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Hi,

The evolution of a close binary is driven by angular momentum loss to gravitational

radiation, so that

(dJ/dt)/J = -(32G^3 M1*M2*(M1 + M2))/5*(c^5)* a^4

From relations mass-radius, (-dM2/dt)/M2 = -(dJ/dt)/J / (4/3 - q) and

R2/a = ((M2)/(M1 + M2))^(1/3)* (0.462)

M2 = m2*Mo, M1 = m1*Mo m2~R2/Ro

I calculated dM/dt ~ 10^-10*(P/2(h))^(-2/3)*Mo/yr for for main-sequence...

But when the secondary becomes degenerate the relations change.

A degenerate star has a mass–radius relation of the form: R2 = Km2^(-1/3) and

P ∝ M2 ^-1, K = 2x10^9cm and (-dM2/dt)/M2 = -(dJ/dt)/J / (2/3 - q) .

I need show that dM/dt ~ 10^-12*(P/2(h))^(-14/3)*Mo/yr. But ,already tried very unsuccessfully.

THis is a question of book : accretion power in astrophisics (JUAN FRANK) cap 4 ,ex 3

thank you very much.

The evolution of a close binary is driven by angular momentum loss to gravitational

radiation, so that

(dJ/dt)/J = -(32G^3 M1*M2*(M1 + M2))/5*(c^5)* a^4

From relations mass-radius, (-dM2/dt)/M2 = -(dJ/dt)/J / (4/3 - q) and

R2/a = ((M2)/(M1 + M2))^(1/3)* (0.462)

M2 = m2*Mo, M1 = m1*Mo m2~R2/Ro

I calculated dM/dt ~ 10^-10*(P/2(h))^(-2/3)*Mo/yr for for main-sequence...

But when the secondary becomes degenerate the relations change.

A degenerate star has a mass–radius relation of the form: R2 = Km2^(-1/3) and

P ∝ M2 ^-1, K = 2x10^9cm and (-dM2/dt)/M2 = -(dJ/dt)/J / (2/3 - q) .

I need show that dM/dt ~ 10^-12*(P/2(h))^(-14/3)*Mo/yr. But ,already tried very unsuccessfully.

THis is a question of book : accretion power in astrophisics (JUAN FRANK) cap 4 ,ex 3

thank you very much.

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