Angular momentum loss by radiation gravitational

[Leandro Souza]

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.

 

[lippyka]

</code>The evolution of a close binary is driven by angular momentum loss to gravitational radiation, so that(dJ/dt)/J = -(32G3M1M2(M1 + M2))/5c5a4 From relations mass-radius, (-dM2/dt)/M2 = -(dJ/dt)/J / (4/3 - q) and R2/a = ((M2)/(M1 + M2))^(1/3)* (0.462)M2 = m2Mo, M1 = m1Mo 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) andP ∝ 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.To solve this, we must first rearrange the formula for angular momentum loss to get it in terms of the period P. We can do this by substituting in the mass-radius relation and the mass-period relation:(dJ/dt)/J = -(32G3M1M2(M1 + M2))/5c5a4 = -(32G3M1M2(M1 + M2))/5c5(2K/M2^(1/3))^4= -(32G3M1M2(M1 + M2))/5c5(2K^4/M2^(4/3))= -(32G3M1M2(M1 + M2))/5c5(2K^4/P^(14/3))Now, we can substitute this