Unformatted text preview: M ’ 1 M ± and R = 10 km. Comment on the possibility of the existence of an atmosphere around a neutron star. 3. (a) Consider a polytropic gas of polytropic index n = 0 in hydrostatic equilibrium with its own gravitational mass, P ( r ) = Kρ ( r ) γ , γ = 1+1 /n . Show that a solution of the Lane-Emden equation is given by the function ξ ( x ) ξ ( x ) = 1-x 2 6 with the boundaries conditions ξ (0) = 1, dξ/dx | = 0. (b) Find the distribution of the normalized density and pressure as function of the dimensionless variable x , ρ ( x ) /ρ and P ( x ) /P , and plot them as function of x ....
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- Fall '09
- Fundamental physics concepts, hydrostatic equilibrium