Using binary system to solve for the Mass

The period and velocity 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 period and velocity of the black hole companion's orbit to do that.

Astronomers can learn a number of things about objects in space by looking at subtle details and changes in the light we receive from those objects. The plot below shows the velocity of Cygnus X-1's optical companion as a function of time. The plot was generated using data from the optical spectrum of the star. The radial velocity we observe changes over time as the star orbits around Cygnus X-1. When the star is moving away from us, the velocity is positive. When the star is moving toward us, the velocity is negative.

From this plot it is possible to determine the tangential velocity and the period of the optical companion. Click on the image for a larger view. It might help to print out the plot so that you can draw on it to find the information you need.

Don't forget to make a note of the values for the period and velocity that you find – you'll need it to solve the mass 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