Electron-positron pair productions in gravitational collapses In collaboration with Wen-Biao Han, & Remo Ruffini ICRANet & Physics Department, University of Rome She-Sheng Xue MG13, Stockholm, July 5 th, 2012

Motivation We attempt to study the possibility of electron- positron pair productions in variations of electrical field and energy in pulsation and collapsing of neutral compact star cores. We show a possible way that gravitational energy can be converted to electromagnetic energy in stellar core collapse and pulsation, possibly accounting for high-energy Gamma-Ray emissions.

t Pair plasma oscillations Already discussed Pairs and photon plasma Hydrodynamic expansion Already discussed Already discussed R. Ruffini, J.D. Salmonson, J.R.Wilson, S.-S. Xue A&A 350 (1999) 334; 359, (2000) 855. R. Ruffini, L. Vitagliano, S.-S. Xue, PLB 573 (2003) 33; 559 (2003) 12. Electron-positron pairs production and evolution in gravitational collapses of charged cores and strong fields R Initial conditions of strong charged cores and Fields are hardly justified !!!

Strong (overcritical) electric fields in surface layer of stellar cores Quark stars (e.g. Usov, PRL 80, 230, 1997;…..); Neutron stars (e.g. M. Rotondo, Jorge A. Rueda, R. Ruffini and S.-S. Xue, Phys. Rev. C83, D84 (2011); Phys. Lett. B701 (2011), Nucl.Phys. A872 (2011).....) Modeling strong and weak interactions, we solve the Einstein- Maxwell-Thomas-Fermi equations, Blue: proton Red: electron Overcritical field Electron-positron pair productions are not permitted by Pauli blocking. + _

Macroscopic and microscopic processes (i) macroscopic processes: gravitational pulsation, and collapse, hydrodynamic… (slowly varying in large length scale), described by equations of fields and rates. (ii) microscopic processes: strong and electroweak interactions, thermal collisions … (fast varying in short length scale), described by equations of fields and rates. Local and instantaneous approximation Equations of states (distribution functions) and particle number conservations. This approximation is adopted in both analytical and numerical approaches. Indeed, it is a good approximation for fields and their variations are small. On the other hand, it is difficult to solve these sets of equations of fields and particles interacting at very different scales: meter and Compton length.

Two space-time scales of the problem There are two space-time scales in core collapses: One is the gravitational interaction scale: in meter and second ; Another is the electromagnetic interaction scale: in Compton length and Compton time. This means it is almost impossible to numerically simulate the two processes together! We treat them independently: the core collapse given by analytical collapse equation and the electron-fluid dynamics calculated numerically in Compton space-time scale.

Electromagnetic field and processes In local and instantaneous approximation, electric field and processes are eliminated in a neutral system, due to electric charge conservation. Internal electric fields can be developed by a dynamics acting differently on positive and negative charges (see for example E. Olson and M. Bailyn, Phys. Rev. D 12, 3030 (1975), and D 13, 2204 (1976), and M. Rotondo, Jorge A. Rueda, R. Ruffini and S.-S. Xue, Phys. Rev. C 83, (2011); Phys. Lett. B 701, 667 (2011)). If electric fields are weak and slowly vary in space and time, the validity of local and instantaneous approximation can be justified. However, electric fields are so strong (overcritical) and fast vary in space and time, that very rapid electric processes, like electron- positron pair productions, can take place. In this case, we are forced to give up the local and instantaneous approximation, and integrate Maxwell equation of fields and rate-equations of particles, as well as equations for energy-momentum conservations. We study this possibility.

Dynamical equations

Baryon core and its gravitational collapse (pulsation) to be determined by Einstein equation for gravitational collapse. Core collapsing velocity

Initial and Equilibrium configurations Blue: proton Red: electron + _

Electric field and Electrons: Maxwell equation, continuous, energy- momentum conservations and equation of state

Oscillations and Relaxation

Oscillation, relaxation and energy-conservation The relaxation from one equilibrium configuration to another Oscillating energy

Electron-positron pair productions in oscillating electric fields Occupied electron levels H. Kleinert, R. Ruffini, S.-S. Xue, PRD 78 (2008)

Pair-production rate

Core gravitational collapse C. Cherubini, R. Ruffini and L. Vitagliano, Phys.~Lett.~B545 (2002) 226.

Dyadosphere of electron and positron pairs The energy-number densities and total energy-number of electron-positron pairs are the same order as that estimated in the model of dyadosphere.

Some remarks. Cores undergo either collapses or pulsations, depending on the balance between attractive gravitational energy and repulsive electric and internal energies. The pulsation frequency can be expressed as The adiabatic approximation we adopted is self-consistently and quantitatively justified by process rates pair plasma oscillation and pair-photon plasma rates. Nevertheless, these results should be further verified by numerical algorithms integrating Einstein-Maxwell equations in gravitational collapses. The possible consequences of these electromagnetic processes discussed could be relevant and important for explaining energetic sources of Soft- Gamma-Ray Repeaters (SGRs) and progenitors of Gamma-Ray Bursts (GRBs).

The existence of a separatrix is a general relativistic effect: the radius of the gravitational trap is The fraction of energy available in the expanding plasma is about 1/2.