GRB as Vacuum Discharge of Schwinger Critical Field at Fireball Surface

ATel #10; R. Lieu, Y. Takahashi (U Ala, Huntsville), T. W.B. Kibble (Imperial College)
on 7 Mar 1998; 00:50 UT
Credential Certification: Richard Lieu (lieur@cspar.uah.edu)

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It has long been recognized[1] that when a static electric field exceeds a critical value E_c corresponding to an electron acceleration of a_c ~2.4 x 10^31 cm per sec per sec, it is unstable with respect to pair production. The `vacuum breakdown' causes a E=E_c field to dissipate its energy in a timescale of ~10^-16 seconds, resulting in a mixture of gamma rays and pair plasma at temperature ~0.5 MeV. This paper outlines a theory of GRB based on the Schwinger mechanism (SM).

The first detection of optical afterglow[2] quickly led us to ascertain that GRB must be cosmological. Furthermore, the high redshift association[3,4] and the presence of deep and rapid modulations in the GRB flux[5] render it generally accepted that the intrinsic energy of a GRB is > 10^52 ergs and the size of the burst region (the `fireball', FB) is < 3 x 10^7 cm.

The data pose difficulties: even for gamma rays the Thomson optical depth of the FB is >> 1, implying radiation cannot escape unless the latter has expanded sufficiently. By then, however, the source size will be incompatible with observations. We emphasize that a relativistic bulk outflow is not an inevitable fate of the FB. If the FB contains 1 M_solar worth of baryonic matter (as we shall assume here) the gravitational potential would be sufficient to bind a system of matter and radiation at kT < 10 MeV within the FB radius.

We propose here an alternative model of GRB. We presume the energy injection at the FB is instantaneous. Since a quantum diffuses very slowly out of the FB, the energy density is simply total GRB energy : source volume. One then obtains U_GRB ~10^29 ergs per cc, or black body temperature of kT ~5 MeV. The dense FB ensures complete thermal equilibrium. This implies electrons and protons also have kT ~5 MeV, and system is bound.

To implement SM, one notes that the radiation pressure exerted by an expanding FB on the ambient matter (or an `envelope') can cause a vacuum breakdown. The radiative electron acceleration is a = sigma_Th U_GRB/m_e ~7 x 10^31 cm s^-2 > a_c. Since proton acceleration is reduced by (m_e/m_p)^3, momentarily the electrons advance radially outwards. This means a field E > E_c must exist because the electrons move with a > a_c with respect to the protons. Such a field will discharge, and will convert the surface flow energy of the FB into thermal energy at kT < 0.5 MeV in an optically thin region just outside it. The discharge will propagate into the FB and `extract' the bulk of its energy into an avalanche of e+ e- pairs. The ensuing annihilation produces gamma rays which can escape to make a GRB.

On the observed GRB duration ~1 - 10 s. A static electric field of strength E ~ E_c must have length > an electron Compton wavelength ~2.5 x 10^-10 cm before it can discharge. Thus the FB radiation must push out the ambient plasma selectively to produce a discharge layer of thickness ~2.5 x 10^-10 cm, the SM will then dissipate field in 10^-16 sec. The ratio of these two nos implies the discharge propagates into the FB at speed 2.5 x 10^6 cm per sec. Given the FB size it will be consumed within the observed timescale. This slow, inward moving discharge layer provides ample time for the gamma rays and pairs already created outside it by the SM to escape from the optically thick FB (none of the created quanta is gravitationally bound).

The theory explains with simplicity the basic observed properties of a GRB, and may also be relevant to supernova explosions.

References

• [1] Schwinger, J. 1951, Phys. Rev. 82, 664.
• [2] van Paradijs, J. et al 1997, Nature, 386, 686.
• [3] Bond, H.E. 1997, IAU Circ 6654.
• [4] Frail, D.A. \& Kulkarni, S.R. 1997, IAU Circ 6662.
• [5] Bhat, P.N. et al, 1992, Nature, 359, 217

GRB as Vaccum Discharge of Super-Schwinger Electric Fields