she-sheng xue icranet, pescara, italy how the gravitational energy transfers to the electromagnetic...

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