Giant planets are thought to have cores in their deep interiors, and the division into a heavy-element core and hydrogen-helium envelope is applied in both formation and structure models. We show that the primordial internal structure depends on the planetary growth rate, in particular, the ratio of heavy elements accretion to gas accretion. For a wide range of likely conditions, this ratio is in one-to-one correspondence with the resulting post-accretion profile of heavy elements within the planet. This flux ratio depends sensitively on the assumed solid surface density in the surrounding nebula. We suggest that giant planets cores might not be distinct from the envelope and includes some hydrogen and helium, and the deep interior can have a gradual heavy-element structure. Accordingly, Jupiters core may not be well-defined. Accurate measurements of Jupiters gravitational field by Juno could put constraints on Jupiters core mass. However, as we suggest here, the definition of Jupiters core is complex, and the cores physical properties (mass, density) depend on the actual definition of the core and on its growth history.
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