Black hole in X-Ray Binary.
(2.75/11.0 points)
An X-ray binary consists of 2 stars with masses (the accreting compact object) and (the donor). The orbits are circular with radii and centered on the center of mass.
(a) Find the orbital period of the binary following the guidelines given in lectures. Express your answer in terms of , and (enter m_1 for , m_2 for , r_1 for , r_2 for , pi for and G for ).
correct
(b) In the case of Cyg X-1 (as discussed in lectures), the orbital period is 5.6 days. The donor star is a “supergiant" with a mass 30 times that of the sun. Doppler shift measurements indicate that the donor star has an orbital speed of about 148 km/sec. Calculate (in meters).
incorrect
(c) Calculate (in meters).
hint: Your calculations will be greatly simplified if instead of you set up your equations in terms of , and using some relation between the distances and the masses. Once you express your equation in terms of , you will find a third order equation in . Only one solution is real; the other two are imaginary. There are various ways to find an approximation for . You can find the solution by trial and error using your calculator, or you can plot the function.
incorrect
(d) Now calculate the mass of the accreting compact object (express that as ratio to the mass of the sun).
incorrect
As discussed in lectures, since this turns out to be substantially larger than 3 times the mass of the sun, it is strongly believed to be a black hole.