The QED-GRB Connection(some things you should remember if the field is strong)

Jeremy S. Heyl - CfASecond Biennial Sackler Conference

23 May 2002

GRBs and QED in the Literature

GRBs and QED in the Literature

Contain GRB420

Contain QED4,183

Contain GRB and QED?

Physics Abstracts1,217,982

Contain GRB10,053

Contain QED220

Contain GRB and QED?

Astrophysics Abstracts754,221

NASA ADS Abstracts2,631,323

GRBs and QED in the Literature

Contain GRB420

Contain QED4,183

Contain GRB and QED5

Physics Abstracts1,217,982

Contain GRB10,053

Contain QED220

Contain GRB and QED10

Astrophysics Abstracts754,221

NASA ADS Abstracts2,631,323

GRBs and QED in the Literature

Contain GRB and QCD4

Contain GRB420

Contain QED4,183

Contain GRB and QED5

Physics Abstracts1,217,982

Contain GRB10,053

Contain QED220

Contain GRB and QED10

Astrophysics Abstracts754,221

NASA ADS Abstracts2,631,323

§ However, if I were pedantic, I would claim thatevery talk at this conference relies on QED (withthe possible exception of those by Eli Waxmanand Vicki Kalogera).

QED Corrections§In a strong magnetic field, electrons, both

real and virtual, occupy Landau levels.l Rates for processes that involve electrons can be

significantly different due to the new phase-space structure.

l The vacuum can be an active participant inphysical processes that we observe.

l The equations governing the electromagneticfield are non-linear.

The field scales of the GRB§The critical magnetic field strength for QED

is 4.4 × 1013 G (1.3 × 10-11 cm-1).l The electron cyclotron energy equals its mass.

§ Estimates of the magnetic field in a GRB:l MHD central engine (Rees Tuesday) - 1015 Gl Kerr BH (van Putten Tuesday) - 1015 Gl Equipartition - 8 × 1016 (εB E51)1/2 R6

-3/2 Gl Magnetar (Usov 1992) - 1016 Gl Virial Magnetic Field is ~ M/R2 ~ 1018 G

The length scales of the GRB§To account for the rapid time variability, the

rengine ~ 106-7 cm.§To avoid making pairs, the γ−rays must be

emitted at r >1013 cm where B ~ 106-8 G,well below BQED.

§The afterglow comes from r > 1015 cm.§If strong-field QED matters, it will be

important in the engine.

What processes may be crucial?§Vacuum magnetization§Vacuum breakdown§Vacuum polarization§Photon splitting/merging§Phase-space structure for real electrons§Strong-field-QED dynamic Casimir effect

Vacuum Magnetization§For B > BQED the vacuum carries a

magnetization which increases nonlinearlywith the strength of the magnetic field. Thisnonlinearity may alter the geometry of thefield (HH97).

§The magnetization of the plasma is generallynegligible.

§If E2 > B2 or E ·B ≠ 0, the magnetizationbecomes complex.

Vacuum Breakdown§The magnetized vacuum is stable because

there are no magnetic monopoles.§However, frame dragging near a Kerr black

hole converts a magnetic field into anelectric field, such that E⋅B ≠ 0 (H01).

l A magnetized Kerr black hole with B > 1012 Gis unstable to pair production. Even in vacuapairs will be produced driving E⋅B ⇒ 0.

l The Goldreich-Julian density is ~ 1017 e- cm-3 orone hundredth the density of air.

Toward an BH Magnetosphere§Start with Wald’s solution for the

electromagnetic field surrounding a rotatingblack hole.

§A vacuum solution to Maxwell’s equations:

§Satisfy the MHD condition by adding anaxion field χ (Thompson & Blaes ‘98).

Aö =P

iAi ö

( i)

Vectorpotential

Killingvector

Structure of the Wald Field§ The EM field

surrounding a rotatingblack hole divides thesurrounding spacetimeinto four regions.

§ The MHD condition issatisfied everywhereexcept at the 4 corners.

§ Here, the requiredcurrent densitydiverges.

J ö = à ÿ ;÷F ö ÷

I M = Gö ÷Gö ÷; J M = Gö ÷Gö ÷

Vacuum Polarization§ The index of refraction

for the parallel mode issignificantly largerthan 1 for B > 1014 G:

§ Photon paths are bent(SHL99).

§ Photons carry moremomentum.

(n à 1) ù 6ùë

B QE D

B ù 1017GB

§ Photons pair produce.

Lensing of a Neutron Star

-1 -0.5 0 0.5 1

f0

=0.2

i=90

x/RNS

-1 -0.5 0 0.5 1

f0=0.2

i=45

x/RNS

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

f0=0.2

i=0

x/RNS

y/R

NS

-3 -2 -1 0 1 2 3

f0

=2

i=90

-3 -2 -1 0 1 2 3

f0=2

i=45

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3f0=2

i=0

y/R N

S

-1 -0.5 0 0.5 1

f0=0.2

i=90

x/RNS

-1 -0.5 0 0.5 1

f0=0.2

i=45

x/RNS

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

f0=0.2

i=0

x/RNS

y/R N

S

-3 -2 -1 0 1 2 3

f0=2

i=90

-3 -2 -1 0 1 2 3

f0=2

i=45

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3f 0=2

i=0

y/R N

S

-1 -0.5 0 0.5 1

f0

=0.2

i=90

x/RNS

-1 -0.5 0 0.5 1

f0=0.2

i=45

x/RNS

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

f0=0.2

i=0

x/RNS

y/R

NS

-3 -2 -1 0 1 2 3

f0

=2

i=90

-3 -2 -1 0 1 2 3

f0=2

i=45

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3f0=2

i=0

y/R N

S

-1 -0.5 0 0.5 1

f0=0.2

i=90

x/RNS

-1 -0.5 0 0.5 1

f0=0.2

i=45

x/RNS

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

f0=0.2

i=0

x/RNS

y/R N

S

-3 -2 -1 0 1 2 3

f0=2

i=90

-3 -2 -1 0 1 2 3

f0=2

i=45

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3f 0=2

i=0

y/R N

S

Polarization from Neutron Stars§ The traveling modes for

light in themagnetosphere aredecoupled by the plasmaand the vacuum (HS00).

§ Radiation from disparateparts of themagnetosphere evolvesso that its polarization isparallel.

Polarization-Limiting Radii§ The polarization modes

of high-energy photonscouple further from thestellar surface thanthose of low-energyphotons.

§ Also, if the direction ofthe magnetic fieldchanges appreciablyduring coupling we geta circular component.

1021Hz

1013Hz

1015Hz

1017Hz

Low-Energy Polarized Images

Zero Hz - QED neglected 1015 Hz - Optical/UV

High-Energy Polarized Images

1021 Hz - Gamma-Ray1017 Hz - Soft X-Ray

Big Trends

§ 330 images,105 rays/image (HS02)

§ ν↑ s1↑§ µ↑ s1↑§ α↑ s1↑§ R↑ s1↓ for ν>1014 Hz§ R↑ s1↑ for ν<1014 Hz

6 km10 km14 km

60°

6 km10 km14 km

30°

Photon Splitting/Merging§ Photon splitting may

be important in SGRs(see works by Baring);however, the emissionfrom GRBs originatesin a weak-field region.

§ The inverse processmay be important forthe dynamics of theplasma.

QED/MHD Shocks§ A fast mode travelling

through a strongmagnetic field willshock in 3α-1(∆B/B)-1

wavelengths (HH99).§ The non-linear

interactions tend tosharpen densitygradients. Shockingmay occur too early.

Neutrino Production/Annihilation§ Neutrinos can drive a

polar outflow.§ The accretion flow

may be neutrino-dominated.

Neutrino Production/Annihilation§ Neutrinos can drive a

polar outflow.§ The accretion flow

may be neutrino-dominated.

Neutrino Production/Annihilation§ Neutrinos can drive a

polar outflow.§ The accretion flow

may be neutrino-dominated.

§ In analogy to thephoton case, the strongmagnetic field opensnew reaction channels(Hardy & Thoma ‘00)

New Neutrino Channels§ A single neutrino can

emit or absorb anelectron-positron pair.

§ A single electron canemit or absorb aneutrino pair.

§ The neutrino ratesincrease with magneticfield and stronglydepend on the fielddirection.

The Casimir effect§ The Casimir effect

results from thedifference in vacuumenergy between tworegions with differentindices of refraction.

§ The classic example isthe slight attractionbetween two closelyspaced metal plates.

§ Accounting for theCasimir force iscrucial in designingnanotechnology.

The Casimir effect - Neutron Star§ Material quickly

accretes onto astrongly magnetizedneutron star pushingthe magnetic fieldloops against the star.

§ The collapse of a loopquickly releases theenergy of the cavity: ~ 1049 erg R6

3 B166 Gnedin &

Kiikov ‘00

The Casimir effect in water§Schwinger ‘92 proposed this as an

explanation for the emission of light and X-rays from water driven with ultrasound.

§Here ~100 Hz accretion instabilities crushloops creating the GRB time structure.

§This might sound crazy, but who wouldhave thought that some massive starsexplode by shooting an ultrarelativistic jetthrough their envelopes.

Summary§The presence of a strong magnetic field

dramatically alters the interaction of lightand matter.

l Some corrections are small (index of refraction).l New processes become possible (photon

splitting, one-photon pair production, etc.)l Processes that are sensitive to the structure of

electron phase-space can be dramaticallyaffected (neutrino emission and absorption).