Probing the interiors of the ice giants: Shock compression of water to 700 GPa and 3.8 g/cm3 M.D. Knudson, M.P. Desjarlais, R.W. Lemke, and T.R. Mattsson Sandia National Laboratories, Albuquerque, New Mexico 87185, USA. M. French, N. Nettelmann, and R. Redmer Universita¨t Rostock, Institut fu¨r Physik, D-18051 Rostock, Germany. (Dated: January 13, 2012) Recently there has been tremendous increase in the number of identified extra-solar planetary systems. Ourunderstandingoftheirformationistiedtoexoplanetinternalstructuremodels,which 2 relyuponequationsofstateoflightelementsandcompoundslikewater. Herewepresentshockcom- 1 pressiondataforwaterwithunprecedentedaccuracythatshowswaterequationsofstatecommonly 0 used in planetary modeling significantly overestimate the compressibility at conditions relevant to 2 planetary interiors. Furthermore, we show its behavior at these conditions, including reflectivity n andisentropicresponse, iswell describedbyarecentfirst-principlesbasedequation ofstate. These a findingsadvocatethiswatermodelbeusedasthestandardformodelingNeptune,Uranus,and“hot J Neptune”exoplanets, and should improveour understandingof these typesof planets. 2 1 PACSnumbers: 96.15.Kc,62.50.-p,64.30.-t ] P The past several years have seen a virtual explosion structureoftheseplanets[13,14]. Anotherimportantre- E in the number of extra-solar planets discovered. Two sultisderivedfromthepredictedphasediagramofwater: . h rapidly growing populations of exoplanets are ice giants the icy giants Uranus and Neptune perhaps contain no p referred to as “hot Neptunes” and “mini-Neptunes”; [1] “ice” but dissociated water at a high ionic conductivity, - o planets roughly the same size as or,respectively, smaller even less so would close-in exoplanets. Hot and mini- r thanNeptune andUranusthattransittheirhoststarsat Neptunesmayevencomprisewaterplasmawithsubstan- t s significantly smaller radii, resulting in higher tempera- tialelectronicconduction. However,the FPEOSforwa- a turesthantheicegiantsinoursolarsystem. Understand- ter has not been widely accepted due to its inability to [ ing of the composition and formation of these planets, reproduce results from laser driven shock wave experi- 1 and thus development of these planetary systems, relies ments in the Mbar regime [15]. v on our knowledge of the equationof state (EOS) of light 2 We present results of magnetically accelerated flyer- elementsandcompoundslikewater,overawidepressure 2 plate experiments on water performed at the Sandia Z 6 andtemperaturerange. Todatemuchofthemodelingof machine [16], a pulsed power accelerator capable of pro- 2 ice giants has employed the ANEOS [2] and Sesame [3] . models for water that were developed decades ago [4, 5]. ducing extremely large current (∼20 MA) and magnetic 1 field densities (∼10 MG) within a short circuit load. 0 Discrepancies between these EOS models lead to signifi- 2 cantdifferencesinpredictedradiusevolutionofNeptune- Thesedata,intherangeof100-450GPaalongtheHugo- 1 massplanets. Dependinguponthetotalamountofheavy niot – the locus of end states achievable through com- : pression by large amplitude shock waves – have consid- v elements, and their distribution within the planetary in- i terior, the resulting variation in predicted radius at a erably higher precision than data obtained with previ- X ously used methods, and support the FP EOS for wa- given age due to the water EOS can range between 5 r ter. The high precision stems from the ability to per- a and 30% [6]. This is a major factor in preventing ac- form well-defined flyer-plate experiments on Z; the mag- curate determination of exoplanet internal composition neticpressure(>500GPa)canpropeltheouteranodeto from their observed radius. velocities approaching 30 km/s, enabling high-precision, Recent quantum molecular dynamics (QMD) calcula- plate-impactEOSmeasurements inthe TPa regime [17– tions of water [7, 8] suggest an EOS that differs signifi- 19]. Furthermore, and more significantly, the present cantly from ANEOS and Sesame. Notably, when incor- work obtained re-shock data of water in the range of porated into planetary models, this first-principles (FP) 200-700 GPa. These data, at high ρ and low T, pro- based EOS predicts a ∼20% cooler core temperature for vide a stringent test of the isentropic response of water Neptune and Uranus [9]. The conductivity properties of in the several Mbar regime, which is directly relevant to this FP model are also noteworthy [10], suggesting that the conditions of interest for planetary modeling of Nep- water is super-ionic [11, 12] at high densities, ρ, and low tune,Uranus[9,14],andpresumablywater-richexoplan- temperatures, T, relevant to planets such as Uranus and ets such as the hot Neptune GJ436b [9, 20, 21]. Finally, Neptune. This predicted property plays a key role in reflectivityontheHugoniotwasmeasuredandcompared dynamo models to explain the enigmatic magnetic field to FP calculations for water [22]. 2 velocity;thisdefinedapointinthepressure-particleve- locity(P−u )plane,asshowninFig.1. Whentheshock p transitsintothewater,areleasewavepropagatesbackto- wardthe flyer-plate,andthusthe stateofthedriveplate is constrained to lie on a release adiabat from this point in the P −u plane, shown in Fig. 1 as the green line. p Theshockedstateofthewaterisconstrainedtoliealong achordintheP−u planewithslopegivenbytheprod- p uct of the measured shock velocity of water, U , and sw the known initial density. The intersection of these two curves provides P and up, shown in Fig. 1 as (P1,up1); The RH jump relations then provide ρ in the shocked state. Uncertainties in all kinematic values were deter- mined through a Monte Carlo technique, which uses a statisticalprocessforpropagationofallrandommeasure- ment errors and systematic errors in the standards [23]. Using this technique, the one-sigma uncertainties in P FIG. 1. P −up diagram for the water experiments for the and ρ were found to be 0.5% and 1%, respectively. case with the additional quartz driveplate. Atotalof8Hugoniotexperimentswereperformedover therangeof100to450GPa. Resultsoftheseexperiments are shown as the red symbols in Fig. 2(a). Also shown An aluminum flyer-plate [23] was magnetically accel- are Hugoniot data of Mitchell and Nellis [28], Volkov erated to peak velocities of 12-27 km/s across a 3-4 mm et al. [29], Celliers et al. [15], and Podurets et al. [30], vacuum gap [17]. The flyer-plate velocity was monitored and the predicted Hugoniot response from ANEOS [2], throughout the entire trajectory using a Velocity Inter- Sesame7150[3],andtherecentFPEOSmodelofFrench ferometer System for Any Reflector (VISAR [24]), at lo- et al. [7, 8]. Note that a reanalysis of the nuclear driven cations above and below an aluminum water cell [23]. A datum of Podurets et al., using an improved aluminum rear quartz window in the cell provided optical access to standardforimpedancematching[27],resultedinaslight thesample. Insomecasesanadditionalquartzplatewas decreaseinρ. Thelow-P endofourdataisingoodagree- placed between the aluminum drive plate and the water ment with the gas gun data of Mitchell and Nellis and sample, enabling data to be obtained using two different theexplosivelydrivenshockdataofVolkovet al. Incon- materialsasthe high-pressurestandard,therebyincreas- trast, our data are significantly less compressible than ing confidence in the measurements. Impact with the thelaserdrivendataofCellierset al., whichtendtosup- cell generated a strong, multi-Mbar shock wave in the port the much more compressible ANEOS and Sesame aluminum drive plate. This shock was then transmitted Hugoniots,albeitwithsignificantlylargeuncertaintyand either directly into the water sample, or into a quartz scatter. Thevastlyreduceduncertaintyinρforourdata, plate and then into the water sample. Upon reaching roughly an order of magnitude, strongly suggest that the rear quartz window, the shock was transmitted into water is much less compressible than the ANEOS and the window and reflected back into the water,which re- Sesame models predict, and that water is instead very shocked the water to a higher P and ρ. In all cases the accuratelydescribedbytheFPEOSofFrenchetal. Fur- shock waves in the water and quartz were of sufficient thermore, the reanalyzed Podurets et al. datum is also amplitude that the resulting shocked material was re- in very good agreement with the FP EOS. Thus, with flecting[15,19,25],enablingtheshockvelocitiestobedi- the exception of the Celliers et al. data, the FP based rectlymeasuredusingthe VISAR. Atotalof18diagnos- modelfor watermatches allexperimentalHugoniotdata tic channels were utilized for each experiment, enabling up to 1.4 TPa. multiple, redundantmeasurementstobe made,resulting In all 8 of the Hugoniot experiments described above, in an overalluncertainty in the measuredflyer-plate and thereflectedshockfromtherearquartzwindowdrovethe shock velocities of a few tenths of a percent [23]. water from the Hugoniot state to a re-shocked state at The shocked state of the water was determined us- higher P and ρ. The measured shock velocity in the wa- ing the impedance matching technique andthe Rankine- ter immediately prior to reflection from the rear quartz Hugoniot (RH) jump relations [26], a set of conditions window defined the initial shocked state of the water. derivedbyconsideringconservationofmass,momentum, The measured shock velocity in the rear quartz window andenergyacrossasteadypropagatingshockwave. The and the known Hugoniot of quartz provided the double- shocked state of the aluminum (quartz) drive plate was shockedP andup forwater,showninFig.1as(P2,up2). determined from the known Hugoniot of aluminum [27] The velocityof the secondshock in the water, Usw2, was (quartz[19])andthemeasuredflyer-plate(quartzshock) then determined by the RH jump relations using the 3 double-shock envelopes - the locus of end states achiev- able through shock and re-shock using a quartz anvil: FP (orange line), ANEOS[2] (pink line), and Sesame [3] (gray line). These re-shock data further confirm the less compressible response of water above 100 GPa. Note that the FP re-shock Hugoniots (red) and isen- tropes (black) are nearly coincident over the ρ range ac- cessed through the re-shock experiments. This is due to a second order contact for the Hugoniot and isentrope at the initial state [26], which is most easily seen by ex- panding the entropy as a function of volume in a Taylor series. This implies that the Hugoniot and isentrope are verycloseinP andρuntil,atlargecompression,therise inT associatedwiththeirreversibleshockbecomeslarge enoughthatthermalpressuresbecomesignificant. Inthe range investigated in this study, the difference in T be- tween the re-shock Hugoniot states and the isentrope at the re-shockρ,asdeterminedbythe FPEOS[7],ranged from 200K (out of 6800K) to 330K (out of 40000K) at the lowest and highest P, respectively. This makes such are-shockmeasurementthebestpossibletestoftheisen- tropic response of the EOS model in this range of P and ρ. Thusthepresentdatavalidatestheisentropicresponse FIG. 2. (a) Water P −ρ Hugoniot. Models: magenta line, of the FP EOS in the P and ρ regime that is intersected ANEOS [2]; black line, Sesame [3]; dotted red line, FP [7]; by the water-richmodels of Neptune and Uranus [9, 14], solidredline,FP[8]. Data: reddiamonds(squares),thiswork shown in green, and the exoplanet GJ436b [20, 21, 23], using aluminum (quartz) standard; open squares, Celliers et shown in blue. al. [15]; black circles, Mitchell and Nellis [28]; black triangle, The VISAR was also used to infer reflectivity, R, of Volkov et al. [29]; blue (cyan) triangle, Podurets et al. [30], asreported (reanalyzed [23]). Planetary adiabats: green line, water (at 532 nm) along the Hugoniot. A quadrature Neptune [9] (Uranus similar); blue line, GJ436b [20, 21, 23]. VISAR was used for all experiments, which provides (b) Water double-shock Hugoniot. Models: Thick (thin) red four measures of the interference signal at 90◦ inter- lines, FPfirst shock (re-shock)Hugoniots [7]; black lines, FP vals. The signals at 180◦ intervals can be subtracted, isentropes[7];(orange,pink,gray)lines,(FP[7],ANEOS[2], ensuring the remaining signal only includes coherent re- Sesame[3])double-shockenvelopes. Data: red(orange)sym- flected laser light (incoherent light, such as self-emission bols, shock (re-shock) Hugoniot data, this work. Planetary fromthehotplasma,wouldequallycontributetoallfour adiabats: as in panel (a). quadrature signals). Comparison of the magnitude of these subtracted signals before and after shock break- out from the water to the quartz rear window provides change in P, (P2 − P1), and up, (up2 −up1). The re- a relative measure of the shocked water R with respect shock ρ was then determined from Usw2, the first shock to shocked quartz [25]. The uncertainty in R was taken ρ, and (up2 −up1). Using the Monte Carlo technique, to be the linear sum of the standard deviation of the the one-sigma uncertainties in P and ρ for the re-shock inferredR fromthe nine independent VISAR signalsob- states were found to be 0.5-1% and 1-2%, respectively. tainedfromeachwatercellandthe reporteduncertainty Although the uncertainty for the re-shock data is larger in R of shocked quartz [25]. than that for the principal Hugoniot data (entirely due R data along the Hugoniot are shown in Fig. 3. Also to the larger uncertainty in the initial state), the accu- shownaredatafromCellierset al.[15]andthepredicted racyofthepresentdataisasignificantimprovementover R fromFP calculationsof FrenchandRedmer [22] using previousre-shockdataofMitchellandNellis[28](uncer- boththePerdew,Burke,andErnzerhof(PBE)andHeyd, tainty in ρ of 4-14%) and the pre-compressed Hugoniot Scuseria, and Ernzerhof (HSE) functionals for exchange data of Lee et al. [31], (uncertainty in ρ of 5-10%). and correlation. It was anticipated that the HSE func- The re-shock data for water are shown in Fig. 2(b), tional,whichincludesthenonlocalFockexchange,would wherefirstandsecondshockstatesarecorrelatedbylike provetobemoreaccurateinthe calculationofR,asthis symbols. Also shown are several FP re-shock Hugoniots functional has been shown to better reproduce the band (thinredlines)andisentropes(thinblacklines)forcom- gapinsemiconductormaterials(PBEisknowntosignifi- parison [7]. These re-shock Hugoniots along with the cantlyunderestimatethebandgap). Incomparisonwith knownHugoniotofquartz[19]wereusedtodeterminethe R data of Celliers et al. [15] it would appear that the 4 0.5 our understanding of these planetary systems. We acknowledge the crew of the Sandia Z facility for 0.4 theircontributionstotheseexperiments,ABandMBfor y assistance in numerical calculations, and support from vit 0.3 cti the DFG via the SFB 652 and the grant Re 882/11-1. e efl 0.2 Sandia National Laboratories is a multi-program labo- R ratory managed and operated by Sandia Corporation, a 0.1 wholly owned subsidiary of Lockheed Martin Corpora- tion, for the U.S. Department of Energy’s National Nu- 0 100 200 300 400 500 clear Security Administration under contract DE-AC04- Pressure (GPa) 94AL85000. FIG.3. Reflectivity(532nm)alongtheprincipalHugoniotof water. Models: red(magenta)line,FPcalculationswithHSE (PBE) functionals [22]. Data: black line, Celliers et al. [15]; red diamonds, this work. [1] W. J. Borucki et al.,Astrophys.J. 736, 19 (2011). [2] S.P.LyonandJ.D.Johnson,TechnicalReportNo.LA- UR-92-3407, Los Alamos, 1992. HSE calculations are less accurate. However, our data [3] F.H.Ree,TechnicalReportNo.UCRL-52190,Lawrence suggest a much lower peak R, which is in significantly Livermore Laboratory, 1976. better agreement with the HSE calculations. We note [4] O. Grasset, J. Schneider, and C. Sotin, Astrophys. J. that two recent data points (∼140 and 260 GPa) from a 693, 722 (2009). group[32]atthe GekkolaserinJapanalsosuggestlower [5] D. C. Swift et al.,Astrophys.J. 744, 59 (2012). R, in very good agreement with our results. These new [6] I.Baraffe,G.Chabrier,andT.Barman,A&A482,315 (2008). resultslendconfidencetotheFPcalculations,whichalso [7] M.French,T.R.Mattsson, N.Nettelmann,andR.Red- predict a super-ionic phase of water at low T and high ρ mer, Phys.Rev.B 79, 054107 (2009). conditions relevant to planetary interiors. Furthermore, [8] M. French and R. Redmer, J. Phys.: Condens. Matter theseresultsstronglysuggestthatattheseconditionswa- 21, 375101 (2009). ter is in a plasma phase, which would imply that a T=0 [9] J.FortneyandN.Nettelmann,SpaceSci.Rev.152,423 KEOSforwaterisnotsufficientformodelingofhotand (2009). mini-Neptunes,andthatwaterwouldbeexpectedtomix [10] M. French, T. R. Mattsson, and R. Redmer, Phys. Rev. B 82, 174108 (2010). in the H/He envelope rather than form an ice shell sep- [11] C. Cavazzoni et al.,Science 283, 44 (1999). arate from an outer H/He envelope. [12] T. R. Mattsson and M. P. Desjarlais, Phys. Rev. Lett. We presented data with unprecedented accuracy for 97, 017801 (2006). shock compressionof water to 0.7 TPa and 3.8 g/cc in a [13] S. Stanley and J. Bloxham, Nature 428, 151 (2004). regimerelevanttowater-richmodelsofUranus,Neptune [14] R. Redmeret al., Icarus211, 798 (2011). and the exoplanet GJ436b. The experimental P, ρ, and [15] P. M. Celliers et al., Phys.Plasmas 11, L41 (2004). Rareinexcellentagreementwithdensityfunctionalthe- [16] M. K.Matzen et al.,Phys. Plasmas 12, 055503 (2005). [17] R. W. Lemkeet al., J. Appl.Phys. 98, 073530 (2005). ory predictions, thereby validating first-principles ther- [18] M. D. Knudson, M. P. Desjarlais, and D. H. Dolan, Sci- modynamic calculations as a sound basis for planetary ence 322, 1822 (2008). modeling, and strongly advocating the FP EOS be the [19] M. D. Knudson and M. P. Desjarlais, Phys. Rev. Lett. standard in modeling water in Neptune, Uranus, and 103, 225501 (2009). “hot Neptune” exoplanets. In particular this work sup- [20] N. Nettelmann et al., Astrophys.J. 733, 2 (2011). ports the prediction of a ∼20% cooler core temperature [21] N. Nettelmann et al., A & A 523, A26 (2010). forNeptuneandUranus[9]. Asthecalculatedamountof [22] M. French and R. Redmer, Phys. Plasmas 18, 043301 (2011). HandHeintheplanetsdecreaseswiththestiffnessofthe [23] FurtherinformationavailableinSupplementalMaterials. water EOS, confidence in the presence of a few percent [24] L. Barker and R. Hollenbach, J. Appl. Phys. 43, 4669 H and He in the deep interior of Neptune and Uranus, (1972). as derived from the (rather stiff) FP EOS based models [25] D. G. Hicks et al.,Phys. Rev.Lett. 97, 025502 (2006). [7,9],isstrengthenedbythiswork. AsHwouldbemetal- [26] G. Duvall and R. Graham, Rev. Mod. Phys. 49, 523 lic, this might influence the generation of the magnetic (1977). field. Furthermore, the validation of the FP EOS in the [27] M. D.Knudson et al.,J. Appl.Phys.94, 4420 (2003). [28] A. Mitchell and W. Nellis, J. Chem. Phys. 76, 6273 regime relevant to planetary interiors all but eliminates (1982). one significant source of uncertainty in the predicted ra- [29] L. P. Volkov et al.,JETP Lett. 31, 513 (1980). dius evolution of Neptune-mass planets within assumed [30] M. A.Podurets et al., Sov.Phys. JETP 35, 375 (1972). composition models. This will improve our understand- [31] K.K.M.Leeet al.,J.Chem.Phys.125, 014701 (2006). ingoftheinteriorstructureoftheseplanets,andperhaps [32] N.OzakiandT.Kimura,privatecommunication(2011).