she-sheng xue icranet, pescara, italy how the gravitational energy transfers to the electromagnetic...
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She-Sheng XUE
ICRANet, Pescara, Italy
how the gravitational energy transfers to the electromagnetic energy for Gamma-Ray-Bursts.
1) Electron-positron production, annihilation and oscillation in super-critical electric field.
2) Super-critical electric field on the surface of collapsing core. 3) Electron-positron-photon plasma formed in gravitational collapses. 4) Hydrodynamic expansion of Electron-positron-photon
plasma.
To understand
Research topics
CRITICAL FIELDS IN PHYSICS AND ASTROPHYSICS OF NEUTRON STARS AND BLACK HOLES
F. Fraschetti (CEA Saclay, France)H. Kleinert (Free University of Berlin , GermanyR. Klippert (ICRANet, Brazile)G. Preparata* (INFN, University of Milan, Italy)V. Popov (ITEP, Moscow, Russia)R. Ruffini (ICRANet, University of Rome, Italy)J. Salmonson (Livemore National Lab., University of California, USA)L. Vitagliano (ICRANet, University of Salerno, Italy)G. Vereshchagin (ICRANet, Minsk, Belarus)J. Wilson* (Livemore National Lab., University of California, USA)S.-S. Xue (ICRANet)
International and ICRANet Participants:
PhD and MS Students:G. De BarrosL. J. Rangel LemosB. Patricelli J. Rueda
M. Rotondo * passed away
E ~ 1054 ergs
T ~ 1 sec.
External layersof the star
Super-critical electric field and charge-separation on the surface of massive collapsing core
Black hole
Dyadosphere(electron-positron and photon plasma outside the collapsing core)
External layers of the star
Black hole
Electron-positron-photon plasma expansion, leading to GRBs
The “Black hole” energy:
E2 = (Mirc2 + Q2/2)2 + (Lc/)2 + p2
141
1644
2
2248
2
4
24
2
22
222
2
22222422
cLQc
G
Mc
G
Mc
LrS
cLQcMcME
irhorizon
ir
initialeextractabl EE %29
initialeextractabl EE %50
Christodoulou, Ruffini, 1971
+ -
cme
;32
e
cmEc ;137~~
2e
cZc
scm
te
182
10~~
Sauter, Heisenberg, Euler, 1935, Schwinger, 1951
Damour & Ruffini 1974
• In a Kerr-Newmann black hole vacuum polarization process occurs if3.2MSun MBH 7.2·106MSun
• Maximum energy extractable 1.8·1054 (MBH/MSun) ergs
• “…naturally leads to a most simple model for the explanation of the recently discovered -rays bursts”
Electron-positron pairs production and Dyadosphere
The Dyadosphere: electron-positron-photon plasma of size ~ 108 cm, temperature ~ 10MeV, and total energy ~ 1051-54 ergs. G. Preparata, R. Ruffini and S.-S. Xue (1998)
Heisenberg
Damour
Preparata Ruffini
E
r
2r
Q
Ec
r+ rdya
eecEE
0 Emax
MeVT
cmn
cmergs
cmr
MGQ
MM
dya
Sun
10
10
/10
10
1.0
20
Example
4/14/1
332
327
8
A specific Dyadosphere exampleEdya
Electron-positron-photon plasma
G. Preparata, R. Ruffini and S.-S. Xue 1998
(Reissner-Nordstrom geometry)
C
dsr
e
QN
T h eD y a d o -to ru s
C . C h e ru b in i,A . G era lico ,J . R u ed a ,R . R u ffin i (2 0 0 7 )
(Kerr-Newmann geometry)
A general formula for the pair-production rate in non-uniform fields
(Kleinert, Ruffini and Xue 2007)
Confined (Sauter) fieldCoulomb field and bound states
in collisions of laser beams and heavy ions, neutron stars and black holes.
Kleinert
What happens to pairs, after they are created in electric fields?
???0~
eecEE
cpt jjE
Polarization current Conduction current
ESptfEeptf pt
, ,
f distribution functions of electrons, positrons and photons, S(E) pair production rate and collisions:
And Maxwell equations (taking into account back reaction)
Vlasov transport equation:
Ruffini, Vitagliano and Xue (2004)
???,0E A naïve expectation !!!
ee
Results of numerical integration
(integration time ~ 102 C)
Discussions:
•The electric field strength as well as the pairs oscillate
•The role of the scatterings is negligible at least in the first phase of the oscillations
•The energy and the number of photons increase with time
Ruffini, Vitagliano and Xue (2004)Ruffini, Vereshchagin and Xue (2007)
Conclusions• The electric field oscillates for a time of the order of
rather than simply going down to 0.
• In the same time the electromagnetic energy is converted into energy of oscillating particles
• Again we find that the microscopic charges are locked in a very
small region: Cl 20
C43 1010
Ruffini, Vitagliano and Xue (2005)
Supercritical field on the surface of massive nuclear cores
Degenerate protons and neutrons inside cores are uniform
(strong, electroweak and gravitational interactions):
Degenerate electrons density
-equilibrium
electric
Electric interaction, equilibrium
Poisson equation for )(rV
Thomas-Fermi system for neutral systems ep NN
mrV /)(
cErE /)(
)(rn
ep nn
(in Compton unit)cRrx ~
surface surface
Ruffini, Rotondo and Xue (2006,2007,2008)
Popov
Super Heavy Nuclei
310pN
5510pNNeutron star cores
Gravitational Collapse of a Charged Stellar Core
De la Cruz, Israel (1967)
Boulware (1973)
Cherubini, Ruffini, Vitagliano (2002)
20
2220
2
0 22M
R
Q
R
MM
d
dRM
QM
An Astrophysical Mechanism of Electromagnetic Energy Extraction:
Pair creation during the gravitational collapse of the masive charged core of an initially neutral star.
t
00 , tR
++
++
++
++
R
If the electric field is magnified by the collapse to E > Ec , then…
2max
2
r
QE
R
QER
R
t
00 , tRee
ee
Plasma oscillations
Already discussed
Thermal equilibrium
To be discussed
An Astrophysical Mechanism of Electromagnetic Energy Extraction
t0,R0
0 1
8Q
R02 2 Ec
2
aT0
4
n0 bT03
Ruffini, Salmonson, Wilson and Xue (1999)
Ruffini, Salmonson, Wilson and Xue (2000) Wilson
Equations of motion of the plasma
constr
nu
T
entropy) ofion (conservat 0
momentum)-energy ofion (conservat 0
The redshift factor
encodes general relativistic effects
2
221
r
Q
r
M
4
00
2
1
100
0
2
0
4
0
2
100
122
2
1
R
rp
n
np
R
r
R
r
n
nc
dt
dr
p 2 p r2 const
nr2 1 const
Ruffini, Vitagliano and Xue (2004)
(II) Part of the plasma expanding outwards
(I) Part of the plasma falling inwards
The existence of a separatrix is a general relativistic effect: the radius of the gravitational trap is
2
2 4
311
2*
MG
Q
c
GMR
The fraction of energy available in the expanding plasma is about 1/2
Fraschgetti, Ruffini, Vitagliano and Xue (2005)
Predictions on luminosity, spectrum and time variability for short GRBs.
(1) The cutoff of high-energy spectrum(2) Black-body in low-energy spectrum(3) Peak-energy around ~ MeV
Fraschgetti, Ruffini, Vitagliano and Xue (2006)
(4) soft to hard evolution in spectrum(5) time-duration about 0.1 second