[Paper Review] The dyadosphere of black holes and gamma-ray bursts

Giuliano Preparata, R. Ruffini+1 more|arXiv (Cornell University)|Oct 12, 1998

Gamma-ray bursts and supernovae10 citations

TL;DR

This paper proposes that extreme electromagnetic fields around certain black holes—electromagnetic black holes (EMBHs)—can trigger vacuum pair production via the Schwinger effect, forming a 'dyadosphere' where electron-positron pairs rapidly form. It shows that such processes in 10M⊙ and 10⁵M⊙ EMBHs can generate relativistic pair-electromagnetic pulses (P.E.M. pulses) with sufficient energy to power observed gamma-ray bursts, including GRB971214 at z=3.4.

ABSTRACT

The "dyadosphere" has been defined (Ruffini, Preparata et al.) as the region outside the horizon of a black hole endowed with an electromagnetic field (abbreviated to EMBH for "electromagnetic black hole") where the electromagnetic field exceeds the critical value, predicted by Heisenberg & Euler for $e^+ e^-$ pair production. In a very short time ($\sim O(\hbar/(mc^2))$), a very large number of pairs is created there. We here give limits on the EMBH parameters leading to a Dyadosphere for $10M_{\odot}$ and $10^5M_{\odot}$ EMBH's, and give as well the pair densities as functions of the radial coordinate. We here assume that the pairs reach thermodynamic equilibrium with a photon gas and estimate the average energy per pair as a function of the EMBH mass. These data give the initial conditions for the analysis of an enormous pair-electromagnetic-pulse or "P.E.M. pulse" which naturally leads to relativistic expansion. Basic energy requirements for gamma ray bursts (GRB), including GRB971214 recently observed at $z=3.4$, can be accounted for by processes occurring in the dyadosphere. In this letter we do not address the problem of forming either the EMBH or the dyadosphere: we establish some inequalities which must be satisfied during their formation process.

Motivation & Objective

• To establish theoretical conditions under which extreme electromagnetic black holes (EMBHs) can form a dyadosphere via vacuum pair production.
• To determine the parameter space (e.g., charge, mass) of EMBHs that support dyadosphere formation for stellar-mass and supermassive black holes.
• To model the initial conditions of pair density and energy distribution in the dyadosphere for subsequent relativistic expansion.
• To assess whether the energy output from the dyadosphere can account for the observed energetics of gamma-ray bursts (GRBs), including high-redshift events like GRB971214.
• To derive inequalities governing the formation process of EMBHs and their dyadospheres without addressing their astrophysical origin.

Proposed method

• Define the dyadosphere as the region outside an EMBH where the electromagnetic field exceeds the Schwinger critical field strength for e⁺e⁻ pair production.
• Use the Heisenberg-Euler effective Lagrangian to estimate the rate of vacuum pair production in strong fields.
• Calculate pair production timescale ∼ħ/(mc²) to show rapid formation of a dense pair plasma.
• Assume thermodynamic equilibrium between the pair plasma and a photon gas to estimate average energy per pair as a function of EMBH mass.
• Model the resulting system as a relativistic pair-electromagnetic pulse (P.E.M. pulse) driven by the initial pressure gradient.
• Derive constraints on EMBH parameters (mass, charge) that allow dyadosphere formation and sufficient energy output for GRBs.

Experimental results

Research questions

• RQ1 What are the critical electromagnetic field strengths and EMBH parameters required for dyadosphere formation in 10M⊙ and 10⁵M⊙ black holes?
• RQ2 How does the pair density vary with radial distance from the EMBH in the dyadosphere?
• RQ3 What is the average energy per electron-positron pair in the dyadosphere, and how does it scale with EMBH mass?
• RQ4 Can the energy released in the dyadosphere process account for the luminosity and total energy of observed gamma-ray bursts, such as GRB971214 at z=3.4?
• RQ5 What physical inequalities must be satisfied during the formation of EMBHs and their dyadospheres to sustain the process?

Key findings

• For 10M⊙ and 10⁵M⊙ EMBHs, the paper derives specific limits on charge and electromagnetic field strength that lead to dyadosphere formation.
• Pair density in the dyadosphere is calculated as a function of radial coordinate, showing high densities near the horizon.
• The average energy per pair in the dyadosphere is estimated based on thermodynamic equilibrium with a photon gas, providing initial conditions for P.E.M. pulse dynamics.
• The resulting P.E.M. pulse is shown to undergo relativistic expansion, consistent with the observed properties of gamma-ray bursts.
• The energy output from the dyadosphere process is sufficient to explain the high luminosity and total energy of GRB971214 at redshift z=3.4.
• The study establishes necessary inequalities for the formation of EMBHs and their dyadospheres, though it does not address the astrophysical origin of these objects.