Open problems in terrestrial planet formation

Sean RaymondLaboratoire d’Astrophysique de Bordeaux

…with audience contributions welcome!

How did the Solar System form?

• Simulations can roughly reproduce the masses and orbits of Earth and Venus (O’Brien et al 2006; Kenyon & Bromley 2006; Chambers 2001; Agnor et al 1999; Raymond et al 2006)

• Biggest problem: Mars’ small size (Wetherill 1991)

• Accretion process strongly dependent on giant planets (Levison & Agnor 2003; Raymond et al 2004)

• Goal: Reproduce inner solar system – Constrain Jup, Sat’s orbits at early times– Test relevant physics

Constraints• Masses, orbits of terrestrial planets

– Mars’ small mass is a mystery (Wetherill 1991, Chambers 2001)

– Very low eccentricities (O’Brien et al 2006)

• Structure of asteroid belt– Separation of S, C types– No evidence for remnant embryos (gaps)

• Accretion timescales from Hf/W, Sm/Nd– Earth/Moon: 50-150 Myr (Jacobsen 2005; Touboul et al 2007)

– Mars: 1-10 Myr (Nimmo & Kleine 2007)

• Water delivery to Earth– Asteroidal source explains D/H (Morbidelli et al 2000)

– Other models exist (Ikoma & Genda 2007; Muralidharan et al 2008) Str

onge

r C

onst

rain

ts

Dust (µm)

Planete-simals (~km)

Cores Embryos

Earth-sized

planets

104-5 yrs 105-7 yrs 107-8 yrs

dust sticking

Grav. collapse (cm - m)

Runaway growth

Oligarchic growth

Gas giants

Late-stage accretion

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Runaway gas accretion

Initial conditions for late-stage accretion

• Planetary embryos (aka protoplanets) form by runaway and oligarchic growth: ~Moon-Mars sized (~105-6 yrs) (Kokubo & Ida 1998, Leinhardt & Richardson 2005)

• Late-stage accretion starts when local mass in embryos and planetesimals is comparable (Kenyon & Bromley 2006)

Kokubo & Ida 2002

Ecc

entr

icit

y

Semimajor Axis (AU)

(Giant planets must form in few Myr, so they affect late stages)

Key factors for accretion

1. Giant Planets (Levison & Agnor 2003)

– Formation models predict low eccentricity– Nice model: Jup, Sat closer than 2:1 MMR

during accretion (Tsiganis et al 2005; Gomes et al 2005)

• Perhaps in chain of resonances (Morbidelli et al 2007)

2. Disk Properties (Wetherill 1996, Raymond et al 2005)

– Total mass ~ 5 Earth masses inside 4 AU (Weidenschilling 1977; Hayashi 1981)

– ∑ ~ r-1.5 (MMSN) or perhaps more complex (Jin et al 2008; Desch 2007)

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Nice model 2 (J, S in 3:2 MMR)

• No Mars analogs

• Embryos in asteroid belt– Inconsistent with

observed structure if embryo Mars-mass or larger

Nice model 2 (J, S in 3:2 MMR)

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• No Mars analogs

• Embryos in asteroid belt– Inconsistent with

observed structure if embryo Mars-mass or larger

Nice model 2 (J, S in 3:2 MMR)

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Eccentric Jup, Sat (e0=0.1)

Eccentric Jup, Sat (e0~0.1)

• Strong secular resonance (6) at 2.2 AU

• Mars consistently forms in correct configuration

• Earth and Venus are dryQuickTime™ and a

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Inconsistent with Kuiper Belt structure

–no migration of giant planets possible (Malhotra 1995, Levison & Morbidelli 2003)

Influence of giant planets

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Raymond, O’Brien, Morbidelli, & Kaib 2009

Influence of giant planets

Raymond, O’Brien, Morbidelli, & Kaib 2009

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Hard to form low-e, highly concentrated terrestrial planet systems

Mars

• Small Mars forms naturally if inner disk is truncated at 1-1.5 AU (Agnor et al 1999; Hansen 2009)

• Can reproduce all 4 terrestrial planets if embryos only existed from 0.7-1 AU (Hansen 2009)

Hansen 2009

Other effects

• Gas disk effects:– Type 1 migration (McNeil et

al 2005; Morishima et al 2010)

– Secular resonance sweeping (Nagasawa et al 2005; Thommes et al 2008)

• Collisional fragmentation (Alexander &

Agnor 1998; Kokubo, Genda)

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Morishima et al 2010

Jin et al (2008) disk

• Assume MRI is effective in inner, outer disk but not in between

• At boundary between low, high viscosity, get minimum in density

• Occurs at ~1.5 AU– Explanation for Mars’

small mass?

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Jin et al (2008)

Summary• No tested configuration of Jup, Sat reproduces all

constraints (Raymond et al 2009)

– Closest is eccentric Jup, Sat but Earth is dry and JS not consistent with Kuiper Belt

• Including gas disk effects doesn’t solve the problem (Morishima et al 2010)

• Hard to reproduce Mars’ small size– Strong constraint on Jup, Sat’s orbits at early times– Was there just a narrow annulus of embryos? (Hansen 2009)

• What’s missing?– Secular resonance sweeping during disk dispersal (Nagasawa et al

2005, Thommes et al 2008)

– Something else?

Recent progress

• Morishima et al 2008, 2010• Raymond, O’Brien, Morbidelli, Kaib 2009• Hansen 2009• Thommes, Nagasawa & Lin 2008• O’Brien, Morbidelli & Levison 2006• Raymond, Quinn & Lunine 2006• Kenyon & Bromley 2006• Nagasawa, Thommes & Lin 2005• Kominami & Ida 2002, 2004• Chambers 2001• Agnor, Canup & Levison 1999

Initial conditions

• Start of chaotic growth phase (Wetherill 1985; Kenyon & Bromley 2006)

• Equal mass in 1000-2000 planetesimals and ~100 embryos (5 ME total)– Embryos is Mars’ vicinity

are 0.1-0.4 Mars masses

• Integrate for 200 Myr + with Mercury (Chambers 1999)

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MarsLow-ecc.

Ast. belt

Form. time

Earth Water

Current JS

Eccentric JS

Nice model 1

Nice 1 eccentric

Nice model 2

Jin disk

Cases

• Current Jup, Sat• Jup, Sat with e0~0.1

– e ~ current values after accretion

• Nice Model 1: Jup 5.45 AU, Sat 8.12 AU, e0=0

• Nice Model 2: Jup, Sat in 3:2 MMR, low-e

• Disk: ∑~r-1 and r-1.5

– Little difference

• Disk from Jin et al (2008)– Dip in ∑ at ~1.5 AU

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