The energy of GW150914

Adapted from IOAA 2021 (Bogotá, remote), theory problem Q1. We have restated it in our own words and kept the original data. The problem uses 35 and 30 solar masses, later estimates for the same black holes. The first published values, used in the text, were 36 and 29, and both give 3 solar masses radiated. The solution was last checked on 23 October 2026.

In GW150914 black holes of 35 and 30 solar masses merged into one of 62 solar masses. Ignore their spin and take the energy released, $E_{\text{GW}}$, to have gone entirely into gravitational waves. A supernova releases $E_{\text{SN}}=2\times {10}^{44}$ J. Estimate $E_{\text{SN}}/E_{\text{GW}}$. (5 points)

Answer$E_{\text{SN}}/E_{\text{GW}}=3.7\times {10}^{-4}$, so the merger gave out about 2700 times as much energy as a supernova, almost all of it in a fraction of a second.