## Project for ASTR7741

Fall Semester, 2007

Separation as a Function of Time During Binary Mass-Transfer

Part I: Conservative System of Point Masses

First, consider two point mass objects, M1 and M2, in circular orbit about one another. Derive an expression for their total (orbital) angular momentum Jorb in terms of their mass ratio "q", total mass "M", and separation "a". Plot "a" versus "q" for fixed "M" and "Jorb". What is the gravitational wave strain "hnorm" as a function of "q"?

Part II: Finite-Sized stars with Spin

Now, consider that each of the two stars has a radius R1 and R2, and that both stars are rotating synchronously with their orbital motion. Write an expression for the system's total angular momentum "Jtot" that includes the spin angular momentum of each star, in addition to the orbital angular momentum. Plot "a" versus "q" assuming the stars remain tidally locked (and conserve "M" and "Jtot") during the mass-transfer event. Finally, what is the gravitational wave strain "hnorm" as a function of "q" under this condition?