  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: $\langle\lambda\rangle\gtrsim84.818\;\rm MeV^4$,
with a standard deviation $\sigma\simeq82.021\;\rm MeV^4$ 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.
