Astrophysics and Space ScienceDOI 10.1007/s•••••-•••-••••-•Proceedings article for the HEDLA 2008 conference in St. Louis. Submitted for publication inComparison of Jupiter Interior Models Derived fromFirst-Principles SimulationsB. Militzer1•W. B. Hubbard2c Springer-Verlag ••••Abstract Recently two groups used first-principlescomputer simulations to model Jupiter’s interior. Whileboth studies relied on the same simulation technique,density functional molecular dynamics, the groups de-rived very different conclusions. In particular estimatesfor the size of Jupiter’s core a nd the metallicity of itshydrogen-helium mantle differed substantially. In thispaper, we disc uss the differences of the approaches andgive an explanation for the differing conclusions.Keywords equation of state, first-principles simula-tions, density functional theory, hydrogen-helium mix-tures, giant planet interiorsThe characterization of the interior str uctur e of gi-ant planets in our solar system is crucial for identifyingtheir formation mechanism and for understanding theevolution of the solar system. Establishing the historyof o ur solar system will help interpreting the observedsimilarities and differences between our and other s o-lar systems. The unexpected diversity among the overthree hundred recently discovered extra solar planetshas challenged existing theories of planetary formationand migration.The planets in our solar system have been studiedin great detail with observations and space miss ionsbut many questions about their interior structures haveremained unanswered. Jupiter is predicted to have arelatively small rocky core of between zero and sevenEarth masses (Saumon et al. 1995; Saumon and Guil-lot 2004 ), which is surprising be c ause similar theoriesB. MilitzerW. B. Hubbard1Departments of Earth and Planetary Science and of Astronomy,University of California, Berkeley, CA 94720, USA.2Lunar and Planetary Laboratory, The University of Arizona,Tucson, AZ 85721, USA.predicted between 10 and 25 Earth masses for the corein Sa tur n (Saumon and Guillot 2004). This predictionfor Jupiter has lent support to c ore-accretion theorieswith comparatively small cores (Pollack et al. 1996),late-stage core erosion s c enarios (Guillot 2004), or sug-gesting that jovian planets are able to form directlyfrom gases without a triggering core (Boss 2007).The small core hypothesis for Jupiter has now beenchallenged in a paper by Militzer, Hubbard, Vor-berger, Tamblyn, and B onev (MHVTB) (Militzer e t al.2008) who used first-principles computer simulations ofhydrogen-helium mixtures to compute the equation ofstate (EOS) in the interior of Jupiter. This work pre-dicts a large core of 14 – 18 Earth masses for Jupiter,which is in line with es timates for Saturn and suggeststhat both planets may have formed by cor e -accretion.The paper further predicts small fraction of planetaryices in Jupiter’s envelope suggesting that the ices wereincorporated into the c ore during formation rather thanaccreted along with the gas envelope. Jupiter is pre-dicted to have an isentropic and fully co nvective enve-lope that is of constant chemical composition. In orderto match the observed gravitational moment J4, theauthors sugges t that Jupiter may not rotate as a solidbody and predicted the existence of deep winds in theinterior leading to differential r otation on cylinder s.The first-principles simulations used in the MHVTBpaper are a major difference compared to chemicalEOS models developed by Saumon, Chabrier, and vanHorn (Saumon and Chabrier 1992; Saumon et al. 1995).With first-principles simulations one simulates a fullyinteracting quantum system of over a hundred electronsand nuclei and therefore avoids a number of approxima-tions used in chemical models. In chemical models onefor example describes hydrogen as an ensemble of sta-ble molecules, atoms, free electrons, and protons andis then required to make a dditional approximations totreat their interactions. These approximations are de-2pendent on the material under consideration and mayalso depend on the tempera tur e a nd pres sure. First-principles methods describe the interactions on a funda-mental level. One is a lso require d to make some approx-imations to solve the many-body Schr¨odinger equationbut those are very different in nature, are not materialsp e c ific and do not depend on the T and P . There fo reone expects EOSs derived from first-principles to bemore accurate than chemical models unless they havebeen fit to experiments. However, no experimental EOSdata are available for the deep interiors of giant gasplanets.The MHVTB paper des c ribed significant differencesbetween the first-principles EOS and chemical models.However these were not solely responsible for the dif-ferent predictions for Jupiter’s interior. In a differentpaper, Nettelmann, Holst, Kietzmann, French, Redmerand Blaschke (NHKFRB) Nettelmann et al. (2 008) alsoused first-principles method to study Jupiter’s interiorbut came to very different conclusions. Very much inline with earlier models, they predict a small core forJupiter and a large amount of heavy elements in theenvelope.In this pape r, we will objectively discuss the differ-ences between the MHVTB and NHKFRB approachesin order to explain how such different conclusions werederived, although we encourage the reader to comparethe two original papers also. The differences betweenthe two papers can be sorted into three categories: (1)differences in DFT-MD simulations, (2) differences inthe subsequent construction of adiabats, and (3 ) dif-ferent assumptions in the models for Jupiter’s interior.We will go through these differences in the followingthree sections and demonstrate that the main differ-ence arises from point (3).1 Comparison of Simulation ParametersIn this section we discuss the differences in the first-principles simulations perfo rmed by the two groups.Although there are differences in the level of accuracy,they are unlikely to be the main reason for the differ-ences in the Jupiter models. Both groups used densityfunctional molecular dynamics (DFT-MD) s imulationsand should derive identical equations of state for hydro-gen, helium, and their mixtures. However, computa-tional details are importa nt for accuracy of the derivedEOS.The NHKFRB group used exclusively VASP codewhile MHVTB used CPMD a s well as the VASP code.MHVTB verified that bo th codes yield identical