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An isothermal core is a central region of a body (planet or star) that is all of the same temperature. In "everyday life", higher pressure results in a higher temperature, so the temperature generally varies by distance from the center of a body held together by self-gravitation. Under some conditions such as very high temperatures and pressures, the ideal gas law may not apply, and this temperature/pressure relationship does not exist, and the material is termed degenerate. Within a star, if fusion occurs in a spherical shell surrounding the core, it will keep such a core at a high temperature, but within it, heat spreads until there is no temperature gradient inward from the burning shell to the center once the temperature is sufficiently high that energy transferred outward balances the energy released. Within the isothermal core, density and pressure will still rise toward the center, but not temperature.
Isothermal cores have been proposed as likely in some types of planets and stars, including neutron stars and some giant stars, and possibly gas giants such as Jupiter. Simulations and other models are sometimes created using an isothermal core as a likely-reasonable approximation.