The Juno spacecraft has measured Jupiter’s gravitational field to high precision through precise Doppler tracking in its polar orbit around Jupiter, compared with the previous values detected by Pioneer 10 and 11 and by Voyager 1 and 2 (Folkner et al. 2017; Bolton et al. 2017; Iess et al. 2018). These new gravity data have improved our knowledge of Jupiter’s interior. The even gravity harmonics are affected by the shape and internal structure of Jupiter in its hydrostatic equilibrium under the effect of rotational distortion. To accurately describe the shape and internal structure of Jupiter, various interior models with new ingredients, such as two-layer and three-layer structure models, have been established by several groups (Guillot & Morel 1995; Guillot 1999; Hubbard 1999, 2013; Anderson & Schubert 2007; Kaspi et al. 2010; Nettelmann et al. 2012; Helled et al. 2015; Vazan et al. 2015; Kong et al. 2016; Wahl et al. 2017; Ni 2018; Guillot et al. 2018; Debras & Chabrier 2019). Most of these models describe the internal structure of Jupiter via the physical laws of nature given an empirical or simulated equation of state (EOS), such as polytropic EOSs, EOSs obtained using the free-energy minimization method (Saumon et al. 1995), and ab initio EOSs (Nettelmann et al. 2008, 2012; French et al. 2012; Becker et al. 2014; Militzer et al. 2008; Militzer & Hubbard 2013; Chabrier et al. 2019). The EOSs describe the microscopic properties of planetary matter and play an important role in calculating the structure and evolution of planets, in spite of uncertainties in the hydrogen–helium phase separation (Hubbard et al. 2002; Saumon & Guillot 2004; Fortney & Nettelmann 2010; Miguel et al. 2016, 2018; Militzer et al. 2016; Debras & Chabrier 2019). Juno’s gravity measurements have demonstrated small values for high-order even gravitational harmonics with respect to the heavy-element abundance measured by the Galileo entry probe (Wahl et al. 2017; Debras & Chabrier 2019). In order to reconcile the calculated gravitational harmonics with these small values of J4 to J8, Wahl et al. (2017) proposed a dilute core model where heavy elements are dissolved in a hydrogen–helium mixture and expanded outward through a portion of Jupiter. Alternatively, these latter authors modified the abundances of helium and heavy elements in the outer molecular envelope to be lower than those measured by the Galileo entry probe. Stimulated by dilute cores, the three-layer structure models for Jupiter have been generalized into four-layer structure models by introducing a dilute core region above central compact cores. Guillot et al. (2018) compared the effective even harmonics 

$J_{2i}^{\mathrm{eff}}(H,m)\;{=}\;J_{2i}^{\mathrm{Juno}}-\bigtriangleup J_{2i}(H,m)$
J2ieff(H,m) = J2iJuno−△J2i(H,m)
 with the ones obtained from interior models assuming rigid rotation to explore the rotation of Jupiter’s deep interior. It is found that Jupiter’s deep interior exhibits an almost rigid-body rotation and Jupiter’s atmospheric zonal flow extends to a depth H of 2000−3500 km. Debras & Chabrier (2019) established new models of Jupiter which satisfy both Juno’s gravity data and the outer helium and heavy element abundances from Galileo, showing a considerable entropy increase between the outer and inner envelopes and an inward decreasing abundance of heavy elements in the inner envelope.
Citation: Ni 2018
Citation function: Background