Transcript A Mechanism for Gravitational Energy Transfering to

Electron-positron pair productions in
gravitational collapses
She-Sheng Xue
In collaboration with
Wen-Biao Han, & Remo Ruffini
ICRANet & Physics Department, University of Rome
MG13, Stockholm, July 5th , 2012
Motivation
We attempt to study the possibility of electronpositron 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.
Electron-positron pairs production and evolution in
gravitational collapses of charged cores and strong fields
R. Ruffini, J.D. Salmonson, J.R.Wilson,
S.-S. Xue A&A 350 (1999) 334; 359, (2000) 855 .
Hydrodynamic
expansion
Already
discussed
e  e 
Pairs and photon
plasma
t
l  20C
R0 , t0 
ee
Pair plasma
oscillations
Already
discussed
103  104 C
Already
discussed
R. Ruffini, L. Vitagliano, S.-S. Xue,
PLB 573 (2003) 33; 559 (2003) 12.
Initial conditions of strong charged cores and
R 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 EinsteinMaxwell-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, 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.
Dynamical equations
Baryon core and its gravitational collapse (pulsation)
Core collapsing velocity
to be determined by Einstein equation for gravitational collapse.
Initial and Equilibrium configurations
Blue:
proton
Red:
electron
+
_
Electric field and Electrons: Maxwell equation, continuous, energymomentum 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) 025001.
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 SoftGamma-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
2GM
R*  2
c
2

3
Q


1  1  
 
4  GM  



The fraction of energy available
in the expanding plasma is
about 1/2.