1. Physical processes in planetary clumps: impact on evolution and structure
Ravit Helled
Institute for Computational Science
Center for Theoretical Astrophysics & Cosmology 
University of Zurich
Physics Colloquium, Dec. 2016

2. If giant planets can for by GI, what should they be like?
Disk Instability
Toomre criteria (1964):
Cooling: disk will fragment when β<3 for β=tcoolΩ
Masses of clumps? Still debated 1-10 MJ
Fast Formation, most efficient at large radial distances
Mayer et al.
If giant planets can for by GI, what should they be like?

3. Objective: connecting planetary formation with composition
Giant planet formation via GI in proto-planetary disks.
Common view:
Giant planets have stellar compositions and no cores
S. Nayakshin, D. Forgan, K. Rice, E. Vorobyov and collaborators

4. Clump Evolution
Protoplanets of a few MJ evolve through 3 phases:
Pre-collapse: a quasi-static contraction with cool internal temperatures, molecular hydrogen, and radius a few thousand times RJ: pre-collapse
2) Dynamical collapse: dissociation of H2 when Tc reaches ~ 2000 K initiating a dynamical collapse (radius is a few times RJ).
3) Contraction on a long time-scale, protoplanets are compact & dense, R~ 1-2 RJ, 109 yrs.
Phase (1) is the crucial one for clumps’ survival, capture of solids, and core formation

5. The structure and evolution equations
P = pressure, ρ = density, g = Gm/r2 the gravity, m = mass, r = radius, G = gravitational const. ∇T ≡ (dlnT/dlnP) = temperature gradient , L = intrinsic luminosity, t = time, S = specific entropy, and ε ̇ = energy source.
Hydrostatic Equilibrium
Thermodynamic
Mass conservation
Energy conservation
The temperature gradient depends on the process by the heat transport mechanism (and this is something we don’t really know).

6. values normalized to Jupiter’s: Te = 124.4 K, Tc = 2×104 K,
Bodenheimer+ 1980
values normalized to Jupiter’s: Te = K, Tc = 2×104 K,
Pc = 3×1013 dyne cm−2
RJup = × 109 cm
Helled

7. Pre-collapse evolution for 3, 5, 7 and 10 MJ: luminosity, radius, central temperature vs. time
Helled & Bodenheimer, 2010

8. The composition of clumps can range from sub-stellar to super-stellar
dm/dt = Re(t)2σ(t)Ω
Planetesimal capture:
Clumps accrete solids in their feeding zone.
Accreted mass (0-100 M⊕) depends on: stellar mass (disk) metallicity, formation location, planetary mass, planetesimal properties (size, velocity, density), disk structure.
Enrichment from birth:
High solid concentrations in spiral arms.
Clumps can be enhanced at birth by ≈ 2.
Helled et al. 2007, 2008
Helled & Schubert, 2008, 2009
See Helled, Bodenheimer, Alibert, Podolak, Nayakshin, Boley, Boss, Fortney, Meru & Mayer , 2014 (PPVI)
Accumulation of solids where clumps form
Boley, Helled & Payne, 2011

9. The environment in which clumps are formed affects the final composition/structure
Enrichment from 1 to 110 M of heavy elements!
0.1 M
accreted mass decreases due to long accretion times
Captured mass vs. radial distance for three
different disk masses (metallicities) and density distributions
0.05 M
0.01 M
The solid, dashed & dotted curves are for density distributions with  = 1/2, 1 and 3/2, respectively.
Higher surface density leads to larger heavy element enrichment.
Lower  values allow more enrichment at larger radial distances.

10. Clumps can have cores
Grain can coagulate, grow, and settle to the center.
Accreted planetesimals can sink to the center and also pollute the envelope with metals.
Smaller clumps will have larger cores:
1 MS ~ 80% of available solids
1 MJ ~ 10% of available solids
3 MJ ~ 10% of available solids
M > 5 MJ no core (hot, fast collapse)
Miller & Fortney, 2011
Differentiated structure?
Core is likely to be composed of silicates (ice sublimates in gaseous envelope)
Helled et al., 2008; Helled & Schubert, 2008

11. The role of Metallicity/Opacity
Evolution of 7 MJ vs. time
with different metallicities with grain growth and settling
Evolution of 7 MJ vs. time
with different metallicities
Blue: solar
Black: solar/3
Red: 3×solar
Blue: solar
Black: solar/3
Red: 3×solar
The dashed, dotted, and dot-dashed curves are Log(Tc) [K], Log(R/RJup) [cm], and Log(L/1026) [erg s-1]
Helled & Bodenheimer, 2011

12. When grain growth is included the evolution timescale reverses
With grain growth & settling the contraction timescale is ~1500 yrs
Pre-collapse evolution timescales for the two different cases considered:
Case I: the opacity is scaled with planetary metallicity and is constant with time.
Case II: the opacity can be reduced with time as a result of grain growth & settling.

13. The influence of the surrounding disk
Use disk model from Bell et al. (1997): Macc= 10-6 M/yr & α=0.01,
include the disk temperature and pressure in boundary conditions.
Disk 1: M ̇ = 10−6 M⊙ yr−1 and α = 10−2
Disk 2: M ̇ = 10−7 M⊙ yr−1 and α = 10−2
Disk 3: 5*disk 1 in mass, same T
Vazan & Helled, 2012

14. The influence of the surrounding disk
1 MJ clump at 10 AU is unable to contract and is expected to dissolve in the disk.
Limits on survival from planetary evolution arguments.
Pre-collapse evolution for 1 MJ for radial distances between 10 and 50 AU.
Vazan & Helled, 2012

15. The influence of the surrounding disk
1 MS dissolve at ∼12 AU;
3 MJ at ∼9 AU, and 5 MJ at ∼7 AU.
Clumps can survive at smaller distances only if they reach these locations after dissociation & contraction.
Pre-collapse evolution for 1 MJ for radial distances between 10 and 50 AU.
Vazan & Helled, 2012

16. Low-mass clumps are more affected by the disk
Pre-collapse time can range between years.
The exact number depends on planet mass, location, disk properties.
Vazan & Helled, 2012
More massive clumps contract faster are less sensitive to the presence of the disk.
Pre-collapse evolution for Saturn-mass MS (red), 1 MJ (blue), 2 MJ (black), and 3 MJ (green) at three radial distances: 10 AU (dashed curves), 20 AU (solid curves), and 50 AU (dotted curves). Shown are the planetary radius R, central temperature Tc, and luminosity L.

17. The Effect of Gas Accretion
1 50AU
Accreting clumps collapse faster due to efficient heat release caused by the gas accretion.
Should be coupled with disk models self-consistently
Vazan & Helled, 2012
Understanding accretion
luminosity
Pre-collapse evolution of 50 AU with gas accretion rates (solid curves) of , and 0.05 Mearth/yr (red, blue and black, respectively). The final masses are 1.29 MJ, 1.9 MJ, and 2.73 MJ, respectively. Also shown is the evolution without accretion (dotted curves) of clumps with initial masses of 1.29 MJ (red), 1.9 MJ (blue), and 2.73 MJ (black).

18. Conclusions
Including physical processes beyond the formation of clumps can significantly affect the clumps evolution and composition.
High metallicity (opacity) leads to slower contraction, accounting for grain growth & settling reverses the trend.
Enrichments in clumps can range from negligible to very large.
The disk has a key influence on the pre-collapse of clumps – there is a critical distance for survival (~ 10 AU for 1 MJ).
More massive clumps are less influenced by the disk.

19. Conclusions Work in progress
Gas accretion leads to shorter contraction time (more massive planets).
Differences in pre-collapse timescale (same mass) can lead to significant differences in the final planetary structure and bulk composition due to different efficiency in planetesimal accretion, core formation etc.
Giant planets, if formed by GI, must form and remain at large radial distances.
Clump evolution must be included in planetary population models in GI.
Work in progress