# National Aeronautics and Space Administration

## Using binary system to solve for the Mass

### The mass of the black hole's companion

Recap: Your astronomy professor has tasked the class with determining the mass of the black hole candidate, Cygnus X-1. You thought of three possible ways to do this, one of which will give you the right answer. You've decided to try using Kepler's Laws, and need the inclination of the system's orbit to do that.

Evidence for both the binary nature of HDE226868 and the link with Cygnus X-1 came when the Copernicus satellite took a closer look at the X-ray source. It was discovered that the overall intensity of the X-rays drops off slightly every 5.6 days – the same time it take for HDE226868 to make one revolution around its partner. Now, the X-rays do not drop off completely, so the X-ray source doesn't move completely behind the star from our point-of-view. At the same time, the X-rays do diminish, so the star does partially block the X-ray source as they orbit. This gives us a clue as to its inclination.

As a refresher, if a system is face-on, or the inclination is 0° the X-ray source would never be blocked.

If the system was edge-on, or the inclination is 90°, then X-ray source would be blocked completely for a portion of each orbit.

Since the X-ray source is partially blocked on each orbit, the system must be inclined at some angle between 0° and 90°. The best estimate for the inclination angle of the Cyg X-1 system is ~30°, though we may have to wait for future missions to get a more definitive answer.

Don't forget to make a note of this – you'll need it to solve the equation!

 A service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA/GSFC