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Planet Formation: Some Theoretical Considerations. Morris Podolak Dept. of Geophysical, Atmospheric and Planetary Sciences Tel Aviv University Exoplanets and Binaries Workshop Tel Aviv University December 2012. Attay Kovetz Ravit Helled Allona Vazan Asia Salner. Nature 1989.

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planet formation some theoretical considerations

Planet Formation: Some Theoretical Considerations

Morris Podolak

Dept. of Geophysical, Atmospheric and Planetary Sciences

Tel Aviv University

Exoplanets and Binaries Workshop Tel Aviv University December 2012


Ravit Helled

Allona Vazan

Asia Salner


Nature 1989

Latham et al., Nature 339 (1989)



  • 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.


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.

Ward (1997)


Planet formation is tough

You build models with all kinds of stuff

You fit all you can see

Then you go talk to Tsevi

And you learn that it’s still not enough!


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.

Stevenson (1982)







Alibert et al. (2005)


How much material remains in the envelope?

Based on Hubickyj et al. (2005)


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%.

Iaroslavitz and Podolak (2006)


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.

Movshovitz et al. (2009)


Subsequent evolution is affected by distribution of material

(and by equation of state).

20% all in core

20% all in envelope

(different EOS)

Baraffe et al. (2008)


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

Vazan et al. ( 2012 unpublished)


a = 4x10-3

a = 4x10-4

Lissauer et al. (2009)


Planet radius

Core radius

D’Angelo et al. (2010))


Summary so far:

Migration gets the planet to the turnover point more quickly.

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

But the corresponding increase in opacity keeps the planet extended.

The supply of gas is limited by the disk properties.

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


Suggestion 2 – Disk instability

160 years

350 years

Boss, 2007

Meyer et al. 2002


Will this instability even form?

    • The disk must be quite massive.
    • The disk must be quite cold.
    • Disk shear will prevent collapse.
    • Instability requires

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.



0.5 AU

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?


  • 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.

0.1 M

0.05 M

0.01 M

Helled & Schubert (2009)



  • 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

God is subtle but not malicious. – Albert Einstein

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

New observations inspire better theory.

Tsevi and I need to keep talking.