Polytropic star structure analysis under Bonnor–Ebert gas sphere astrophysical configuration thorough investigating analytical solutions to the related Lane–Emden equation

In this paper, Bonnor–Ebert gas sphere model of polytropic stars has been investigated through an analytical approach. Two confirmed and well-established methods have been used: the Enhanced Lagrangian Formulation Method ELFM and the Boubaker Polynomials Expansion Scheme BPES. Solutions to the related generalized Lane–Emden equation of the second kind have been expressed and plotted. Results have given evidence to the relevance of the dimensionless Bonnor–Ebert radius, in good agreement with some recently proposed profiles.