Constraining Electromagnetic Signals from Black Holes with Hair

Abstract: We constrain a broad class of "hairy" black hole models capable of directly sourcing electromagnetic radiation during a binary black hole merger. This signal is generic and model-independent since it is characterized by the black hole mass ($M$) and the fraction of that mass released as radiation ($\epsilon$). For field energy densities surpassing the Schwinger limit, this mechanism triggers pair-production to produce a gamma-ray burst. By cross-referencing gravitational wave events with gamma-ray observations, we place upper bounds of $\epsilon<10^{-5}-10^{-4}$ for $10-50$ $M_\odot$ black holes depending on the black hole mass. We discuss the weak detection of a gamma-ray burst following GW150914 and show that this event is consistent with rapid electromagnetic emission directly from a "hairy" black hole with $\epsilon\sim10^{-7}-10^{-6}$. Below the Schwinger limit, ambient charged particles are rapidly accelerated to nearly the speed of light by the strong electromagnetic field. For 1-50 $M_\odot$ black holes and $\epsilon$ ranging from $10^{-20}$ to $10^{-7}$, the typical proton energies are $\sim20$ GeV-20 TeV and electron energies are $\sim0.01-10$ GeV. At these energies, cosmic ray protons and electrons quickly diffuse into the Milky Way's background magnetic field, making it difficult to identify a point source producing them. Overall, constraining $\epsilon$ in this less energetic regime becomes difficult and future constraints may need to consider specific models of "hairy" black holes.