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Abstract
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It is shown that, due to the effects of non-extensivity, the ordinary well-known Jeans mass limit (𝑀𝐽 ), resting on Newton’s gravity and Gibbs statistics, may not be valid everywhere. Indeed, the Tsallis formalism allows smaller values for Jeans mass compared to 𝑀𝐽 , which may justify star formation in cases like Bok globules whose masses are smaller than 𝑀𝐽 . The values of non-extensive parameter 𝑞 corresponding to some Bok objects are also computed. Thereinafter, the Lane–Emden equation is also calculated as the result of satisfying the condition of hydrostatic equilibrium. The research is concluded by introducing a novel Lane–Emden equation to provide a more detailed exploration of the effects of non-extensivity on stellar equilibrium. This equation, accompanied by analytical solutions, can be useful for modeling the behavior of low-mass stars and would provide insights into the distribution of density, pressure, and temperature in self-gravitating systems like protoplanetary disks and neutron stars.
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