Planet Formation: Some Theoretical Considerations

Morris PodolakDept. of Geophysical, Atmospheric and

Planetary SciencesTel Aviv University

Exoplanets and Binaries Workshop Tel Aviv University December 2012

Attay KovetzRavit HelledAllona VazanAsia Salner

Nature 1989 Latham et al., Nature 339 (1989)

Argument• To form a Jupiter-mass planet, with a lot of H, He you need a massive core to attract the gas.• To form a massive core you need a lot of solids in the disk.• To get a lot of solids you need to be far enough from the star for ice to be stable, i.e. beyond the snow line.• The snow line has got to be at several AU from the star.

Conclusion: You cannot have a giant planet at 0.3 AU.… unless the planet moves.

Ward (1997)

More realistic physics changes this picture. Including magnetic fields, turbulence, realistic temperature gradients, etc. can lengthen the lifetime against migration, and even reverse its direction.

Planet formation is toughYou build models with all kinds of stuffYou fit all you can seeThen you go talk to TseviAnd you learn that it’s still not enough!

Pollack et al. (1996)

Mamajek (2009) based on Haisch et al. (2001)

Fortney & Nettelmann (2010)

How do we get around the timescale problem?

Suggestion 1 – Speed up the Core Accretion Scenario

• Grow a larger core initially by utilizing migration.

• Increase the molecular weight of the envelope.• Decrease the opacity in the envelope. • Decrease the accretion rate during envelope contraction.

7/12

7/3

7/15

/ln/1043.2

coreplanet

corecore

core

RRdtdM

MM

Stevenson (1982)

solids

gas

8 15 15

Alibert et al. (2005)

How much material remains in the envelope?

Based on Hubickyj et al. (2005)

Iaroslavitz and Podolak (2006)

Most of the rock sediments to the core.Most of the ice remains as vapor in the envelope.

The molecular weight increase can reduce the critical core mass by ~10%.

The grain size distribution in the envelope is not that of interstellar clouds.

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rmQtrmF

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Movshovitz and Podolak (2008)

Movshovitz et al. (2009)

This calculation does not allow grains to break up. Including grain breakup leads to smaller grains and the opacity goes back up. The question is still open.

Fortney et al. (2009)

Baraffe et al. (2008)

20% all in core

20% all in envelope(different EOS)

Subsequent evolution is affected by distribution of material

(and by equation of state).

Vazan et al. ( 2012 unpublished)

Increased molecular weight in the envelope makes the planet smaller, but the associated opacity increase will reverse this effect and keep the planet inflated.

Lissauer et al. (2009)

a 4x10-4

a 4x10-3

D’Angelo et al. (2010))

Planet radius

Core radius

1. Migration gets the planet to the turnover point more quickly.

2. Higher molecular weight in the envelope makes the planet more compact.

3. But the corresponding increase in opacity keeps the planet extended.

4. The supply of gas is limited by the disk properties.

We still need to put all this together into a self-consistent model.

Summary so far:

Suggestion 2 – Disk instability

Boss, 2007 Meyer et al. 2002

160 years 350 years

Will this instability even form?• The disk must be quite massive.• The disk must be quite cold.• Disk shear will prevent collapse.• Instability requires

1~

GcQ s

How do you get the proper high-Z enhancement?

• Traditional models of Jupiter and Saturn seem to require dense cores.

• Jupiter’s envelope is enhanced over solar composition by a factor of ~ 3.

• Saturn’s envelope is enhanced by even larger values.

Helled et al. (2006)

0.5 AU

Jupiter-massclump

Helled et al. (2006)

Microphysical Considerations

• Grains collide and grow.• Grains settle towards the center.• As the protoplanet contracts it gets hotter.• How much mass can settle towards the center before it gets too hot for individual grains to survive?

Fortney & Nettelmann (2010) after Saumon & Guillot (2004)

Assumptions• Planetesimals uniformly distributed in space.In fact planetesimal orbits get perturbed by close encounters and their eccentricities change.• Planetesimals all move with the same velocity relative to the protoplanet.In fact different eccentricities mean different encounter velocities.• If a planetesimal is captured the other planetesimals re-arrange themselves so that their space distribution remains uniform. In fact they don’t, and in addition, planetesimals originating in different regions may have different compositions, and it is interesting to see the effect of this on the capture rates.• Only 2 – body interactions (planetesimal + planet) are considered.In fact for big protoplanets (with initial radii of the order of the Hill sphere radius) you really need to consider 3 – body interactions.• If the planetesimal is not captured, its interaction with the protoplanet is ignored.In fact this is not a good assumption.• No planetesimals are ejected from the system.In fact planetsimals may be ejected after close encounters with the protoplanet.

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Planetesimal

Rmin

(AU)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Planetesimal

Rmin

(AU)

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.05

0.1

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0.35

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0.45

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Planetesimal

Rmin

(AU)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.1

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0.8

0.9

1

Time (yr)

Mas

s fra

ction

Helled et al. (2006)

Outer

All Planetesimals

Inner

Haghighipour and Podolak (unpublished)

Vazan & Helled (2012)

Helled & Schubert (2009)

0.1 M

0.05 M

0.01 M

Summary

• Accretion is almost certainly a mechanism for planet formation (e.g. terrestrial planets), so we should expect cores at all distances from the star.• The size of the core increases with increasing distance from the star… but so does the time to form it.• Can the core accretion scenario form the gas giant planets we see in our solar system and in others? Probably, but there are still unanswered questions.• Can the disk instability scenario form the gas giant planets we see in our solar system? This is less clear, but it may be a viable hypothesis for gas giants at large distances.

Not only is the universe stranger than we imagine, it is stranger than we can imagine. – Sir Arthur Eddington

There is a tendency to stop looking for more physics once the model fits the observations.

New observations inspire better theory.

God is subtle but not malicious. – Albert Einstein

Tsevi and I need to keep talking.