We consider here a robust study of stellar dynamics for White Dwarf Stars with polytropic matter in the weak field approximation using the Lane-Emden equation from the brane-world scenario. We also derive an analytical solution to the nonlocal energy density and show the behavior and sensitivity of these stars to the presence of extra dimensions. Similarly, we analyze its stability and compactness, in order to show whether it is possible to be close to the conventional wisdom of white dwarfs dynamics. Our results predicts an average value of brane tension as: $langlelambdaranglegtrsim84.818;rm MeV^4$, with a standard deviation $sigmasimeq82.021;rm MeV^4$ which comes from a sample of dwarf stars, being weaker than other astrophysical observations but remaining above of cosmological results provided by nucleosynthesis among others.
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