collapses In collaboration with WenBiao Han amp Remo Ruffini ICRANet amp Physics Department University of Rome SheSheng Xue MG13 Stockholm July 5 ID: 188475
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Slide1
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
, 2012Slide2
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. Slide3
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 !!!Slide4
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: protonRed: electron
Overcritical field
Electron-positron pair productions are not
permitted by Pauli blocking.
+
_Slide5
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 approximationEquations 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.
Slide6
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.Slide7
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, 045805 (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.Slide8
Dynamical equationsSlide9
Baryon core and its gravitational collapse (pulsation)
to be determined by Einstein equation for gravitational collapse.Core collapsing velocitySlide10Slide11
Initial and Equilibrium configurations
Blue: protonRed: electron
+_Slide12
Electric field and Electrons: Maxwell equation, continuous, energy-momentum conservations and equation of stateSlide13
Oscillations and RelaxationSlide14
Oscillation, relaxation and energy-conservation
The relaxation from one equilibrium configuration to another
Oscillating energySlide15
Electron-positron pair productions in oscillating electric fields
Occupied electron levelsH. Kleinert, R. Ruffini, S.-S. Xue, PRD 78 (2008) 025001.Slide16
Pair-production rateSlide17
Core gravitational collapse
C. Cherubini, R. Ruffini and L. Vitagliano, Phys.~Lett.~B545 (2002) 226.Slide18
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.Slide19
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).Slide20
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.