THE STATE OF KNOWLEDGE OF ICE GIANT INTERIORS

Brigette Hesman (UMD / NASA GSFC)

with significant contributions from:

Tristan Guillot (Observatoire de la Cote d’Azur)

Nadine Nettelmann (UC Santa Cruz)

Ravit Helled (Tel-Aviv University)

Workshop on the Study of Ice Giant Planets 7/30/14 1 WHY INTERIORS?

• What is the motivation for studying Ice Giant interiors?

Two-fold:

1. Interiors of the planets are a historical record of the planetary formation process

- we need to investigate the full continuum our solar system’s planetary interiors to build the architecture of the early solar system

- these studies provide constraints on the physical and chemical properties of protoplanetary disks

2. Uranus and Neptune are the Super-Earth’s/Mini-Neptune’s of our solar system

- a class of exo-planets similar in size to our Ice Giants is continuing to grow due to the highly successful Kepler mission

- studying the interiors of our local Ice Giants provides the foundation for entangling the composition of extra-solar planets

Workshop on the Study of Ice Giant Planets 7/30/14 2 THE “ICE GIANTS”

• Uranus and Neptune were classified as the Ice Giants to distinguish them from the Gas

Giants because of their smaller gaseous envelopes (10-20% of their mass as H2 and He)

• Uranus and Neptune have historically been thought of as icy twins ➔ Very similar mass, radii, gravitational moments, rotation periods ➔ Assumed to be water rich based on formation theories

Uranus: 14.5 M⊕ @ 19.2 AU Neptune: 17.1 M⊕ @ 30 AU

THEREFORE, VERY SIMILAR INTERIORS … RIGHT?

MAYBE / MAYBE NOT

Workshop on the Study of Ice Giant Planets 7/30/14 3 DICHOTOMY

URANUS NEPTUNE • Low internal heat flux • Strong internal heat flux • High obliquity (98°) • Saturn-like obliquity • Dense narrow rings • Extended dust disk with diffuse rings • 5 of the largest satellites on • 2 major satellites on irregular regular orbits orbits

Different Formation Histories?

Different Internal Structures?

Workshop on the Study of Ice Giant Planets 7/30/14 4 DIFFERENT FORMATION HISTORIES?

Standard Formation Model (Core Accretion): Three phases of formation: Phase 1: Initial core accumulates planetesimals (presumably rocks) by runaway accretion Phase 2: Low rate of accretion of gas and planetesimals Phase 3: Collapse of gas onto core of planet which provides hydrogen envelope

• Uranus and Neptune probably never reached phase 3 – “failed giant planets” • Hydrogen and helium in the envelopes of these two planets was probably acquired in stage 2 … therefore, small envelopes

BUT

• Problems: formation timescales, critical core mass, getting a Uranus-like composition Multiple other models to solve issues: 1. Formation closer to the sun (Nice Model) 2. Disk physics/chemistry – disk evolution, enhancing the solids 3. High accretion rates 4. A combination …

All formation models have trouble creating the dichotomy we see in Uranus and Neptune

Workshop on the Study of Ice Giant Planets 7/30/14 5 DIFFERENT FORMATION HISTORIES?

Standard Formation Model (Core Accretion): Three phases of formation: Phase 1: Initial core accumulates planetesimals (presumably rocks) by runaway accretion Phase 2: Low rate of accretion of gas and planetesimals Phase 3: Collapse of gas onto core of planet which provides hydrogen envelope Maybe Uranus and • Uranus and Neptune probably never reached phase 3 – “failed giant planets” Neptune formed in the • Hydrogen and helium in the envelopes of these two planets was probably acquired in stage 2 … therefore, small envelopes same method and did have similar structures BUT after formation. Then • Problems: formation timescales, critical core mass, getting a Uranus-like composition Multiple other models to solve issues: why the DICHOTOMY? 1. Formation closer to the sun (Nice Model) 2. Disk physics/chemistry – disk evolution, enhancing the solids 3. High accretion rates 4. A combination …

All formation models have trouble creating the dichotomy we see in Uranus and Neptune

Workshop on the Study of Ice Giant Planets 7/30/14 6 DIFFERENT INTERNAL STRUCTURE? The Possible Role of Giant Impacts Uranus: Oblique Collision Neptune: Radial Collision

Angular momentum deposition causes: Energy of impact causes: 1. Inhibition of core convection 1. Core mixing resulting in an adiabatic and 2. Strong tilt of planet mixed interior 2. Efficient cooling

A more thorough understanding of these planets interiors will reveal details about their formation and evolution in our solar system Workshop on the Study of Ice Giant Planets 7/30/14 7 DEFINING THE INTERIOR

The gravitational field of a rotating planet:

r, θ, φ are spherical polar coordinates M = total planetary mass a = equatorial radius (at the 1bar level) J2n = gravitational moments P2n = Legendre polynomials ω = angular velocity of rotation

With M and Jn constrain the INTERIOR DENSITY, ρ(r)

Workshop on the Study of Ice Giant Planets 7/30/14 8 The Astrophysical Journal,726:15(7pp),2011January1 Helled et al.

Jupiter and Neptune that fit their measured gravitational fields are 4 derived using Monte Carlo searches (Marley et al. 1995;Podolak J6 et al. 2000). This approach is free of preconceived notions about planetary structure and composition and is not limited by the 3 J4 EOSs of assumed materials. Once the density profiles that fit the gravitational coefficients are found, conclusions regarding their nctions u J2 possible compositions can be inferred using theoretical EOSs 2

tion f (Marley et al. 1995). u J0 In this paper, we apply the method previously used in our models of Saturn (Anderson & Schubert 2007; Helled et al. Contrib 1 2009a)toderivecontinuousradialdensityandpressureprofiles core CORE “SAMPLING” that fit the mass, radius, and gravitational moments of Uranus and Neptune. The use of a smooth function for the density 0 0.0 0.2 0.4 0.6 0.8 1.0 with no discontinuities allows us to test whether Uranus and The Astrophysical Journal,726:15(7pp),2011January1 Helled et al. Helled et al. (2011) Normalized Mean Radius β Neptune could have interiors with no density (and composition) Jupiter and Neptune that fit theirNeptu measuredne gravitational fields are discontinuities. Section 2 summarizes the models and results. In 4 4derived using Monte Carlo searches (Marley et al. 1995;Podolak Section 3,weusephysicalequationofstatetablestoinferwhat J6 et al. 2000). This approach is free of preconceived notions about these density distributions imply about the internal composition J planetary structure and composition and is not6 limited by the of Uranus and Neptune. Conclusions are discussed in Section 4. 3 J4 3 EOSs of assumed materials. Once the densityJ4 profiles that fit the gravitational coefficients are found, conclusions regarding their 2. INTERIOR MODEL: FINDING RADIAL PROFILES OF nctions nctions

u DENSITY AND PRESSURE u J2 possible compositions can be inferred using theoretical EOSs 2 2 J2 tion f tion f (Marley et al. 1995). J0 The procedure used to derive the interior model is described in u u J0 In this paper, we apply the method previously used in our detail in Anderson & Schubert (2007)andHelledetal.(2009a). models of Saturn (Anderson & Schubert 2007; Helled et al. Contrib Contrib 1 1 The method is briefly summarized below. 2009a )toderivecontinuousradialdensityandpressureprofiles core core The gravitational field of a rotating planet is given by that fit the mass, radius, and gravitational moments of Uranus 2n and Neptune. The use of a smooth function for the density GM ∞ a 1 2 2 2 0 0 U 1 J2nP2n (cos θ) + ω r sin θ, 0.0 0.2 0.4 0.6 0.8 1.0 0.0with no discontinuities 0.2 0.4 allows us 0.6 to test whether 0.8 Uranus 1.0 and = r − r 2 ! n 1 % Normalized Mean Radius β Neptune could haveNormalized interiors Mean with Radi nous β density (and composition) "= # $ (1) Neptune Figurediscontinuities. 1. Normalized integrands Section of2 thesummarizes gravitational the moments models (contribution and results. In 4 functions)Section of Jupiter3,weusephysicalequationofstatetablestoinferwhat (top) and Neptune (bottom). The values are normalized to where (r, θ, φ) are spherical polar coordinates, G is the gravita- Ice Giants have advantage of gravitational moments sampling the core! make the area under each curve equal unity. J is equivalent to the planetary these density distributions imply0 about the internal composition tional constant, M is the total planetary mass, and ω is the angular J6 mass. The range of possible core sizes is indicated. Here, core designates a regionof of Uranus heavy elements and Neptune. below the Conclusions H/He envelope. are It is discussed clear that Neptune’s in Section 4. velocity of rotation. We assume that the planets rotate as solid 3 (Uranus’) interior is better sampled by the gravitational harmonics compared to J4 bodies with Voyager rotation periods (Table 1), although this Jupiter (Saturn).2. INTERIOR MODEL: FINDING RADIAL PROFILES OF assumption is a simplification since the interior rotation profiles nctions u (A color version of this figureDENSITY is available AND in the online PRESSURE journal.) of Uranus and Neptune are actually poorly known and could 2 J2

tion f J0 The procedure used to derive the interior model is described in be more complex (Helled et al. 2010). The potential U is rep- u uses physicaldetail in equationsAnderson of & state Schubert (EOSs) (2007 of the)andHelledetal.( assumed materials2009a). resented as an expansion in even Legendre polynomials, P2n Workshop on the Study of Ice Giant Planets 7/30/14 9

Contrib 1 to deriveThe method a density is briefly(and associated summarized pressure below. and temperature) (Kaula 1968;Zharkov&Trubitsyn1978). The planet is defined core profile thatThe best gravitational fits the measured field of a gravitational rotating planet coefficients. is given by The by its total mass, equatorial radius a at the 1 bar pressure level, physical parameters of the planets, such as mass and equatorial and harmonic coefficients J2n,whichareinferredfromDoppler 2n radius, areGM used as additional∞ a constraints. The masses1 2 2 and2 tracking data of a spacecraft in the planet’s vicinity. 0 U 1 J2nP2n (cos θ) + ω r sin θ, 0.0 0.2 0.4 0.6 0.8 1.0 compositions= r of the three− layersr are modified until2 the model The measured gravitational coefficients of Uranus and Nep- ! n 1 % Normalized Mean Radius β fits the measured gravitational"= # coefficients.$ The models typically tune are listed in Table 1.Theobservedgravitationalcoefficients (1) Figure 1. Normalized integrands of the gravitational moments (contribution assume an adiabatic structure, with the adiabat being set to the J2, J4 correspond to the arbitrary reference equatorial radii Rref functions) of Jupiter (top) and Neptune (bottom). The values are normalized to measuredwhere temperature (r, θ, φ) are at spherical the 1 bar polar pressure coordinates, level (HubbardG is the et gravita- al. of 26,200 km and 25,225 km for Uranus and Neptune, respec- make the area under each curve equal unity. J0 is equivalent to the planetary 1991;Podolaketal.1995). Although this method has succeeded tively (Jacobson et al. 2006;Table1). Another physical property mass. The range of possible core sizes is indicated. Here, core designates a tional constant, M is the total planetary mass, and ω is the angular region of heavy elements below the H/He envelope. It is clear that Neptune’s in findingvelocity a model of rotation. that fits We both assumeJ2 and thatJ4 for the Neptune, planets norotate model as solid that is used in the interior model is the equatorial radius. For (Uranus’) interior is better sampled by the gravitational harmonics compared to of thisbodies type has with beenVoyager foundrotation that fits periods both J2 (Tableand J41),of although Uranus. this Uranus the radio occultation of Voyager 2yieldedtworadii Jupiter (Saturn). For example,assumption Podolak is a simplification et al. (1995)foundthatinordertofitthe since the interior rotation profiles on ingress and egress. These were nearly equatorial occulta- (A color version of this figure is available in the online journal.) observedof Uranus parameters and Neptune for Uranus, are it actually was necessary poorly to known assume and that could tions and they provided essentially direct measurements of the the densitybe more in complex the ice shell (Helled was et10% al. lower2010). than The given potential by then-U is rep- planet’s equatorial radius. Uranus’ equatorial radius was found uses physical equations of state (EOSs) of the assumed materials currentresented EOSs. as In anaddition, expansion the ratio in even of ice Legendre to rock in polynomials, this model P2n to be 25,559 4km.Neptune’soccultationgeometrywasnot to derive a density (and associated pressure and temperature) was 30(Kaula by mass,1968 roughly;Zharkov&Trubitsyn 10 times the solar1978 ratio.). The Podolak planetet is definedal. equatorial. The± geometry of Voyager 2radio-occultationmea- profile that best fits the measured gravitational coefficients. The (1995by)pointoutthatUranus’lowerdensitymightbeexplained its total mass, equatorial radius a at the 1 bar pressure level, surements was such that egress data were more difficult to inter- physical parameters of the planets, such as mass and equatorial by higherand harmonic internal temperature coefficients ifJ the2n,whichareinferredfromDoppler planet is not fully adiabatic. pret, resulting in one reliable planetocentric radius measurement radius, are used as additional constraints. The masses and Anon-adiabaticstructureforUranusisanappealingoptionsincetracking data of a spacecraft in the planet’s vicinity. on egress at a latitude of 42◦.26 S (Tyler et al. 1989;Lindal1992, compositions of the three layers are modified until the model it suggestsThe an measured explanation gravitational for the low coefficients heat flux of theUranus planet and in Nep- Figure 7). The radius at this latitude was found to be 24,601 fits the measured gravitational coefficients. The models typically termstune of an are interior listed in that Table is not1.Theobservedgravitationalcoefficients fully convective. 4km.Lindal(1992)derivedanequatorialradiusof24,766± ± assume an adiabatic structure, with the adiabat being set to the AsecondapproachtomodeltheinteriorsofUranusandJ2, J4 correspond to the arbitrary reference equatorial radii Rref 15 km for Neptune’s 1 bar isosurface using wind velocities measured temperature at the 1 bar pressure level (Hubbard et al. Neptuneof 26,200 makes km no and a priori 25,225 assumptions km for Uranus regarding and Neptune, planetary respec- (Smith et al. 1989), with the large error reflecting the uncer- 1991;Podolaketal.1995). Although this method has succeeded structuretively and (Jacobson composition. et al. 2006 The radial;Table density1). Another profiles physical of Uranus property tainties in the extrapolation of the occultation measurement to in finding a model that fits both J2 and J4 for Neptune, no model that is used in the interior model is the equatorial radius. For of this type has been found that fits both J2 and J4 of Uranus. Uranus the radio occultation of Voyager 2yieldedtworadii2 For example, Podolak et al. (1995)foundthatinordertofitthe on ingress and egress. These were nearly equatorial occulta- observed parameters for Uranus, it was necessary to assume that tions and they provided essentially direct measurements of the the density in the ice shell was 10% lower than given by then- planet’s equatorial radius. Uranus’ equatorial radius was found current EOSs. In addition, the ratio of ice to rock in this model to be 25,559 4km.Neptune’soccultationgeometrywasnot was 30 by mass, roughly 10 times the solar ratio. Podolak et al. equatorial. The± geometry of Voyager 2radio-occultationmea- (1995)pointoutthatUranus’lowerdensitymightbeexplained surements was such that egress data were more difficult to inter- by higher internal temperature if the planet is not fully adiabatic. pret, resulting in one reliable planetocentric radius measurement Anon-adiabaticstructureforUranusisanappealingoptionsince on egress at a latitude of 42◦.26 S (Tyler et al. 1989;Lindal1992, it suggests an explanation for the low heat flux of the planet in Figure 7). The radius at this latitude was found to be 24,601 terms of an interior that is not fully convective. 4km.Lindal(1992)derivedanequatorialradiusof24,766± AsecondapproachtomodeltheinteriorsofUranusand 15 km for Neptune’s 1 bar isosurface using wind velocities± Neptune makes no a priori assumptions regarding planetary (Smith et al. 1989), with the large error reflecting the uncer- structure and composition. The radial density profiles of Uranus tainties in the extrapolation of the occultation measurement to

2 OBSERVATIONAL CONSTRAINTS

• Take an assumed internal density profile and modify until it fits observed parameters of planet

What Observational Constraints are needed? • Mass • Equatorial radius • Angular velocity of rotation (ω) • Gravitational moments (up to J6) • Planetary shape – flattening or oblateness • 1 bar Temperature

The more accurate the observed parameters the better we can model the interior structure!

AND

• Assumed density profile is approached via: • Standard: 3-layers – use known EOS for a core of rocks, icy shell, gaseous envelope • Empirical: density profile represented by analytic function with sufficient free coefficients to adjust to the given constraints

Workshop on the Study of Ice Giant Planets 7/30/14 10 R. Helled et al. / Icarus 210 (2010) 446–454 DATA 447

Voyager observations are the only ones we have of the icy• giants’ Data taken from JPL database: Table 1 http://ssd.jpl.nasa.gov radio signals and we are unable to assess the stability of the radio• These data were obtained by Voyager: Physical data, taken from JPL database: Lindalhttp://ssd.jpl.nasa.gov (1992), Lindal, Jacobson et al. (1987) (2003), Jacobson et al. (2006), Lindal (1992), and Lindal et al. (1987). R is the reference periodicities. Not to be left unsaid is the possibility of deep differ-• The Voyager values were revised by long-term observation of the planets satellite ref equatorial radius in respect to the measured gravitational harmonics J2 and J4, a and c ential rotation in the interior of a giant planet which, in the ex- motions and updated in Jacobson (2003), Jacobson et al. (2006) are the equatorial and polar radii, respectively. treme case, does not even admit the notion of a single bulk Parameter Uranus Neptune rotation period. P (rotation period) 17.24 h 16.11 h All the above motivates us to describe what we know about the 3 2 GM (km sÀ ) 5,793,964 ± 6 6,835,100. ± 10 rotation periods and shapes of the icy giants and explore what pos- Rref (km) 26,200 25,225 sibilities exist to possibly reconcile these observations. J ( 106) 3341.29 ± 0.72 3408.43 ± 4.50 2 Â J ( 106) 30.44 ± 1.02 33.40 ± 2.90 4 Â À À 1.1. Rotation a (km) 25,559 ± 4 24,764 ± 15 c (km) 24,973 ± 20 24,341 ± 30 f (flattening) 0.02293 ± 0.0008 0.0171 ± 0.0014 The atmospheres of Uranus and Neptune are typically associ- 1 ated with strong zonal winds with velocities up to 200 m s•À J2 and J4 are the gravitational harmonics and 1 400 m sÀ , respectively. Uranus and Neptune wind velocities are• Rref is arbitrary reference equatorial radii for these measurements • the strongest observed in the Solar System; the energy sourcea is equatorial radius (measured at 1 bar pressure level) to measurement on egress at a latitude of 42.26° south. The radius • For Uranus Voyager occultation near equator to produce this value À drive such energetic atmospheric winds is unknown. These wind at this latitude is 24,601 ± 4 km. Lindal (1992) extrapolated this • For Neptune Voyager occultation at mid-latitudes required extrapolation speeds, however, are relative to assumed solid-body rotation peri- single measurement both to the equator and to the south pole, • c is the polar radius -- inferred for both planets ods of the planets based on Voyager 2 measurements of periodic using Neptune’s wind velocities available at that time (Smith Workshop on the Study of Ice Giant Planets 7/30/14 11 variations in the planets’ radio signals and fits to the magnetic field et al., 1989; Hammel et al., 1989), to obtain the equatorial and po- observations. The Voyager 2 rotation periods of Uranus and Nep- lar radii given in Table 1; the standard errors of ±15 km and ±30 km tune based on radio data are 17.24 h (Desch et al., 1986; Warwick reflect the uncertainties in the extrapolation. et al., 1986) and 16.11 h (Warwick et al., 1989), respectively. The The available shape data for both Uranus and Neptune are Voyager 2 rotation period of Uranus inferred from fits to the mag- therefore quite limited and measurements might be even more netic field data is 17.29 h (Ness et al., 1986; Desch et al., 1986) in uncertain due to the challenging orbit determination at the large approximate agreement with the radio period. However, the rms distances of the outer Solar System. We conclude that the shapes residuals of the uranian magnetic field fits exhibit a broad mini- of Uranus and Neptune are not well known though the cited shapes mum in the period ranging from 16.6 h to 18 h (Desch et al., listed in Table 1 are prevalent in the literature. Stellar occultations 1986). For Neptune no accurate magnetic field period could be de- (e.g., French et al., 1998, 1987; Millis et al., 1987), which provide rived due to the short Voyager 2 flyby, though a good fit to the information on the atmospheres of the planets at microbar pres- magnetic data was obtained for a rotation period of 16 h 3 min sure levels, do not constrain the 1 bar level planetary shapes be- (Ness et al., 1989). cause of the unknown wind systems between the vastly different pressures. 2. Gravitational fields and shapes The solid-body rotation periods based on the Voyager radio periods and listed in Table 1 disagree with the shapes summarized The external potential U of a rotating planet can be expressed in in the same table. This is not surprising since the values of the a truncated series of even zonal harmonics by (Kaula, 1968), equatorial and polar radii for Neptune and the polar radius for Ura- nus have been inferred by Lindal’s extrapolation using zonal wind 2n 2 GM 1 a 1 GM r 2 velocities, not the Voyager rotation rate. To demonstrate the point U 1 j P2n l q 1 l ; 1 r r 2n a a ¼ À n 1 ð Þ!þ 2 ð À Þ ð Þ that the commonly used planetary radii of Uranus and Neptune ¼   X should not be used with Voyager’s radio periods we evaluate Eq. where GM is the gravitational constant times the total planetary (1) at both the equator (/ = 0, r = a) and pole (/ = p/2, r = c), equate mass, a is the equatorial radius, j2n are the gravitational coefficients, the expressions, solve for the assumed constant x0, and convert x0 and P2n are the Legendre polynomials. The point where the poten- to the period of rotation srot to obtain the rotation period which is tial is evaluated is given by the planetocentric radius r and latitude associated with the planetary figure by / (l = sin/). The second term on the right side is the centrifugal po- 2 3 1=2 tential. The parameter q x a /GM, where x0 is the angular veloc- 3 3 5 ¼ 0 a a 1 a 3 a À ity of rotation. srot 2p 1 j2 j4 : ¼ rffiffiffiffiffiffiffiffiffiffiffi2GM c À À 2 þ c À À 8 þ c Observations of the motion of planetary rings and satellites and     2 also radio Doppler measurements of the Voyager 2 flybys, have ð Þ yielded values of GM and the gravitational coefficients j2 and j4 In (2), we retain only the gravitational coefficients j2 and for both Uranus and Neptune. The sixth harmonic j6 has never been j4. The parameter values needed to evaluate the right side of detected for either planet. A summary of the values of these quan- Eq. (2) for Uranus and Neptune are listed in Table 1. The tities can be found on the NASA/JPL website http://ssd.jpl.nasa.gov/ gravitational coefficients j2 and j4 are modified from the mea- ?gravity_fields_op. Both gravitational fields from this website are sured J2 and J4 to fit equatorial radii of 25,559 and 24,764 km, given in Table 1. for Uranus and Neptune, respectively. The shape-associated For Uranus the occultation of Voyager 2 yielded two radii on in- rotation period of Uranus is found to be about 15.62 h, while gress and egress. This was a nearly equatorial occultation and it the period associated with Neptune’s shape is found to be provided essentially a direct measurement of the equatorial radius 16.85 h; these shape-associated rotation periods are rather dif-  to ±4 km, as given in Table 1. However, there is no measurement of ferent from the Voyager radio and magnetic periods of both the polar radius of Uranus. Lindal et al. (1987) extrapolated the planets. It is therefore important to realize that Voyager’s rota- equatorial radius to the pole using wind velocities (Smith et al., tion periods cannot be used together with the planetary shapes 1989) to obtain the polar radius listed in Table 1 with the larger listed in Table 1. It must also be emphasized that the planetary formal uncertainty of ±20 km. shapes themselves are uncertain. Below, we investigate different The Neptune occultation geometry was not equatorial, and fur- approaches to reconcile the shapes and rotation periods of ther, only one planetocentric radius measurement was possible, a Uranus and Neptune. ROTATIONAL PERIODS

• Voyager measurements of rotation may not represent the planet’s deep interior rotation • Wind and shape data used to modify the rotation rates

Uranus: P ~ 16.58h (V: 17.24h) Neptune: P ~ 17.46h (V: 16.11h)

Helled et al. (2010)

Workshop on the Study of Ice Giant Planets 7/30/14 12 GRAVITATIONAL MOMENTS Nettelmann et al. (2013)

Even with the re-analysis we need better moments and ones measured out to greater harmonics.

Workshop on the Study of Ice Giant Planets 7/30/14 13 SHAPE MATTERS!

Planetary shape must be used to constrain the interior structure.

The shapes of Uranus and Neptune are not well determined. - Equatorial radius not well measured - Polar radius never measured

Workshop on the Study of Ice Giant Planets 7/30/14 14 STANDARD INTERIOR MODEL

• Standard model for icy planets is 3 layers: 1. Central core of rocks (silicates, iron) 2. Icy shell also referred to as inner envelope

(ices: H2O, CH4, NH3, H2S) 3. Gaseous envelope (H2 and He with some heavier elements mixed in)

• Models assume adiabatic structure with the adiabat set to a measured temperature at 1bar pressure level Disadvantages: • Physical Equations Of State (EOS) for these species may not be accurate for pressure and temperature regime we are working in • Discontinuities between layers don’t allow for mixing • Fails to create a Uranus with measured gravitational moments Workshop on the Study of Ice Giant Planets 7/30/14 15 EMPIRICAL INTERIOR MODEL

• Empirical density model for icy planets: • Pressure-density profiles approached in an empirical sense and free parameters adjusted until fit to the measured data • Retrieved empirical profile then interpreted in terms of physical EOS of

hydrogen, helium, ice (H2O) and rock (SiO2) to test physical plausibility of retrieval Advantage: • Allows for continuous (rather than sharp) density gradients • More flexibility in input assumptions Uranus and Neptune empirical ρ(p) relations. Helled et al. (2011) Disadvantages: • Current constraint data inaccurate so there is significant degeneracy in the derived compositions Workshop on the Study of Ice Giant Planets 7/30/14 16 ICY PLANETS? Based on current studies can we say if Uranus and Neptune are icy?

GRAY: assuming

H2O as high-Z Black solid curves: BLACK: assuming polynomial fits to the gravitational data SiO2 as high-Z

Helled et al. (2011) Not necessarily!

Workshop on the Study of Ice Giant Planets 7/30/14 17 IS IMPROVING THE EOS THE ANSWER?

• Voyager gravity data require presence of light elements in the deep interior, and small cores typical structure model

• Equation of State for hydrogen, helium, and water He H2 affects interior structure models of giant planets 2000 K 0.8 RN 0.1 Mbar • Nettelmann et al (2013) tested ab initio equation water

of state data for a mixture of H, He, and H2O to interior models • EOS data for the major components 6000 K rock 7 Mbar combined by linear mixing into a new data 2 M⊕ table • Called LM-REOS: linear mixing Rostock equation of state

Workshop on the Study of Ice Giant Planets 7/30/14 18 IS IMPROVING THE EOS THE ANSWER?

• Originally both planets cooling time was found to be too long by several Gyrs • Applying improved EOS data shortens Neptune’s cooling time • Teff can be explained by a convective interior He BUT H2 • Uranus still cools several Gyrs too slowly

water

Workshop on the Study of Ice Giant Planets 7/30/14 19 MORE COMPLICATION • Using improved moments constrains the metallicity for Neptune … BUT Using Voyager Rotation Periods Using Modified Rotation Periods

Tc (K) Transition Pc (Mbar) pressure Mc (M⊕ ) (Gpa)

Mass fraction of metals in the outer envelope (Z1) and in the inner envelope (Z2) Nettelmann et al. (2013) of 3-layer models of Uranus and Neptune

Workshop on the Study of Ice Giant Planets 7/30/14 20 MORE COMPLICATION • Using improved moments constrains the metallicity for Neptune … BUT Using Voyager Rotation Periods Using Modified Rotation Periods

Tc (K) Transition Pc (Mbar) pressure Mc (M⊕ ) (Gpa)

The modified rotation periods broaden the range of possible Neptune metallicities and provide for non-overlapping Uranus and Neptune interior structure.

Mass fraction of metals in the outer envelope (Z1) and in the inner envelope (Z2) Nettelmann et al. (2013) of 3-layer models of Uranus and Neptune

Workshop on the Study of Ice Giant Planets 7/30/14 21 INTERIOR MODELS PLAGUED BY UNCERTAINTY

Summary of Nettelmann et al. (2013): • Applied improved gravitational moments by Jacobson • Applied improved EOS that involves a mixture of H, He, and H2O • Applied modified rotation periods

Outcome • The observational constraints just aren’t good enough! • Tighter present constraints still encompass many of the previous models

BUT … • Models were produced that suggest Uranus and Neptune could be quite different • Uranus: • outer envelope ~ solar metallicity

• inner envelope transitioning at 0.9MU with ~90% by mass heavy elements • Neptune: • less centrally condensed planet • transition at 0.6MN with a more moderate increase in metallicity

Workshop on the Study of Ice Giant Planets 7/30/14 22 ADDITIONAL CHALLENGES

1. D/H appears enriched -- suggests mixing from ice-rich deep interior

2. Helium abundance consistent with protosolar value -- suggest opposite conclusion to 1

3. Neptune tropospheric CO abundance indicates > 70% heavy elements by mass in the atmosphere, while standard structure models allow for < 60%

Workshop on the Study of Ice Giant Planets 7/30/14 23 KEY ABUNDANCE MEASUREMENTS 632 F. Hersant et al. / Planetary and Space Science 52 (2004) 623–641 • Helium would have• beenIs it solar? there if water was in solar proportions. If Uranus-Neptune O/H based on CO in Neptune the non-trapping• of CO resulted from the non-accessibility 1000 of some cages,Neon the above-mentioned number is only a lower limit of O/H• inSolar if temperatures in the outer disk Saturn. This implies an amount of ice in N2 fully the solar nebularemained high enough, no lower (when vaporized) thansupersolar 0.4 times trapped the water abundanceotherwise given in Table 1. Implications of this result• areAr discussed, Kr in Section 6.8. 100 • Ar, Kr predicted to be solar 5.3. Uranus and Neptune • Xe Calculated

• Expected to be supersolar (highly?) Ratio to solar Uranus and Neptune di!er from Jupiter and Saturn by 10 the fact• C, N, S that these planets never reached phase 3 of the Predicted scenario of• PollackSupersolar et al. (1996), but accurate values are , namely that no hydro- dynamic collapsereally important of hydrogen ever occurred, because the nebula• dissipatedD prior to the epoch when the cores of the planets acquired the mass required to generate the hydro- 1 dynamic instability.• Origin of ices Hydrogen present in the envelopes of Ar Kr Xe C N OS the two• planetsDisequilibrium species, isotopic ratios was slowly acquired during phase 2. There- Fig. 7.Enrichments in Uranus and Neptune in the case of CO Enrichments in Uranus and Neptune in the case of CO being fully fore these envelopes are small compared to the mass of their trapped:being fully trapped: measurements (error bars) and measurements (error bars) and calculations, calibrated on CH4=H2 cores. Podolak et al. (2000) estimated that the maximum gas ratiocalculations, calibrated on CH of 30 (diamond), 45 (circle) and4/H 602 ratio of 30 (diamond) 45 (square). For comparison the content (hydrogen+helium) for Uranus is 4.2 Earth masses asterisk shows(circle), and 60 (square). ( the enrichment in N if NHersant2 had been et al. 2004) trapped. The cross (EM), and 3.2EM for Neptune, to be compared to the total (x) is the predicted O/H value of Lodders and Fegley (1994) in Neptune. Workshop on the Study of Ice Giant Planets 7/30/14 24 masses of the planets of 14.6EM and 17.2EM, respectively. These considerations imply that we cannot calculate the enrichments with respect to the solar abundance as we did in the form of ammonia in the troposphere of Uranus and for Saturn. However, we can derive some information from Neptune (Fegley and Prinn, 1986), this would have strongly the abundances of minor species derived from ground based depressed the centimeter spectrum of the two planets with observations, namely from CH4, NH3, and H2S. The abun- respect to observations (de Pater et al., 1991). dances of the two last species are unfortunately uncertain In fact, the analysis of the microwave spectra of Uranus (for a review of the composition of Uranus and Neptune, see and Neptune made by a number of authors (see for a re- Gautier et al., 1995). Adopting the value of de Pater et al. view Gautier et al., 1995) has revealed an important con- (1991) for the S enrichment in Neptune (from 10 to 30), we straint on the S/N ratio in these planets. As pointed out for see that the uncertainty is much higher than that in Saturn. the ÿrst time by Gulkis et al. (1978), the interpretation of Moreover, the N/H ratio in the deep troposphere is not well the centimeter spectrum implies a substantial depletion of determined neither. Therefore, in this case, we feel safer to NH3 in the upper troposphere. This has been interpreted by calibrate on methane for which the CH4=H2 ratio is between these authors, and subsequently conÿrmed by many others, 30 and 60 times the solar abundance, for both Uranus and as resulting from the formation of NH4SH clouds from the Neptune (Gautier et al., 1995). We made the assumption combination of NH3 with H2S (as in Saturn). This in turn that C/H was solar in the nebula and that CO=CH4 = 10 ev- requires a substantially oversolar S/N ratio, implying, in the erywhere (Table 1). framework of our scenario, that H2S was well trapped in Assuming that H2S=H2 in the gaseous phase in the region the feeding zone while N2 was never clathrated. The mod- of formation of these planets was equal to 0.57 times the est enrichment in nitrogen indicated at the bottom of Fig. solar abundance, as at 5 and 10 AU, and that N2=NH3 = 10, 7 results only from the trapping of the NH3 hydrate. In the we can infer, by using the Eq. (2), the enrichments in S and absence of NH3, the N/H ratio would have been solar since N, as shown in Fig. 7, and given in Table 3. presumably N2 was always mixed with hydrogen. For the theoretical enrichments shown in Fig. 7, we took The S enrichment of 25 calculated from the lower value into account the uncertainty in the measurements of CH4=H2, of CH4=H2 is compatible with the conclusions (see Table 3) and we calculated the enrichments of the other species for of de Pater et al. (1991), derived from the analysis of the the lower, the central, and the upper measured values of radio spectra of Uranus and Neptune. It might be that the the methane abundance. However, the amplitude of the N theory of the trapping of volatiles by clathration provides enrichment depends upon the e"ciency of the trapping of for the ÿrst time a physical explanation of the high sulfur N2 in the feeding zone of Uranus and Neptune. enrichment that modelers have been obliged to assume for If all N2 had been clathrated in the feeding zones, the three decades. calculated N enrichment would have been as high as 44 (as Ar and Kr are predicted to be solar in Uranus and Nep- indicated by an asterisk in Fig. 7). Since nitrogen must be tune, since they were presumably uniformly mixed with SO HOW FAR HAVE WE COME?

PAST • We thought Uranus and Neptune were icy and very similar planets with similar interiors • 3-layer interior with rock, ice, and gas • Formed via core accretion in the solar nebula NOW • We know better than to believe our assumptions! • Voyager measurements while valuable still left great uncertainty • We have learned that the Ice Giants may not: • have an ice-rich inner envelope • have similar interior structure • have formed together in the solar nebula in the same way • have evolved similarly (i.e. late large impact differences)

Workshop on the Study of Ice Giant Planets 7/30/14 25 CONCLUSIONS

• To make significant strides in interior models we need: • Improved gravity fields – out to at least J6 • 1bar temperatures for both planets • Shapes of both planets – true measurements of the polar radius (both U&N) and equatorial (N) • Rotation rates • Intrinsic luminosities to higher accuracy • Atmospheric abundances • Envelope metallicities below the water cloud • High pressure-temperature equations of state

• Ideally we need a Juno-like mission with a deep entry probe to get below the water cloud!

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