We have derived four coupled first-order differential equations describing stellar structure. Let us rewrite them here: dP(r) GM(r)p(r) (3.56) dr r2 dM(r) = 4rr²p(r), dr (3.57) dT(r) 3L(r)« (r)p(r) (3.58) dr 4Jt p24acT(r)³’ dL(r) (3.59) 4Jt r? p(r)e(r). dr We can define four boundary conditions for these equations, for example, (3.60) M(r = 0) = 0, %3D %3D (3.61) L(r = 0) = 0, %3D (3.62) P(r = r.) = 0, (3.63) M(r = r.) = M,, %3D
We have derived four coupled first-order differential equations describing stellar structure. Let us rewrite them here: dP(r) GM(r)p(r) (3.56) dr r2 dM(r) = 4rr²p(r), dr (3.57) dT(r) 3L(r)« (r)p(r) (3.58) dr 4Jt p24acT(r)³’ dL(r) (3.59) 4Jt r? p(r)e(r). dr We can define four boundary conditions for these equations, for example, (3.60) M(r = 0) = 0, %3D %3D (3.61) L(r = 0) = 0, %3D (3.62) P(r = r.) = 0, (3.63) M(r = r.) = M,, %3D
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Consider a hypothetical star of radius R, with density rho that is constant,i.e., independent of radius. The star is composed of a classical, nonrelativistic, ideal gas of fully ionized hydrogen. Solve the equations of stellar structure for the pressure profile, P(r), with the boundary condition P(R)=0
An image of the stellar structure equations is attached.
Transcribed Image Text:We have derived four coupled first-order differential equations describing stellar structure.
Let us rewrite them here:
dP(r)
GM(r)p(r)
(3.56)
dr
r2
dM(r)
= 4rr²p(r),
dr
(3.57)
dT(r)
3L(r)« (r)p(r)
(3.58)
dr
4Jt p24acT(r)³’
dL(r)
(3.59)
4Jt r? p(r)e(r).
dr
We can define four boundary conditions for these equations, for example,
(3.60)
M(r = 0) = 0,
%3D
%3D
(3.61)
L(r = 0) = 0,
%3D
(3.62)
P(r = r.) = 0,
(3.63)
M(r = r.) = M,,
%3D
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