Transcript The prompt and afterglow emission of GRB991216

CRITICAL FIELDS IN PHYSICS AND ASTROPHYSICS
OF NEUTRON STARS AND BLACK HOLES
Research topics
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
how the gravitational energy transfers to the electromagnetic
energy for Gamma-Ray-Bursts.
She-Sheng XUE
ICRANet, Pescara, Italy
International and ICRANet Participants:
F. Fraschetti
H. Kleinert
R. Klippert
G. Preparata*
V. Popov
R. Ruffini
J. Salmonson
L. Vitagliano
G. Vereshchagin
J. Wilson*
S.-S. Xue
PhD and MS Students:
(CEA Saclay, France)
(Free University of Berlin , Germany
(ICRANet, Brazile)
(INFN, University of Milan, Italy)
(ITEP, Moscow, Russia)
(ICRANet, University of Rome, Italy)
(Livemore National Lab., University of California, USA)
(ICRANet, University of Salerno, Italy)
(ICRANet, Minsk, Belarus)
(Livemore National Lab., University of California, USA)
(ICRANet)
G. De Barros
L. J. Rangel Lemos
B. Patricelli
J. Rueda
M. Rotondo
* passed away
E ~ 1054 ergs
T ~ 1 sec.
External layers
of 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 + Q2/2r)2 + (Lc/r)2 + p2
2

Q 2  L2 c 2
2
2 4
2
E  M c   M ir c    2
2r 
r

 2
 G2  2
L2 
S  4r  4  rhorizon  2 2   16  4  M ir
cM 

c 
2
1  G2  4
  Q  4 L2 c 2  1
4  8 
r c 


Eextractable  29%Einitial
Eextractable  50%Einitial
Christodoulou, Ruffini, 1971
Electron-positron pairs production and Dyadosphere
+
-
m 2c 3
Ec 
;
e

c
18

t
~
~
10
s
Z c ~ 2 ~ 137;
2
me c
e

me c
Sauter, Heisenberg, Euler, 1935,
Schwinger, 1951
Heisenberg
Damour & Ruffini 1974
•
•
•
In a Kerr-Newmann black hole vacuum polarization process occurs if
3.2MSun  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 g-rays bursts”
Damour
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)
Ruffini
A specific Dyadosphere example
Edya
E  Ec
E
0  ee
Example
M  20 M Sun
Emax
Q
r2
Ec
Q  0.1 G M

rdya  108 cm
  10 27 ergs / cm 3
n  1032 cm 3
T   1/ 4 1/ 4  10 MeV
r+
rdya
r
Q rds
N 
e C
Electron-positron-photon plasma
(Reissner-Nordstrom geometry)
G. Preparata, R. Ruffini and S.-S. Xue 1998
Dyado-torus
(Kerr-Newmann geometry)
C. Cherubini,
A. Geralico,
J. Rueda,
R. Ruffini (2007)
A general formula for the pair-production rate in non-uniform fields
in collisions of laser beams
and heavy ions, neutron stars
and black holes.
Kleinert
(Kleinert, Ruffini and Xue 2007)
Confined (Sauter) field
Coulomb field and bound states
What happens to pairs, after they are created in electric fields?
E ~ Ec
0  e  e   ???
E  0, ???
A naïve expectation !!!
Vlasov transport equation:



 t f t , p   eE  p f t , p   S E 
f distribution functions of electrons, positrons and photons,
S(E) pair production rate and collisions:
e  e  g  g
And Maxwell equations (taking into account back reaction)



 t E   j p  jc
Polarization current
Conduction current
Ruffini, Vitagliano and Xue (2004)
Results of numerical
integration
(integration time ~ 102 tC)
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 103  104t C
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:
l  20C
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):
  -equilibrium 
Degenerate electrons density
Electric interaction, equilibrium 
e
l
Poisson equation for V (r )
e
c
tThomas-Fermi system for neutral systems
N p  Ne
n(r )
V (r ) / m
Popov
n p  ne
E (r ) / Ec
Super Heavy
Nuclei
N p  10
N p  10
surface
x ~ r  Rc
(in Compton unit)
surface
3
55
Neutron star cores
Ruffini, Rotondo and Xue (2006,2007,2008)
Gravitational Collapse of a Charged Stellar Core
2
M
dR  
Q 

2


M

M



M
 0
 
0

d
t
2
R
2
R

 

2
2
0
2
M Q
De la Cruz, Israel (1967)
Boulware (1973)
Cherubini, Ruffini, Vitagliano (2002)
An Astrophysical Mechanism of
Electromagnetic Energy Extraction:
Pair creation during the gravitational collapse of the masive
charged core of an initially neutral star.
Q
ER  2
R

Q
Emax  2
r
t
+
+
+
+
R0 , t0 
+
+
+
+
R
If the electric field is magnified by the collapse to E > Ec , then…
An Astrophysical Mechanism of
Electromagnetic Energy Extraction
e  e g
t
R0 , t0 
Thermal
equilibrium
To be
discussed
Plasma
oscillations
Already
discussed
ee
t0 ,R0

1  Q
0  8 R 02

R
Ruffini, Salmonson, Wilson and Xue (1999)
Ruffini, Salmonson, Wilson and Xue (2000)
Wilson
n0  bT03
2

4
 E  aT0

2
c
Equations of motion of the plasma
  T   0 (conservat ion of energy - momentum)
  nu   0 (conservat ion of entropy)
r  const
The redshift factor
a encodes general
relativistic effects

2M Q 2
a  1
 2
r
r
2
2



p

g

p
r

  const
n g r2a 1  const
(I) Part of the plasma
falling inwards
  na 1  2  r  4 
 dr 
2 2
   
   c a 1  
1  
 dt 
  n0a 0   R0  
2
2
2
 r     p  n0a 01   p  r 
   

    
1 
 R0    0  na    0  R0 
4
(II) Part of the plasma
expanding outwards
Ruffini, Vitagliano and Xue (2004)
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
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 (2005)
(4) soft to hard evolution in spectrum
(5) time-duration about 0.1 second
Fraschgetti, Ruffini, Vitagliano and Xue (2006)