Black Hole Radii

I set the alarm for 8:55 AM. Brutal, but I wanted to watch live the National Science Foundation Event Horizon Telescope news conference. I was expecting the first image of a black hole, and the EHT team did not disappoint. But the black hole was not the Milky Way’s Sgr A*, but M87*, a thousand times further but a thousand times larger (billions rather than millions of solar masses).

For Astronomy Table lunch at Kitt’s Soup & Bread, I quickly created the graphic below to illustrate various radii of a mass M Schwarzschild black hole, a good approximation to this rotating Kerr black hole. The event horizon with reduced circumference R_s = 2 G M / c^2 is the point of no return, the causal disconnection from which even light can’t escape. The innermost stable circular orbit at 3R_s marks the inner edge of the accretion disk. Massless particles like photons can orbit even closer, at the 1.5R_s photon sphere, where you can see your back by looking straight ahead! The ring of light (mainly 1.3 mm synchrotron radiation) in the EHT photo comes from photons with impact parameter \sim 2.6R_s that just graze the photon sphere and can orbit multiple times before spiraling in or out.

Schwarzschild ("black shield") black hole with event horizon, unstable photon sphere, grazing photon sphere, and innermost stable circular orbit

Schwarzschild (“black shield”) black hole with event horizon, unstable photon sphere, grazing photon sphere, and innermost stable circular orbit

About John F. Lindner

John F. Lindner was born in Sleepy Hollow New York and educated at the University of Vermont and Caltech. He is a professor of physics and astronomy at The College of Wooster. He has enjoyed multiple yearlong sabbaticals at Georgia Tech, University of Portland, University of Hawai'i, and North Carolina State University. His research interests include nonlinear dynamics, celestial mechanics, and variable stars.
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