{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hwk8 - M ’ 1 M ± and R = 10 km Comment on the...

This preview shows page 1. Sign up to view the full content.

AST371 - Introduction to Astrophysics Assignment 8 - Oct. 28, 2009 1. Consider an ideal gas that undergoes an adiabatic process. Starting with the relationship T ( r ) T 0 = P ( r ) P 0 ( γ - 1) where T 0 and P 0 are respectively the temperature and the pressure at the center of the distribution ( r = 0), show that the temperature distribution is given by dT ( r ) dr = T ( r ) P ( r ) γ - 1 γ dP ( r ) dr 2. Consider an ideal gas of H atoms in a stellar atmosphere, i.e., in a region just outside of the star, where the acceleration g = - GM r can be assumed to be constant; M is the mass of the star. Assuming hydrostatic equilibrium of the gas with the mass of the star, calculate the scale height of a gas of T = 10 6 K in the atmosphere of a neutron star, for which
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern