# Presentation: 316640

## Prospects for terrestrial planets in the Solar System and elsewhere

**Prospects for terrestrial planets in the Solar System and elsewhere**

**Sean Raymond **
**University of Colorado **

**Credit: Nahks Tr’Enhl**

## Collaborators

- <date/time>

- Tom Quinn (Washington)
- Jonathan Lunine (Arizona)
- Avi Mandell (NASA Goddard)
- Steinn Sigurdsson (Penn St.)

- Rory Barnes (Washington)
- Eric Gaidos (Hawaii)
- Nate Kaib (Washington)
- Brian Jackson (Arizona)
- Rick Greenberg (Arizona)

- Thanks to NASA Astrobiology for funding

## Outline

- <date/time>

- Overview of Terrestrial Planet Formation
- Solar System terrestrial planets
- Other Systems
- Solar System-like cases
- Hot Jupiter systems
- Known exoplanet systems
- “Hot Super Earths”
- Telling apart formation models
- Tidal evolution model constraints
- Conclusions

## Stages of terrestrial planet formation

## Stages of Planet Formation

- No more gas

- while gas remains

## Growth of a terrestrial planet

- Dust (μm)

- Planete-simals (~km)

- Embryos (103km)

- Earth-sized planets (104km)

- 104-5 yrs

- 105-6 yrs

- 107-8 yrs

## Composition of condensable material

- <date/time>

- Feeding zone: origin of planetary material

## The Catch-22 of Earth’s water

- <date/time>

- Liquid water: T > 273 K (with 1 bar atm.)
- To form ice in disk: T < 170 K

## Where did Earth get its water?

- <date/time>

- Late Veneer: Earth formed dry, accreted water from bombardment of comets (e.g., Owen & Bar-Nun 1995), or ...
- →Some of Earth’s “building blocks” came from primordial asteroid region: Earth did not form entirely from local material (Morbidelli et al 2000)

## Isotopic evidence

- Earth water D/H matches carbonaceous chondrites (Lecuyer et al 1998, Robert & Epstein 1982)
- Comets’ D/H too high, nebular gas too low (Bockelee-Morvan et al 1998, Geiss & Gloecker 1998)
- Earth matches C, N isotope ratios of CCs (Marty & Yokuchi 2006)
- Model: Primordial asteroid material as main source of Earth’s water (Morbidelli et al 2000)
- Key uncertainties: D/H of comets, Earth’s D/H evolution (Genda & Ikoma 2007)

## Formation of Solar System Terrestrial Planets

## Raymond, Quinn & Lunine 2006

**Raymond, Quinn & Lunine 2006**

## Model for Solar System Formation

**Successes**
- Masses and orbits of terrestrial planets (Wetherill; Agnor et al 1999; Chambers 2001; O’Brien et al 2006)
- Earth water from  primitive asteroidal bodies (Morbidelli et al 2000; Marty et al 2006)
**Shortcomings**
- Mars is too small (unexplained – Wetherill 1991; Raymond et al 2009)
- Mercury is too small and too iron-rich (giant impact? Benz et al 1988, Wetherill 1988)
- Not included: collisional fragmentation (Asphaug et al 2006), water depletion from impacts and hydrodynamic escape (Matsui & Abe 1986, Canup & Pierazzo 2006, Genda & Abe 2005)

- Agnor, Canup & Levison 1999

## Terrestrial planet formation in other environments

- Systems like ours
- “Hot Jupiter” systems
- Known exoplanet systems

## Diversity in planetary systems like our own

- <date/time>

**Semimajor Axis (AU)**

**Eccentricity**

**Raymond, Quinn & Lunine 2004**

## Eccentric giant planets  dry terrestrial planets

- <date/time>

**Raymond, Quinn & Lunine 2004**

**Eccentric giant planets ******** dry terrestrial planets**

## Differences in Planetary Systems come from Two Sources

- Stochastic noise(Wetherill 1996; Chambers & Wetherill 1998)
- Systematic variations
- A.  Disk Properties (Chambers & Cassen 2002; Raymond et al 2004, 2005, 2006)
- Disk mass, density profile
- B.  Giant planets (Chambers & Cassen 2002; Levison & Agnor 2003; Raymond 2006)
- Eccentricity, Semimajor Axis, Mass

## Giant Planet Migration

**Hot** Jupiter

- Jupiter

**Close-in giant planets are thought to have migrated to their current locations because of interactions with the protoplanetary disk.  How does this affect terrestrial planet formation?**

## Important New Processes

- Giant Planet Migration (“type 2”--Ward 1997)
- Massive planets (>Saturn-mass) open a gap in disk, follow disk accretion
- Aerodynamic Gas Drag (Adachi et al 1976)
- Causes strong eccentricity, inclination damping, slow orbital infall

- Phil Armitage

## Slide 20

## Raymond, Mandell & Sigurdsson 2006

**Raymond, Mandell & Sigurdsson 2006**

## Credit: Nahks Tr’Enhl

## Credit: Nahks Tr’Enhl

## The Known Extra-solar Planets

- Eccentric orbits
- Median e ~ 0.25
- Range of masses
- Median ~ 1 MJup
- Range of orbital distances
- Median ~ 1 AU
- 40 multi-planet systems
- Which of these could harbor Earth-like planets?

## About 1/3 of known exoplanet systems could have formed a planet in the hab. zone

- Mandell, Raymond & Sigurdsson 2007

**Giant planets exterior to Earth-like planets**

**Giant planets interior to Earth-like planets**

**Giant planet too close to HZ -- no habitable planets**

## Close-in Big Terrestrial Planetsaka « hot Super Earths »

- Close-in Big Terrestrial Planetsaka « hot Super Earths »

- Google search for “hot Earth”

##  “hot Super Earths”

- 1-10 Earth masses
- “mini-Neptunes” or “super-Earths”?
- GJ 581, GJ 876, HD 40307, ...

## Ways to make “Hot Earths”        (Zhou et al 2005; Gaidos et al 2007; Raymond, Barnes & Mandell 2008)

- In situ accretion (if sufficient local mass)
- Type 1 Migration (Terquem  & Papaloizou 2007)
- Shepherding during giant planet migration
- Sweeping secular resonances (Zhou et al 2005)
- Tidal circularization of eccentric planets (Raymond, Barnes, Mandell 2008)
- Photo-evaporation of hot Neptunes

## Type 1 migration

- For 0.1-10 ME, back-reaction from tidally-generated density waves (Ward 1986)
- Forms chains of resonant planets

- Phil Armitage

- Terquem & Papaloizou 2007

## Hot Earths at the end of migration: average 3-5 Earth masses (but depends on disk mass)

- Hot Earths at the end of migration: average 3-5 Earth masses (but depends on disk mass)

**Semimajor Axis (AU)**

## Photo-evaporation of close-in gaseous planets

- Evaporation to the core occurs only for very close-in planets and more easily for less massive planets
- Sensitive to star’s XUV flux over time (Hubbard et al 2007, Baraffe et al 2004)

- Raymond, Barnes & Mandell 2008

## Observable Quantities (ideal case)

- Planetary system architecture
- RV, transits, transit timing
- Hot Earth Compositions
- Planetary radii from transit depth
- Icy planets ~50% larger than rocky for given mass (Valencia et al 2007a,b; Fortney et al 2007; Seager et al 2007; Sotin et al 2007)
- Thick atmospheres are tricky (Adams et al 2008)

- 50% water

- rocky

- Fortney, Marley, Barnes (2007)

## Raymond, Barnes & Mandell 2008

| “Hot Earth” form. model | System Architecture | Hot Earth Composition |
| --- | --- | --- |
| In Situ Formation | Several hot Earths, spaced by ~40 RHill | Dry |
| Type 1 Migration | Chain of hot Earths in/near resonance | Icy |
| Giant planet shepherding | Hot Earth just inside strong giant planet resonances (2:1) | Moderate: few percent water by mass |
| Disk dissipation shepherding | Hot Earths with two interacting giants | ? |
| Photo-evaporation | Correlation with stellar age | Icy (giant planet core) |
| Tidal Circularization | Isolated hot Earth, eccentricity source  | ? |

## Best candidates based on the known systems (Mayor et al 2008): transits needed to differentiate (COROT, Kepler)

| “Hot Earth” form. model | System Architecture | Hot Earth Composition |
| --- | --- | --- |
| In Situ Formation | Several hot Earths, spaced by ~40 RHill | Dry |
| Type 1 Migration | Chain of hot Earths in/near resonance | Icy |

- Raymond, Barnes & Mandell 2008

- Best candidates based on the known systems (Mayor et al 2008): transits needed to differentiate (COROT, Kepler)

## Tidal evolution of close-in planets

- Could Gliese 581 c have formed in the habitable zone?
- Can we constrain the interior structure of HD 40307 b?

## Tidal Evolution Model (Kaula 1964; Goldreich & Soter 1966)

- Requires “tidal locking” (not synchronous rotation)
- No net torque on planet during orbit
- Slow stellar rotation  orbital decay
- Semimajor axis and eccentricity decrease in time
*Q* = Tidal Dissipation function
- Small *Q*, small *a*, large *e*  more evolution
- [For large *e*, model may slightly underestimate evolution]

- Tide on planet from star

- Tide on star from planet

## Example: Earth orbiting a 0.2 Solar-mass star with e0 = 0.84

- Example: Earth orbiting a 0.2 Solar-mass star with e0 = 0.84

**Blue = limits of HZ (depend on ecc.)**

**Dashed = circular orbit with equivalent flux**

## Gliese 581 (Udry et al 2007)

- 3 known planets: M sin i from 5 to 15 Mearth
- Planets c and d at inner, outer edges of HZ:
- require ~100% cloud cover for habitability
- Tides important for planets b, c: ec ~ 0.2

- Selsis et al 2007

- 0.31 MSun

## Gliese 581 c’s past habitability

- Not
- habitable

- HZ for 0% clouds

- 50%

- 100%

-  = 6.75 g/cc (iron?)

-  = 4.7 g/cc (silicates?)

-  = 3.4 g/cc (water-rich?)

- Barnes, Raymond, Jackson, Greenberg 2008

-  Back in time (Gyr) 

- Age of Gliese 581 uncertain:
- Kinematics: >2-3 Gyr
- Very low X-ray flux: 8-10 Gyr
- (Delfosse et al 1998, Selsis et al 2007)

## Evolution of GJ 581 b, c

- Constraints:
- Planets b, c can’t cross 3:1 MMR
- Dynamical stability
-  Planet c was probably never in HZ
- Planet b gaseous
- Constrains planet c’s internal structure (Qc > Earth today)

- Barnes, Raymond, Jackson, Greenberg 2008

-  Back in time (Gyr) 

## HD 40307 (Mayor et al 2008)

- (Best-fit eccentricities consistent with zero)

- Stellar properties:
- M = 0.75 MSun
- Age = 6.1 ± 1.6 Gyr

## Past evolution of HD 40307 b

- Even with e0=10-10, past evolution crosses resonance  if Qc’ ~ 500 (Earth)
-  e0 must be 0

- Barnes et al 2009

## Constraints on e0, Q’ of HD 40307 b

- Two viable scenarios
- Planet b is gaseous (Q’ ~104 or larger)
- Planet b is rocky (Q’ ~ 500) and e0 is zero
- To constrain Q’, need 2+ planets, accurate determination of non-zero e0

- Barnes et al 2009

## Conclusions

- Accretion models predict a diversity in terrestrial planet mass, orbit, composition
- Hot Jupiter systems should also contain “hot Earths” and water worlds
- About 1/3 of known giant planet systems are good candidates for habitable planets
- Many ways to form “hot Super Earths”
- Need transit + RV data to differentiate
- Tides important for close-in planets
- Need good e to constrain internal structure

## Additional Information

- <date/time>

- sean.raymond@colorado.edu

## Additional Slides

## The Solar Nebula

- Raymond, Quinn & Lunine 2004; based on Abe et al 2000

- Disk temperature profile imprinted on primitive bodies;
- Lifetime of gaseous disk is few Myr

## The (liquid water) Habitable Zone

- Limit of tidal effects

- HZ

- Selsis et al 2007

## The Eccentric Habitable Zone

- Orbit-averaged flux is key for climate (Williams & Pollard 2002)
- Orbit-averaged flux F ~ a-2 (1-e2)-1/2
- a  = semimajor axis
- e = eccentricity
- HZ is farther out for high eccentricity

- Barnes, Raymond, Jackson, Greenberg 2007

## Implications for habitability

- Eccentric planets have finite “habitable lifetimes”
- Flux can vary hugely over orbit
- Synchronous rotation does not happen until eccentricity is zero

- Barnes, Raymond, Jackson, Greenberg 2008

## Tidal Heating

- Orbital energy dissipation leads to large amount of heat
- Heat flux >> Earth’s or Io’s for several Gyr in this case

- Jackson, Barnes, Greenberg Raymond 2008

## Accretion around low-mass stars

- Disk mass scales ~linearly with stellar mass with large scatter (Andrews & Williams 2005, 2007; Scholz et al 2006)
- Little mass to build habitable planets in situ
- In situ accretion vs migration testable with transits
- Rocky vs icy

- Raymond, Scalo & Meadows 2007

##   Time (yrs)

-   Time (yrs)

- Distance (AU)

## Tool: N-body integrator

- Hybrid symplectic integrator *Mercury* (Chambers 1999)
- Solve Hamilton’s equations for N bodies
- Split H = HA + HB
- A = unpertubed Kepler orbit, B = grav. kicks from other bodies
- Solve pieces separately (B numerically for close encounters)
- Combine in drift-kick-drift scheme: eAeBeA
- Fast, conserves energy well for dominant central mass (has been extensively tested)
- Assume inelastic collisions conserving water
- Added functionality: gas drag, giant planet migration (Mandell, Raymond & Sigurdsson 2006)
- Integrate 50-2000 particles for ~200 Myr
- Requires few days to 16 months of CPU time (~ N2)

## Initial conditions for late-stage accretion

- <date/time>

- Reality: In inner Solar System, equal mass in
- 50 -- few hundred embryos
- Trillions of km-sized planetesimals
- Simulations: limited to ~1000 particles
- Sim 0: starts in late stages of olig. growth
- 1885 initial particles between 0.5 and 5 AU
- Total mass 9.9 MEarth
- Jup. at 5.5 AU, e=0
- 0.0008 < M < 0.01 ME
- Embryo mass increases as r3/4 for ~r-3/2 disk (Lissauer 1987)

- Raymond, Quinn & Lunine 2006