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1. A simple model of a star of radius R assumes (not very realistically!) that the density p is constant. We further assume that the star is made up of pure hydrogen, obeying the ideal gas law. (a) We assume that the gas pressure P drops to zero at the star's surface, e.g., we adopt the boundary condition P(R) = 0; for this part, solve the equations of stellar structure to get the pressure profile P = P(r). (Note: in this particular case, it does not matter whether you use the boundary condition P(R) = 0 or dP/dr = 0 at r=0!) (b) Find the temperature profile T = T(r). (c) If the nuclear energy generation rate & scales with temperature as ε ~ Tª, determine the radius at which & drops to 10% of its central value.

1. A simple model of a star of radius R assumes (not very realistically!) that the density p is constant. We further assume that the star is made up of pure hydrogen, obeying the ideal gas law. (a) We assume that the gas pressure P drops to zero at the star's surface, e.g., we adopt the boundary condition P(R) = 0; for this part, solve the equations of stellar structure to get the pressure profile P = P(r). (Note: in this particular case, it does not matter whether you use the boundary condition P(R) = 0 or dP/dr = 0 at r=0!) (b) Find the temperature profile T = T(r). (c) If the nuclear energy generation rate & scales with temperature as ε ~ Tª, determine the radius at which & drops to 10% of its central value.

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1. A simple model of a star of radius R assumes (not very realistically!) that the density p is constant. We further assume that the star is made up of pure hydrogen, obeying the ideal gas law. (a) We assume that the gas pressure P drops to zero at the star's surface, e.g., we adopt the boundary condition P(R) = 0; for this part, solve the equations of stellar structure to get the pressure profile P = P(r). (Note: in this particular case, it does not matter whether you use the boundary condition P(R) = 0 or dP/dr = 0 at r=0!) (b) Find the temperature profile T = T(r). (c) If the nuclear energy generation rate ɛ scales with temperature as ɛ * T, determine the radius at which ɛ drops to 10% of its central value. (d) Suppose that ɛ ~ T17. immediately above? What would be the corresponding radius, as computed in (c)
Transcribed Image Text:1. A simple model of a star of radius R assumes (not very realistically!) that the density p is constant. We further assume that the star is made up of pure hydrogen, obeying the ideal gas law. (a) We assume that the gas pressure P drops to zero at the star's surface, e.g., we adopt the boundary condition P(R) = 0; for this part, solve the equations of stellar structure to get the pressure profile P = P(r). (Note: in this particular case, it does not matter whether you use the boundary condition P(R) = 0 or dP/dr = 0 at r=0!) (b) Find the temperature profile T = T(r). (c) If the nuclear energy generation rate ɛ scales with temperature as ɛ * T, determine the radius at which ɛ drops to 10% of its central value. (d) Suppose that ɛ ~ T17. immediately above? What would be the corresponding radius, as computed in (c)
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