possible approach. One big body & many small background planetesimals (surface density) Alibert et al ( 3 m isolation (4πr2 Σ) 2 (3M ) 1 2 Gravitational focussing! vrel key parameter. Without radial excursion, growth goes up until the isolation mass is reached: the protoplanet has accreted all planetesimals in its gravitational reach (in the feeding zone, width ca 5 Hill sphere radii) ( a ) ( 3 Σ 1AU 10gcm 2 Safronov 1969 ) 3/2 M.

19 Growth as a function of semimajor axis Mordasini et al xMMSN (!=7 g/cm 2 ) 5xMMSN Growth is faster at small distances ig. 7. Snapshots of the embryo mass (solid line) as a function of semimajor axis at four moments in time for two different solid surface densities. he dashed line is the isolation mass. The dotted line is M But stops at smaller masses. emb,0 = 0.6 M. The initial solid surface density at 1 AU is 7 g/cm 2 (left panel) and 5 g/cm 2 (right panel). It should be kept in mind that this kind of calculationno is neededgiant to generate the planet start time t start in whensitu. the embryo is put into he formation model. The real evolution of the solid core for M > 0.6 M is in general much more complex than plotted here. In this figure, we ave continued the calculations up to the isolation mass to allow comparison with other models. Quick and massive: Beyond the iceline 2.7 AU) Higher!: Protoplanets more that the massive resulting sub-population & quicker: of observablegp syntheticcores planets he results are quite similar, even if core growth proceeds at arge orbital distances somewhat faster in our model. Compared reasonably well reproduces the observed population (Paper II).

20 Monte carlo method Monte Carlo (probabilistic), particle-in-a-box (statistical); discrete (masses); adaptive (superparticles) Stirring increase of random velocities (e, i) Gas drag damping Collisions Dynamical friction energy equipartition Annulus at 1 AU 7 km initial size Dot size: total mass in size bin Color: relative random velocity v/vh (vh=" RH) Ormel et al subm.

21 Example: runaway and olig. growth -early phase: runaway growth. low random velocities fast growth big bodies decouple -later phase: oligarchic growth. big bodies heat smaller higher random velocities slower growth big bodies grow in lockstep -finally: isolation mass oligarchs separated by a few RH Ormel et al subm.

22 4. Formation of terrestrial planets

23 Terrestrial planet formation Once damping influence of the gas disk gone, eccentricity grows, and growth from Miso (oligarchs) w MEarth to final masses by giant impacts starts. Evolution until long time stable configuration is reached. Constraints (for the solar system): 1. the orbits, in particular the small eccentricities (Earth: 0.03) 2. the masse, in particular Mars small mass 3. the formation time of Earth from isotope dating ( Myr) 4. the bulk structure of the asteroid belt (no big bodies) 5. Earth relatively large water content (mass fraction 10-3 ) 6. influence from Jupiter & Saturn Method: N body simulation.

24 Solar system MEarth Excitation at MMRs Diffusion Substantial radial mixing S.N. Raymond et al. / Icarus 203 (2009) Raymond et al oligarchs + small pl. dotsize prop. M1/3 4 terrestrial planets with masses between MEarth M, Tform, ecc. and water content ok, but Mars to massive, and 3 addit. bodies Giant planets? When where? 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 scale on the x axis). The color of each body corresponds to its water content by mass, from red (dry) to blue (5% water). Jupiter is shown as the large shown. Low eccentricity, water rich But mars too large Addit. bodies

25 Giant impacts - Impact of bodies of similar size - shaping planetary systems - formation of the Moon, composition of the Earth - blasting Mercury s mantle - making exoplanets visible... Red, yellow: mantel Dark & light blue: iron

26 5. Formation of giant planets

27 Direct collapse model Q = c s κ/πgσ 1.7 #cool!#orb GJ 758B Klahr et al. in prep Thalmann et al M: 34 MJ (10-39 MJ) Teff: K a:~55 AU e:~0.69 Allowed region Min. from Toomre criterion for grav. instability Impossible at small separations Max. from cooling criterion (#cool!#orb) Numerically demanding...

28 Core accretion model Perri & Cameron 1974, Mizuno et al. 1978, Mizuno 1980, Bodenheimer & Pollack 1986, Pollack et al. 1996, Lissauer et al Follow the growth in solids and gas of an initially small solid core (ices, rocks) surrounded by a gaseous envelope (H2 & He) in the protoplanetary disk. envelope growth: 1D structure equations (similar to stellar structure) core growth: collisional accretion of background planetesimals velocity dispersion of planetesimal is key parameter (runaway, oligarchic, orderly) 1) dr3 dm = 3 4πρ mass conservation 2) dp dm = G(m + M core) 4πr 4 hydrostatic equilibrium 3) dl dm = du dt + P dρ ρ 2 dt + ɛ acc energy conservation dt 4) dp = ad or rad energy transfer heating by infalling planetesimals

29 Accretion of gas: comparison planets are not 1D recently, 3D self-gravitating radiation hydrodynamical models of gas accretion with a realistic core size (Ayliffe & Bate 2009, Paardekooper & Mellema 2008) Ayliffe & Bate 2009 Ayliffe & Bate 2009 (3D) Papaloizou & Nelson 2005 (1D) 1D, 15 Mearth 3D, 10 Mearth 1D, 5 Mearth Consistent accretion rates in 1D and 3D

30 Jupiter in-situ formation Main model assumptions (as Pollack et al. 1996): in situ formation (no migration) standard opacities Phase I: Rapid build up of a core. Until isolation mass: Emptying planetesimal feeding zone Phase II: Slow accretion of gas and planetesimals Phase III: Runaway gas accretion at Mcore> Mcrit Mass Mass [MEarth] Total Core Envelope Phase I Phase II Phase III Disk gone Total Gas Solids 0 1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 7e+06 8e+06 9e+06 Time [yr] Time [Yr] 9 Myr Radius [RJup] [Jupiter Luminosities] Luminosity [LJupiter] 100 Radius [Jupiter Radii] Total Core Capture Capture Runaway solids accretion Total Time [Yr] Runaway gas accretion e+06 1e+07 1e+08 1e+09 1e+10 Time [yr] Core e+06 1e+07 1e+08 1e+09 1e+10 Time [yr] Rapid, but not dynamic collapse Time [Yr] Slow contraction Slow cooling 10 Gyr 10 Gyr

31 Luminosities (a) Two peaks: Planetesimal accretion Fi of m ac in al ru lo tim is Lissauer et al L L=10 Sun Gas runaway accretion L= LSun T= yrs!"#$%&$'%&'()*'+%,-%&./#/*,' 0123"%4/5&6 Constrains dm/dt (b) Klahr & Kley 2006 Hot blob around the planet Size: few RH: AU (1 MJ,5 AU) Temp K Detectable in the mid-ir Might also cast shadows Fig. 13. Model DR: temperature in the midplane of the protoplanetary disk after 121 orbits. Brightness corresponds to the logarithm of tem- Wolf 2008 Fig. 8. The planet s luminosity as a function of time is shown for all of the runs which resulted in planets of mass equal to that of Jupiter. Diamonds denote bifurcaformation. We conclude that at least for the time when Jupiter is accreting its mass there can be no formation of a satellite!"#$ tion times. (a) The companion to Figs. 4 and 5, shows data from five pre-bifurcation system. runs as thick solid lines and post-bifurcation results from selected cases in high %&&'(#)"*$ viscosity disks as narrow lines. (b) The companion to Figs. 6 and 7, shows the post4. Conclusions +(,)"*$$$$$$$$$$$$ bifurcation luminosity of nine runs that produce planets of mass 1M J. Note in all We have performed full 3D radiation hydrodynamical simucases the steep increase in luminosity as the rate of gas accretion accelerates after lations of embedded protoplanets in disks, and compare the -'".*/$#0($ results in detail to the standard isothermal approach. crossover; this is a real physical consequence of the core nucleated accretion model Mean torques and migration rates are not strongly af12-*(# fected by the treatment of the thermodynamics in the case of of giant planet formation. The value at which luminosity peaks depends upon the Jupiter mass planets. This might change for lower mass planplanetary mass at which disk hydrodynamics begins to limit the rate of mass acets, which are more embedded in the disk. The fluctuations of 23""'78/.#4*' the torques on the other hand are much stronger, in particucretion, and thus on the viscosity and surface density of the disk in the vicinity of lar in higher resolution cases. Similar effects have been ob9/%$)(&*77' the planet. Those simulations in which accretion of gas is tapered off exhibit a corserved in high resolution nested grid simulations (D Angelo et al. 2002, 2003b) and also MHD simulations of planet-disk :/5.%;* "3$-$4$ responding taper in luminosity; the curve for run 3lRH J is probably most realistic, interactions (Papaloizou & Nelson 2003; Nelson & Papaloizou 2003; Winters et al. 2003). In some cases the torques even4-.')$/)56$7)#0$ as this run has!"#$%& the most plausible treatment of the tail off in gas accretion. (For in!"'#$%& change their sign for a short period. terpretation of the references to color in this figure legend, the reader is referred to -*$(89(//(/$ We find that planets are most likely to form a circumplane- H. Klahr and W. Kley: 3D-radiation hydro simulations of disk-planet interactions. I $m si p d p w n to ru o fo to d in th h ev p re p ex al

32 Extending the models Similar timescales of various processes:! migration "! formation #! disk evolution & extend model to include in a self consistent way (Alibert, Mordasini, Benz 2004) 1) type I and type II planetary migration (Lin & Papaloizou 86; Ward 97; Tanaka et al. 02). Isothermal Type I reduced by constant factor f1 (free parameter). Currently working on eliminating f1 (Dittkrist et al. in prep). 2) disk evolution (1+1 D) %-disk with photoevaporation (Papaloizou & Terquem 1999), now also with irradiation from the host star (Fouchet et al. submitted). Simplifications (most important) One embryo per disk, no systems (including Nbody also work in progress) Formation only until the gas disk disappears: No mass growth/loss after disk dispersal (Terrestrial planets, Ice giants, evaporating planets) No eccentricity, planets on circular orbits No particular stopping mechanism, amin=0.1 AU

33 Models meet observations Jupiter slow type I fast type I species measured computed Alibert et al. 2005b Saturn species measured computed

34 Migration and planetesimal disk ~100km accretion ejection Kalas et al Iceline Migration path Inner edge of FZ Outer edge of FZ Log(Planetesimal surface density) Paardekooper Mellema 2004 Planet shapes the planetesimal disk: effect on the dust

35 Migration and gas disk Disk accretion rate (Msun/yr) Start of runaway gas accreation Planet migration path Accretion onto the planet strongly influences the evolution of the gas disk itself

36 Gap formation 3 4 H + 50 R H qr 1 Crida et al Gap opening & gap width constrains disk and planetary properties (mp, scale height H, viscosity) Kley & Dirksen 2006 Gap formation crucial for -accretion rate -migration rate (type I vs II) Wolf & Klahr 2008 Σ t = M_jup 2 M_jup 3 M_jup 4 M_jup 5 M_jup r Large scale signs of planetdisk interaction also visible outside the gap (density waves of a Jupiter mass planet) in scattered light (VIS, near IR).

37 Gaps and accretion rates Lubow et al Kley & Dirksen 2006 Accretion Rate Transition See also Papaloizou et al Gap reduces accretion rate > 1 MJ Veras & Armitage 2004 ( Mp ) ( 1/ e M p ) 1.5M J +0.04, M J Sufficiently massive Planet Mass planets [M star ] (>3-5 MJ): sudden transition of Mass accretion rate onto planet the disk state from circular to increases strongly again. eccentric. More massive planets Limits to 6-10 MJ Detectable?

38 Gaps and migration rates Migration rates change by 1-2 orders of magnitude from type I to type II Type I: Planets seem to migrate so fast that within the disk s lifetime they fall into the star disk lifetimes (Ward 1997) simple linear theory for isothermal disks cannot be the final word!

39 Migration: Beyond linear models... 1) Turbulence in disk (Nelson & Papaloizou 2003) 2) Opacity transition regions (Menou & Goodman 2004) 3) Radiation effects (Paardekooper & Mellema 2008; Kley & Crida 2008, Kley, Bitsch & Klahr 2009, Paardekooper et al. 2009) 4) Dead zones (Ida & Lin 2008; Terquem 2008) Need observational guidance and tests Disk structure matters a lot!

40 6. Planetary population synthesis

41 Principle Extended core accretion model Formation model tested in the Solar System (Alibert, Mordasini, Benz 2004) Initial Conditions: Probability distributions & parameters Disk gas mass Disk dust mass Disk lifetime Mordasini et al. 2009a Mordasini et al. 2009b From observations red line shows the total number of known extrasolar planetary compan Observed population No match: improve, change parameters Draw and compute synthetic planet population Apply observational detection bias Comparison: Observable sub-population - Distribution of semi-major axis - Distribution of masses - Fraction of hot/cold Jupiters - Metallicity effect Match Cross check Couple to other detection methods Predictions (going back to the full synthetic population) Model solution found!

42 Initial conditions Some can be constrained by observations, some from theoretical arguments and some are just educated guesses. Four Monte Carlo variables with probability distributions Dust-to-gas ratio (solid surface density). Derived from observed (stellar) metallicities. Initial gas surface density. Derived from observed protoplanetary (dust) disk masses. Photoevaporation rate. Derived from observed lifetime distribution of protplanetary disks. Initial semimajor axis of the small planetary seed put into the disk. Uniform in log(a). Parameters (fixed for one synthetic population) Type I migration rate reduction factor f1 Disk viscosity parameter % (0.007) Planetesimal size (R=100 km) Initial solid surface distribution (! r -3/2 ) Stellar mass

43 : Planetary formation tracks Mstar=1 M" Nominal model f1=0.001 Time Mass Starting mass Mordasini, Alibert, Benz, 2009 Mordasini, Alibert, Benz, Naef 2009 Semi-major axis

44 Synthetic Population Nominal Model: alpha= 7x10-3, f1=0.001, M=1 M" Text Mordasini et al. 2009a The variation of the initial conditions within the observed limits (protoplanetary disk properties) produces synthetic planets of a very large diversity. Planets that reached inner boarder of computational disk A number of clusters can be identified. Iceline clump Planetary desert Failed cores Fig. 14. Final mass M versus final distance a of all N synt synthetic planets of the planetary population orbiting G type stars using the parameters and distributions described in 3 (α = , f I = 0.001). The feeding limit at a touch is plotted as dashed line. Planets migrating into

45 Planetary Initial Mass Function PIMF Mordasini et al. 2009b Peak at low masses Neptunian Bump Minimum: Planetary desert Flat Giant s Plateau Superjupiter Tail MStar=1 MSun Nominal Model Type Mass (MEarth) % (Super)-Earth < 7 58 Neptunian Intermediate Jovian Super-Jupiter > Model incompleteness Complex structure, dominated by low mass planets Consistent w. non-detection of Jupiters around 90-95% stars. Maxima at masses similar to Solar System planets. Model predicts that planets with M < 30 MEarth account for over 75% of all planets

46 PIMF: Dependence on disk properties Metallicity Disk Low mass mass Disk lifetime planets Udry, Mayor, Benz et al Observation Weak metallicity effect for Neptunes Fe/H mainly just scales PIMF for giant planets: Fe/H: threshold, but final mass not given by Fe/H higher number of giants but not more massive [Fe/H] dist. of Hot Neptunes: flat! [Fe/H] dist. of all known planets Disk mass changes the MF P<20 Disk d lifetime changes both. shape for giant planets. Long living disks: giants High disk mass: giant more numerous and Metal poor systems produce more small bodies planets Minimum of higher metallicity mass, effect but for Super-Earths higher & mass Neptunes less of lower mass. -Correlation with MD

47 Mass distribution Blue lines: Observational comparison sample for radial velocity Black lines: Detectable synthetic sub-population Number of Planets Planet Mass Distribution dn/dm! M Planets Keck, Lick, AAT Marcy et al Mass: KS 96% M sin i (M JUP ) The mass distribution is very well reproduced.

48 Towards the underlying mass distribution Observation Udry & Santos 2007 All instruments HARPS (1 m/s) Observational bias Synthetic 10 m/s (KS) 1m/s 0.1 m/s Full Population? Hints of the Neptunian bump and the minimum at 30 M!? If confirmed, very strong sign of c. a. Dryness of the planetary desert

49 Tasks Dust growth Break (?) the meter barrier (bouncing & fragmentation) Planetesimal formation Solved by local collapse models? (fragmentation?) Formation of giant planet cores Timescale issue Migration Realistic type I migration, incl. outward migration Planets at large distances Core accretion +... vs. direct collapse model Statistics will tell Formation of multiple planetary systems Keeping the detailled physics describing one embryo Statistics of system architectures

50 Conclusions The discovery of a whole population of exoplanets is providing important clues toward a better understanding of planet formation. -constrain formation models in a statistical sense -use the full wealth of observational data -...but don t forget the solar system. A comprehensive picture of planet formation is still beyond present capabilities: - pieces are available but don t fit well together yet... Field still observationally driven but theory beginning to be able -to make quantitative statements -to interpretate the detections -to make testable predictions Observation will remain the necessary guideline for theoretical progress. Observe directly formation (gaps, luminosity,..)!