The giant challenges in our understanding of giant planet...

OHP colloquium, Okt2015 N.Nettelmann @ U Rostock Internal structure models

The giant challenges in our understanding of giant planet internal structures

Nadine Nettelmann (U Rostock)

acknowledgements: R. Redmer, M. French, M. Bethkenhagen, A. Becker (U Rostock), J.J. Fortney, (UCSC), S. Hamel (LLNL)

Introduction Method of GP internal structure modeling

EGPs: M-R relations & composition estimates Jupiter & Saturn: EOS, standard models, new approaches

Uranus & Neptune: ices and ice-rich models

Republic of Kasakhstan

UCSC

Keck

NASACassini / NASA

M. French / VASP

Sun


1-100 bar , ~100-1000 K

• mostly H-He M-R

• high pressures ( < ~100 Mbar) M-R

• warm (~10 000 K)

luminosity, formation theory

• non-ideal, dense matter, conducting , H+, e-, ionized C,N,O plasma / conducting,

convective, adiabatic

fluid, mostly H2 , convective, adiabatic

~1 Mbar, few 1000 K

~5 - 50 Mbar, ~5 - 150,000 K

Introduction

<100 Mbar

transition region

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1-100 bar , ~100-1000 K

~1 Mbar, few 1000 K

~5 - 50 Mbar, ~5 - 150,000 K

Introduction

<100 Mbar

what do we mean by “internal structure“ ? • composition (e.g. bulk water content, bulk rock content)

• size and number of chemically distinct layers (e.g. core)

what do we want to know, and why ? • core mass -> formation (!?!)

• bulk enrichment -> formation

• atmospheric energy balance -> fundamental science

• magnetic dynamo operation -> fundamental science

fluid, mostly H2 , convective, adiabatic

transition region

plasma / conducting, convective, adiabatic

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Outline

Method of EGP internal structure modeling EGPs: M-R relations & composition estimates Jupiter & Saturn

Uranus & Neptune


EGP structure: general assumptions

ad∇

• 2 Layer (core + envelope)

• adiabatic interior

• radiative atmosphere (BC)

• hydrostatic equilibrium

a t m o s p h e r e

5 / 37


general assumptions : adiabatic interior

2D EOS { T, P, ρ(T, P), s(T,P) } -> 1D path { T(P)s, ρ(P)s } at constant entropy s

output: internal Temperature – Pressure – Density profile input: (i) entropy

(ii) EOS of single components, (ii) composition

LOW-MASS STARS / BROWN DWARFS thermal convection because of high opacity adiabatic

EARTH: thermal convection + thermal diffiusion

(Fe) core -- (Mg,Si,O) mantle boundary: magnetic field

T ad( )∇ >∇

5T ad( ~ 10 )−∇ −∇

T ad( )∇ ∇�

T ad( )∇ =∇

T ( , , , ,..., )tot TF κ γ η κ∇

logT log

d Td P∇ ≡

6 / 37


atmosphere (boundary condition)

output: entropy s input: inbound heat flow Teq (Tstar, obital a) ; outbound heat flow Teff ; model atmosphere (composition, opacities, Teff, ...)

9.5 AU (Saturn)

0.1 AU

atmospheric Pressure – Temperature profiles

hot / young / weakly

irradiated

cold / old / strongly

irradiated

➢ Fortney, Marley, Barnes 2007

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general assumptions : 2-Layer structure

HeHO,C,N, Si, Mg

rocks, ices

adiabatic, convective,

homogeneousFree parameters: • core mass (Mcore)

• envelope Z (Zenv)

• composition of Z-material (Zi)

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hydrostatic equilibrium

Boundary Conditions: (i) P(M) ~ 0 , (ii) r(0) = 0 input: P-ρ- relation , i.e. EOSs & composition { Mcore, Zenv, Zi }

output: R(M) for given ρ(P) -> M-R relations

alternative output: bulk Z, i.e. one of { Mcore, Zenv, Zi } for given R(M)

44dP Gmdm rπ

= −

2 1(4 )dr rdm

π ρ −=

0.... pm M=

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Outline

Method of GP internal structure modeling

EGPs : M-R relations & composition estimates Jupiter & Saturn

Uranus & Neptune


M-R relations for given compositions

➢ Fortney, Marley, Barnes 2007

• Zenv = 0

• Zice = Zrocks = 0.5

• Mcore = 10...100 MEarth

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EGP composition estimates for observed Mp-Rp

weakly irradiated (Miller &Fortney 2011)

(Guillot 2006) (Maciejewski et al 2011)

(Deleuil et al 2011) perhaps brown dwarfs (Leconte, Baraffe, Chabrier 2009)

Jup

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results for Mz, Zp for weakly irradiated planets

➢ Miller & Fortney 2011

MZ ~ 10 ME, Zp ~ 2-10x ZstarZ p

lane

t / Z

star

Mz

/ MEa

rth

Zp

planet

MZM

=

?

?

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Tidal Love number k2 breaks the degeneracy

Given: Mp , Rp , . + temperature profile and atmospheric boundary condition

The total heavy element content can be determined, but not the core mass or envelope enrichment .

Given: Mp , Rp , and the Love number k2 . + temperature profile and atmospheric bounday condition

Assuming a 2L structure, both Mcore and Zenv can be

determined.

H

H H He

core

envelope metallicity

He

He

➢ Kramm et al. (2011), A&A

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➢ Kramm, Nettelmann, Fortney et al 2012 ➢ Batygin et al 2009 ➢ Winn et al 2010

Mp = 0.85 MJ , Rp = 1.3 RJ , and also k2 = 0.27-0.38

HAT-P-13b model, similar to Jupiter

HHem

e

t

a

l

s

HAT-P13b, the only planet with inferred k2

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Observable Solar GP Extrasolar GP

Mass Mp 14.5 – 318 MEarth RV & Transit

Radius Rp equatorial radius Req mean R (Transit)

Pressure P (Rp) 1 bar 1 mbar

T (Rp) 70 - 170 K 500 - 2000 K

mean helium mass fraction Y 0.27 (solar) 0.25 - 0.28

atmospheric He mass fraction Y1 0.27 Y1 = Y

atmospheric metallicity Z1 2 x solar spectroscopy

period of rotation ω 9 – 17 h ω orbital period (days)

gravitational moments J2n J2, J4, J6 -

Love number k2 - k2 (e, TTV )

age 4.56 Gyr 0.3 – 10 Gyr

Teff 60 - 120 K secondary eclipse / imaging

≤

≈≥

Observational constraintsobservational constraints

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Outline


EGPs: M-R relations & composition estimates

Jupiter & Saturn EOS, standard models, new approaches

Uranus & Neptune


EOS from simulations in comparison with experiments

DEUTERIUM [1,2] quasi-isentropic and isothermal compression

WATER [3] single & double shock compression

M. French / VASP

[1] Becker et al 2013

[2] Loubeyre et al 2007

[3] Knudson et al 201218 / 37


Single shock experiments to probe the H EOS

The different H EOS are stiff/compressible at individual pressure levels.

Sesame: chem. picture ➢ Los Alamos database

SCvHi: chem. picture ➢ Saumon et al. (1995), ApJS

H-REOS: simulations ➢ Holst et al. (2008), PRB

Experiments:

➢ Knudson & Desjarlais (2009) ➢ Boriskov et al. (2005) ➢ Knudson et al. (2004), PRB

➢ Nellis et al (1983)

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Jupiter standard models

Yatm=0.238

helium

hydrogen

Zouter = Zinner(J2) ➢ Saumon & Guillot 2004 ➢ Militzer, Hubbard et al . 2008 (Y=0.238)

Zouter(J4), Zinner(J2) ➢ Chabrier et al 1992 ➢ Guillot 1999 ➢ Nettelmann et al 2008,2012, . Becker et al 2014

1-10 Mbar, 6-11 000 K

~40 Mbar, 17-21 000 K

T1bar=165-170 K

OCNSP...

spacetelescope.org

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Core mass and outer envelope metallicity of Jupiter models with different EOS

Ab initio LM-REOS.2 gives Jupiter models in agreement with the

measured noble gas abundances, while SCvHi and Sesame EOS

support the values of N,C.

SCvHi

Sesame

LM-REOS

heavy element abundance (solar units) in the outer envelope

The maximum core mass is predicted to be 3 ME (Sesame),

5 ME (SCvHi), and 8 ME (LM-REOS).

P1-2

➢ Atreya et al. 2003, PSS

➢ Lodders 2003, ApJ

➢ Saumon & Guillot (2004), ApJ ➢ Fortney & Nettelmann (2010)

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Expected O/H measurement by Juno (2016)

A discrimination of the competing Jupiter models (and EOS) is in reach if the O:H abundance will be measured by Juno.

3--12x solar

4--7

< 4.5 LM-REOS.2

SCvHi EOS

Sesame EOS

outer envelope metallicity (solar units)

NASA

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challenge: Jupiter‘s atmospheric helium depletion

Observed He depletion suggests helium rain.

23 / 37


challenge: SATURN’s excess luminosity

Jupiter: standard models reproduce all observational constraints

Saturn: standard models predict too low luminosity

7 / 3224 / 37


challenge: SATURN‘s dipolar magnetic field

➢ Stevenson 1980, 1982 ➢ Cao, Russell, Christensen et al 2011 ➢ Cao, Russell, Wicht et al 2012

H2, He poorly conducting convective

H/He demixing zone? (gradual He concentration? stably stratified? differentially rotating ? filtering of non-dipolar components?) H+, He rain

dynamo-generation of mag. field (convective, metallic)

core

Saturn‘s magnetic field is highly axis-symmetric. A thick stable, and/or differentially rotating region can axisymmetrize the B-field. Such a region may result from H/He demixing or core erosion.

1 Mbar, ~ 5000 K

H+, He

Cassini / NASA

www.lasp.colorado.edu/~bagenal/

< 1°

Magnetic axis Rotation axis

25 / 37


Inhomogeneous & Superadiabatic interior with layered instead of overturning convection?

➢ Leconte & Chabrier 2012, A&A

µ

An inhomogeneous, superadiabatic planet may be ~50% more enriched in heavy elements.

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Semi-convection can dramatically change the cooling behavior. Figures show L(t) for different mixing lengths of layered-convection.

1 MJup, Z-gradient (Vazan et al 2015)

1 MSat, Z-gradient (Leconte & Chabrier 2013)

1 MJup, He-gradient (Nettelmann et al 2015)

log

L / L

sun

log time (Gyr)

time (Gyr)

Teff

(K)

Teff

(K)

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Outline


EGPs: M-R relations & composition estimates

Jupiter & Saturn

Uranus & Neptune: ices and ice-rich models for Uranus


Voyager 2 flyby 1986 Voyager 2 flyby 1989

Uranus Neptune

• Mass: 14.5 M , Radius: 4 R

• mean densitiy : 1.3 g/cm3

• orbital distance : 19.2 AU

• heat flow Teff ~ 59 K

• irradiation Teq ~ 59 K

⊕ ⊕ • Mass: 17 M , Radius: 3.9 R

• mean densitiy : 1.7 g/cm3

• orbital distance : 30 AU

• Teff ~ 59 K

• Teq ~ 46 K

⊕ ⊕

observational constraints

EGPs: - GJ 436b

- HAT-p 11b

- Kepler 4b

Cassini/NASASun

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phase diagrams

WATER

➢ Redmer et al 2010, Icarus

➢ Bethkenhagen, French, Redmer 2013. PRB

AMMONIA

Superionic

Dissociated

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phase diagram of 1:1 water-ammonia mixture

➢ Bethkenhagen, Cebulla, Redmer, Hamel 2015

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Phase diagram of synthetic URANUS mixture (H:O:C:N ~ 28:7:4:1)

➢ Chau, Hamel, Nellis 2011

Carbon clustering or superionic deep interior?

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Experiments (gas-gun):

reverberating shock

single shock

Theory: computer simulations


Standard URANUS model with H2O-CH4-NH3 EOS

assumptions: heavy elements = water, ammonia, methane

rocks confined to core 3-layer structure, adiabatic outstanding property: icy lower mantle achievements: presence of magnetic dynamo, O/C/N = solar

less convincing: ice/rock ratio ~ 15x solar

too high luminosity (~too long cooling time)

molecular

ionic

super-ionic

poly-mers

molecular: H2O, N2, H2, CH4 molecules

➢ Betkenhagen et al, in prep ➢ Podolak & Reynolds 1987

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challenge: Uranus‘ low luminosity

too long cooling time (too high luminosity) of adiabatic models, whatever one varies

➢ Hubbard & Marley 1980

➢ Hubbard et al 1995

➢ Fortney et al 2011 ➢ Nettelmann et al 2013

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Uranus: compositional and thermal layer boundary

(cm2/s)

4.5 Gyr

If the layer boundary is diffusive, it‘ll stay stably stratified forever. This suggests presence of thermal boundary layer.

35 / 37


First Uranus model with (very simplified) thermal boundary can explain both the luminosity and the gravity data.

➢ Nettelmann, Wang, Fortney, Hamel et al, submitted

1

T eff

(K)

L = LincTeq

36 / 37


Summary

• EGP: measured M-R allow to derive bulk mass of heavy elements.

• EGP: internal structure models indicate MZ >= 10 ME.

• Tidal Love number k2 may break the degeneracy.

• Interior models usually applied to EGPs do not hold for the solar GPs.

• Jupiter: O/H to be measured by Juno

• layered-convection consistent with luminosity of Jupiter and Saturn

• Uranus‘ may be ice-rock rich, without solid ices.

• Outlook: construction of solar GP models that also are consistent with the observed magnetic fields

Thank you for attention


Appendix


H phase diagrams

21 / 41

Log Pressure (Mbar)

solid H2 solid H

degenerate TCP

classical TCP

fluid H2

fluid H

0-2-4-6 2 4 6

2

0

3

4

5

Log

T (K

)

Liquid-Liquid Transition

(ab initio sims)

➢ McMahon et al (2012), Rev. Mod. Phys.➢ Stevenson (1982), Ann. Rev. E&Planet Sci.

1 Mbar

Wigner & Huntington (1935): prediction of metallization of solid H at sufficiently high densities as ,

2/3~kin elE ρ 1/3~ie elE ρ−

Ebeling et al 1985 Saumon, Chabrier et al 1995 Schlanges, Bonitz et al 1995

Fortov et al 2007, quasi-isentropic compression


Reflectivity signal inferred from Z-machine experiment

24 / 41

absorption at 532 nm

deuterium transparent

deuterium metallizes

➢ Knudson et al (2015), . Science


Liquid-Liquid transition in D found at 3 Mbar using Sandia‘s Z-machine

25 / 41

PIMD

➢ PIMD: Morales et al 2013, PRL

➢ PBE: Lorenzen et al 2010, Morales et al 2010

➢ vdw-DF2: Lee et al 2010

PBE DF1 NQE

vdW-DF2 NQE

HSE DF2

➢ Knudson et al (2015), . Science


simple thermal boundary layer model for Uranus

ΔT across layer boundary is varied with time (linear increase with T1bar)

ΔT (today) is adjusted to yield the proper cooling tome (luminosity)

11 / 20


Brown dwarf radii, effect of H-He-REOS.3

• H-He REOS.3 predicts ~2 % larger radii for brown dwarfs.

• PLATO (launch 2024) accuracy <2%

• possible test of BD composition ~ stellar composition

➢ Becker, Lorenzen, Fortney, Nettelmann, Schöttler, Redmer 2014, ApJS

➢ Saumon, Chabrier, van Horn (1995), ApJS ➢ PLATO: Rauer et al 2013

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weak irradiation : Firr < 150 FEarth

➢ Miller & Fortney 2011

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