Matter closest to the black hole in Cygnus X-1 orbits at approximately what fraction of the speed of light?

Matter closest to the black hole in Cygnus X-1 orbits at approximately what fraction of the speed of light?

• A. 1/4
• B. 1/2
• C. 3/4
• D. 1

Answer: (B)

Matter in an accretion disk around a black hole can reach relativistic orbital speeds, especially right at the inner edge of the disk. For a non-spinning black hole, the innermost stable circular orbit sits at six gravitational radii, r = 6GM/c^2. Using the Newtonian estimate v ≈ sqrt(GM/r) gives v ≈ c / sqrt(6) ≈ 0.41c, a little over 40% of light speed. If the black hole spins, the inner edge can move closer and the orbital speed climbs, often reaching about half the speed of light for the inner disk regions in Cygnus X-1. So the closest matter is moving at roughly one-half of c. The other fractions would imply slower or much faster conditions than the typical inner-disk dynamics near such a system, with speeds approaching but not reaching the speed of light.

Matter in an accretion disk around a black hole can reach relativistic orbital speeds, especially right at the inner edge of the disk. For a non-spinning black hole, the innermost stable circular orbit sits at six gravitational radii, r = 6GM/c^2. Using the Newtonian estimate v ≈ sqrt(GM/r) gives v ≈ c / sqrt(6) ≈ 0.41c, a little over 40% of light speed. If the black hole spins, the inner edge can move closer and the orbital speed climbs, often reaching about half the speed of light for the inner disk regions in Cygnus X-1. So the closest matter is moving at roughly one-half of c. The other fractions would imply slower or much faster conditions than the typical inner-disk dynamics near such a system, with speeds approaching but not reaching the speed of light.