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Shocks from Exploding Primordial Black Holes in the Early Universe

Miguel Vanvlasselaer, Sokratis Trifinopoulos, Alexandra P. Klipfel, David I. Kaiser

Abstract

We investigate how Hawking radiation from low-mass primordial black holes deposits energy into the early-universe plasma and show that the resulting phenomena are hydrodynamic rather than purely diffusive. Combining analytic arguments with relativistic hydrodynamic simulations, we find that the plasma first develops a quasi-steady outflow during the slow evaporation stage, while the final runaway phase of evaporation produces an expanding fireball that launches a shock wave into the surrounding medium. We characterize the thermalization scale of the Hawking products, the conditions under which shocks form, and the evolution and propagation of shocks. Additionally, we show that these shocks can locally restore electroweak symmetry, identifying exploding PBHs as a potentially important source of out-of-equilibrium dynamics in the early universe with profound phenomenological implications.

Shocks from Exploding Primordial Black Holes in the Early Universe

Abstract

We investigate how Hawking radiation from low-mass primordial black holes deposits energy into the early-universe plasma and show that the resulting phenomena are hydrodynamic rather than purely diffusive. Combining analytic arguments with relativistic hydrodynamic simulations, we find that the plasma first develops a quasi-steady outflow during the slow evaporation stage, while the final runaway phase of evaporation produces an expanding fireball that launches a shock wave into the surrounding medium. We characterize the thermalization scale of the Hawking products, the conditions under which shocks form, and the evolution and propagation of shocks. Additionally, we show that these shocks can locally restore electroweak symmetry, identifying exploding PBHs as a potentially important source of out-of-equilibrium dynamics in the early universe with profound phenomenological implications.
Paper Structure (46 sections, 157 equations, 19 figures, 1 table)

This paper contains 46 sections, 157 equations, 19 figures, 1 table.

Table of Contents

  1. Introduction
  2. Notation and conventions
  3. Hawking evaporation of primordial black holes
  4. Energy injection in the plasma from evaporation and fluid motion
  5. Thermalization of the Hawking-radiated particles
  6. Heat transfer and fluid flow
  7. The hydrodynamical description
  8. Hydrodynamical evolution
  9. Timescales involved in the energy injection
  10. Hydrodynamic transport of energy long before the explosion
  11. Hydrodynamical evolution of the shock wave: instantaneous energy injection
  12. Overview of the instantaneous picture
  13. Phase 1: Formation and propagation of the relativistic shock (Blandford-McKee regime)
  14. Dependence of shock on initial fireball.
  15. The shock evolution: analytical results.
  16. ...and 31 more sections

Figures (19)

  • Figure 1: ( Top) Primary Hawking emission spectra for a PBH with $M = 10^6 \, {\rm g}$. ( Bottom) Total primary Hawking spectra summed over all SM particle species for PBH masses from $M=10^{-5} \, {\rm g}$ (dark red) to $M=10^9 \, {\rm g}$ (black). Plots prepared with BlackHawk v2.2Arbey:2019mbcArbey:2021mbl.
  • Figure 2: Total emitted power from a single PBH as a function of time for several values of initial mass $M_i$. See Eq. (\ref{['eq:TotalInjectionTime']}). The PBHs are initialized at $t_{\rm EW}\simeq10^{-11}\,{\rm s}$ and the emission is truncated at $M(t)=10^{-5}\,{\rm g}$ when the PBHs approach the Planck scale.
  • Figure 3: Dependence of the initial fireball radius $L_{\rm fb}$ on the background temperature, from Eq. \ref{['eq:Lfb']}. This sets the initial size of the over-pressured sphere of plasma surrounding the PBH after it explodes and instantaneously injects energy $E_{\rm inj}=M_{\rm thres}(T_{\rm b})$.
  • Figure 4: ( Top) Threshold PBH mass for instantaneous energy injection from Eq. (\ref{['eq:Mthres']}) as a function of cosmological background temperature $T_{\rm b}$. ( Bottom) Initial temperature of the fireball $T_{\rm fb}$ as a function of background temperature $T_{\rm b}$ at the time of the PBH explosion. The parameter $K$ sets the amount of injected energy, with $K=1$ corresponding to the purely instantaneous injection case. The inset plot shows the minimum background temperature $T_{\rm min}$ such that a PBH explosion will create a fireball with $T_{\rm fb}>T_{\rm EW}\simeq162 \, {\rm GeV}$ (See Sec. \ref{['sec:Pheno_impl']} for discussion of EW symmetry breaking).
  • Figure 5: Convergence to the Steady State profile ( Left) Behavior of the fluid velocity for the case of slow energy injection, earlier than the PBH explosion. The injected power in this simulation is fixed to $P_{\rm num} = 450$ and it is injected on a radius being $2L_{\rm LPM}$. ( Right) Same for the temperature. One observes that the velocity and the temperature profiles each reach a time-independent steady state solution.
  • ...and 14 more figures