Transcript The prompt and afterglow emission of GRB991216

CRITICAL FIELDS IN PHYSICS AND ASTROPHYSICS
``DYADOSPHERE’’
1) Electron-positron production, annihilation, oscillation and thermolization in
super-critical electric field.
2) ``Melting’’ phase transition: the nucleon matter core, nuclei
matter surroundings.
3) Super-critical electric field on the surface of collapsing core.
4) Electron-positron-photon plasma (dyadosphere) formed in
gravitational collapses.
5) 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
E ~ 1054 ergs
T ~ 1 sec.
External layers
of nuclei matter
Step 1
electrically neutral
Melting density
c  3 10 g / cm
14
3
Nucleon matter phase
Super-critical electric field and
charge-separation on the surface of
massive collapsing core of nucleon
matter.
Nuclei matter phase
Charge separation
Supercritical field
Density
k   1/ 3 ( fm) 1
proton Fermi-energy
in nuclei matter
Fermi-energy
(MeV)
proton Fermi-energy
in nucleon matter
Bethe, Borner and Sato, 1971
``We see that the slops of the two curves are quite different,
indicating a sharp transition... Thus, at the crossing point
the nuclei will melt and cease to exist. This melting is completely
sharp…within a one-percent of density change.’’
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 )
n p  ne
V (r ) / m
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)
Step-2
Black hole
Dyadosphere
(electron-positron and photon plasma
outside the collapsing core)
Gravitational Collapse of a Charged Stellar Core
Equation
2
M
dR  
Q 

  M 02

M0
   M 
d  
2R 2R 

2
2
0
2
M Q
Solution:
De la Cruz, Israel (1967); Boulware (1973);
Cherubini, Ruffini, Vitagliano (2002)
This gives the rate of gravitational
collapsing, and we can obtain the
rate of opening up phase-space for
electrons.
Pair creation during the gravitational collapse of the
massive charged core of an initially neutral star.
Q
ER  2
R

Q
Emax  2
r
t
+
+
+
+
R0 , t0 
+
+
+
+
R
It will be shown that the electric field is magnified
by the collapse to E > Ec , ….
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    
And Maxwell equations (taking into account back reaction)



 t E   j p  jc
Polarization current
Conduction current
Ruffini, Vitagliano and Xue (2004)
Results of 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)
(i) E  Ec
(ii ) E  Ec
Electric energy to pair numbers
to pair’s kinetic energy
Time and space scale of oscillations
• The electric field oscillates for a time of the order of 103  104 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
compared with
gravitational collapse
time-space scale
Phase-space and Pauli
blocking
Ruffini, Vitagliano and Xue (2005)
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
External layers of
nuclei matter
Step-3
Black
hole
Electron-positron-photon plasma
expansion, leading to GRBs
Core collapsing, plasma formation and
expansion
e  e 
Aksenov, Ruffini
Vereshchagin(2007)
Thermal
equilibrium
t
R0 , t0 
Already
discussed
Plasma
oscillations
ee
R
Ruffini, Salmonson, Wilson and Xue (1999)
Ruffini, Salmonson, Wilson and Xue (2000)
t0 ,R0

1  Q
0  8 R 02

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



p
r

  const
n  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)