# Presentation: 049601

## Electromagnetic Models of Gamma Ray Bursts:A Tutorial

- Roger Blandford
- KIPAC
- Stanford
- With thanks to Jonathan Granot** **

- Ohio State University

- Apr 8 04

## Outline

**Outline**

- Some Reasons to Consider EM Models
- Variations on a Theme
- General Principles
- Formal Approaches
- Sketch EM Model for Long GRBs

**Physics not phenomenology**

- Ohio State University

- Apr 8 04

## Some reasons to consider EM models

- Fireball model presents some difficulties
- Hard to create large entropy outflows
*Like the early universe **S(GRB)~10**6**k**; **S(COS) ~10**10**k*
- Hard to make high Mach number flows
*M ~ ***
*Real flows shock and dissipate long before reaching this level of organization*
- Pairs may annihilate and radiation may decouple from the jet before it accelerates the baryons to ultrarelativistic speed
*Within **~10** stellar radii*
- If magnetic field is invoked to create the jet power, how do you get rid of it so efficiently?
*Must become less important than a small admixture of protons*

- Ohio State University

- Apr 8 04

## More reasons to consider EM models

- Other collimated, relativistic, bipolar outflows are not radiation-dominated; electro/hydromagnetic models are most commonly invoked now.
- Pulsar wind nebulae
- AGN jets
- Galactic superluminal sources
- Magnetic fields provide active collimation
- Hoop stress
*Some AGN jets (eg Pictor A) are extremely collimated*

- Ohio State University

- Apr 8 04

## Pulsar Wind Nebulae

- Spinning, magnetized neutron stars release energy electromagnetically
- Polar jets are common and an appealing interpretation is that you see X-ray synchrotron emission from rapidly cooling electrons where the electrical currents flow

- Ohio State University

- Apr 8 04

## Pictor A

- Magnetic Pinch?

- Ohio State University

- Apr 8 04

## Electromagnetic Models

- Basic hypothesis is that the energy is released electromagnetically by a central spinning object and then transported to the main emission site where it is dissipated in the form of electrons and positrons which radiated Synchrotron and inverse Compton radiation
- Applies to all essentially ultrarelativistic outflows

- Ohio State University

- Apr 8 04

## Variations on a theme

- GRB Sources
- Spinning black holes
*Up to **29 %** of the mass of a hole is extractable *
- Relativistic accretion disks/tori
*More energy may come from the disk than the hole*
- Millisecond magnetars
*Can release their spin energy in minutes as required*

- Ohio State University

- Apr 8 04

## More Variations

- Energy transport
- AC transmission
*e.g. chaotic electromagnetic fields with length scale         **~ 100-1000 km**, characteristic of the source variation*
- E~B as relativistic
*Dynamically like radiation-dominated outflow*
- Scalar pressure
- No active collimation
*Natural particle acceleration mechanisms*

- Ohio State University

- Apr 8 04

## More Variations

- Energy transport
- Global DC transmission
*Large scale order in magnetic field*
*Large scale current circuits*
*Toroidal magnetic field dominates parallel field far from the source*
- If flux is conserved, parallel field ~ (Area)-1
- If current conserved toroidal field ~ (Area)-1/2
*E ~ B** still and energy carried by **Poynting flux ~ B**2**c*
- Center of momentum frame moves relativistically
*Need equipartition particle pressure along axis to oppose hoop stress of toroidal field in comoving frame.*

- Ohio State University

- Apr 8 04

## More Variations

- Energy Transport
- Local DC transmission
*Episodic ejection of magnetically-confined jet segments *
*No large scale current circuits*
*Relativistic motion*
*Changing polarity of parallel field reflects changing polarity of disk field*
*Disk may eject loops of toroidal field or be launched and collimated by vertical field*

- Ohio State University

- Apr 8 04

## General Principles

- Generation
- Collimation
- Propagation
- Dissipation

- Ohio State University

- Apr 8 04

## Generation

- Disks advect magnetic field and generate it through the magnetorotational instability.
- Most electromagnetic source models are some sort of unipolar induction mechanism; the details vary
- Generally, a rotating magnetic field generates an EMF ~  B, which drives a current
- The relevant impedance is generally that of free space under relativistic, electromagnetic conditions - ~ 100.
- The power is roughly EMF x Current x Coefficients
- A current description (plus boundary conditions) is equivalent to an electromagnetic field description. Both descriptions can convey insight

- Ohio State University

- Apr 8 04

## 
Unipolar Induction
Rules of thumb: 
B R2 ; V ~  
I~ V / Z0 ;  P ~ V I
              PWN       AGN        GRB  
B          1012 G      104 G          1016 G
        10 Hz      10-5 Hz     103 Hz
R       106 cm     1015 cm     106 cm
V       1016.5 V    1020.5 V    1022.5 V
I       1014.5 A    1018.5 A    1020.5 A
P       1031 W     1039 W     1043 W   (W =107 erg/s)

**M**

****

***Unipolar Induction***
- Rules of thumb:
- B R2 ; V ~ 
- I~ V / Z0 ;  P ~ V I
-               **PWN       AGN        GRB  **
**B**          **10****12**** G     **** ****10****4**** G **         **10****16**** G**
******       **** ****10 Hz      10****-5**** Hz **** **** ****  10****3**** Hz**
**R****       10****6**** cm     10****15**** cm  **** **** **** 10****6**** cm**
**V****     **** **** 10****16.5**** V    10****20.5**** V    10****22.5**** V**
**I    **** ****  ****10****14.5**** A    10****18.5**** A    10****20.5**** A**
**P****       10****31**** W     10****39 ****W****     ****10****43**** W   ****(W =10****7**** erg/s)**

***Generation***

- Ohio State University

- Apr 8 04

## Simulations are transforming our understanding

- MHD
- 3D
- GR
- Plot of magnetic energy density

*Villiers et al*

- Ohio State University

- Apr 8 04

## Consequences of large EMFs

- Particle energy density / EM energy density
- Can be as small as rL/L ~ mec2/eV
- In practice, it won’t be!
- Vacuum is an excellent conductor thanks to QED
- Electric field  rapid breakdown
*accelerate electron, scatter photon, create pair and repeat *
- This ensures that B2 - E2 > 0
- It is hard to produce entropy under these conditions
*Not a criticism of neutrino models!*

- Ohio State University

- Apr 8 04

## Dipolar vs Quadrupolar Current Flow

- It has generally been assumed that disk field has odd parity and the currents are even parity
- If large disks trap only a tiny fraction of the radial field present at their outer radii, then the opposite may be closer to the truth.

- Ohio State University

- Apr 8 04

## Asymmetric Outflows/Jets

**X**

**Can you measure the toroidal field pattern?**

**Even Field**
**Odd Current**

**Odd Field**
**Even Current**

**Hybrid**
**Mixed Parity**

**B**

**I**

- Ohio State University

- Apr 8 04

## Collimation

- Rotating stars (or gas clouds) can provide hydrodynamic collimation of outflow
- “Twin exhaust” mechanism
- Magnetic collimation is much more powerful and will operate in spherically symmetric surroundings
- Principles illustrated by cylindrically symmetric jet

- Ohio State University

- Apr 8 04

## Simple Model of Cylindrical Jet

- Current I flows along jet walls radius r
- Return current flows along cylinder radius R
- Magnify confining pressure: Pjet=Pext(R/r)2
- Equivalently, cavity adjusts to R=(2Pext)-1/2I
- Pjet is mixture of particles and tangled field

- Pext

- Pjet

- R

- r

- I

- I

- Ohio State University

- Apr 8 04

## Propagation

- As can be seen from the preceding table, putative electromagnetic sources generate 1022.5 V EMFs (ample for the most energetic cosmic rays!).
- Most fireball models implicitly assume that the associated current ~ 1020.5 A shorts out and dissipates close to the source and creates heat.
- Electromagnetic jet models propose that the current flows out into the emission region and we observe the dissipation - like a luminous light filament.

- Ohio State University

- Apr 8 04

## Electromagnetic models of 

**Electromagnetic models of **
**extragalactic radio sources and**
**pulsar wind nebulae **

- Nonthermal emission
- is ohmic dissipation
- of current flow?

- 1018 not 1017 A

**DC not AC**

**Magnetic field**

- Ohio State University

- Apr 8 04

## Propagation

- Jets terminate, sharing their momentum with a shocked external medium
- In the case of GRBs the jet only lasts for minutes and becomes a spherical cap while the external shock remains relativistic
- AGN and PWN jets evolve differently but the underlying physical processes should be similar

- Ohio State University

- Apr 8 04

## Dissipation

- Relativistic particles by shock Fermi acceleration.
- This is demonstrably true in the solar system and probably the case in the SNR, though the details are controversial
- This is problematic in the case of GRBs
- If shocks are relativistic and especially pair dominated simulations do not exhibit acceleration [Spitkovsky?]
- Strong fields  weak shocks
- Other dissipation mechanisms worth considering

- Ohio State University

- Apr 8 04

## Cylindrical Jet (again)

- Jets are likely to have a relativistic velocity gradient (r) and there has to be internal pressure to balance magnetic hoop stress
- Force balance:
- Electromagnetic and fluid jet powers
- Rough equipartition of energy

- Ohio State University

- Apr 8 04

## Dissipation

- Relativistic electromagnetic jets are likely pair-dominated
- They are also likely to be locally unstable, though velocity gradients may convey global stability
- The best candidate acceleration mechanism seems to be to develop a turbulence spectrum of EM modes cascading down to short wavelengths where they are absorbed by stochastic particle acceleration
- Needs simulation!

- Ohio State University

- Apr 8 04

## Other Particle Acceleration Mechanisms

- Internal shocks are ineffectual
- Shear flow in jets
- Full potential difference is available for particles accelerated via polarization drift along E
- UHECR??
- Fast/intermediate wave spectrum
- Nonlinear wave acceleration (Blandford 1973)
- Charge starvation (Thompson & Blaes 1997)
- Force-free allows E>B - catastrophic breakdown

- Ohio State University

- Apr 8 04

## Let there be Light

**Let there be Light**

- Faraday
- Maxwell
- Definition
- Initial Condition

** **** **** ****Maxwell Tensor, Poynting Flux**

- Ohio State University

- Apr 8 04

## Electromagnetic Velocity

**L-C Circuit**
**Near Solenoid, ****E < B**
**U = (E x B)/B^2 < 1**
**Near Capacitor, ****E > B**
**U = (E x B)/E^2 < 1**
**Resistive wire **** ****E****||**** **** ****E x B**** into wire where the energy dissipated**
**Astrophysical Sources**
**V ~ 10 ****15**** - 10****22**** Volts**
**QED effects **** ****E < B**
**Cosmic sources have inductance.**
**Velocity of frame in which ****E = 0**

**I**

**U**

**U**

**U**

**U**

**+Q**

**-Q**

- ExB

- Ohio State University

- Apr 8 04

## Force-Free Limit of Relativistic MHD

**Force-Free Limit of Relativistic MHD**

- Ignore inertia of matter  =UM/UP>>2, 1
- Electromagnetic stress acts on electromagnetic energy density
- Fast and intermediate wave characteristics
- Simpler than RMHD

- Ohio State University

- Apr 8 04

## Gravitational binding energy  EM energy flux
Organized, anisotropic, axisymmetric current flow/Poynting flux 
VEM=E/B ~ c
Electromagnetic acceleration   ~100, M ~ 1
Pairs combine, s escape, E,B dominate
Poynting flux catches shocked CSM ~ 1016cm
Current dissipation-> pairs ->GRB
Relativistic internal motions -> variability
Sweep up CSM at ~ 1017cm
Field incorporated from magnetic piston, electron shock acceleration
Anisotropic afterglow 

**Organized, anisotropic, axisymmetric current flow/**Poynting flux
- VEM=E/B ~ c
- Electromagnetic acceleration   ~100, M ~ 1
- Pairs combine, s escape, E,B dominate
- Poynting flux catches shocked CSM ~ 1016cm
- Current dissipation-> pairs ->GRB
- Relativistic internal motions -> variability
- Sweep up CSM at ~ 1017cm
- Field incorporated from magnetic piston, electron shock acceleration
- Anisotropic afterglow

**Electromagnetic GRB Model**

- Ohio State University

- Apr 8 04

## Sketch EM Model of Long Bursts

- I Energy Release
- II Bubble Inflation
- III Shell Expansion
- IV Blast Wave

- Ohio State University

- Apr 8 04

## I Energy Release

- Long bursts
- Spinning Black Hole + Torus
- Millisecond Magnetar
- LEM ~ R2B2c
- B ~ 1014 G, ~ 3 kHz, E ~ 1052 erg, ts ~ 100 s ~ 106 tdyn
- V ~ 1022.5 V ,  I ~ 1020.5 A
- Stationary, axisymmetric DC current flow
- Short bursts admit more possibilities
- e.g. coalescing neutron stars

- Ohio State University

- Apr 8 04

## Collapsar/hypernova within stripped star, R ~ 1011 cm
Surface return current, surface stress ~ (I/Rsin)2 
Anisotropric expansion in absence of rotation
Dissipation inevitable if V < c/ln(max/min) ~ 0.1c; otherwise not
cf PWN
Rationale for fireball model?
Compute evolution given envelope dynamics; tbreakout ~ 10 s
Biconical expansion outside star dictated by CSM
Shell forms when r > cts ~ 3 x 1012 cm; ultrarelativistic expansion 
Thermal precursor measure of dissipation? 

- Surface return current, surface stress ~ (I/Rsin)2
- Anisotropric expansion in absence of rotation
- Dissipation inevitable if V < c/ln(max/min) ~ 0.1c; otherwise not
- cf PWN
- Rationale for fireball model?
- Compute evolution given envelope dynamics; tbreakout ~ 10 s
- Biconical expansion outside star dictated by CSM
- Shell forms when r > cts ~ 3 x 1012 cm; ultrarelativistic expansion
- Thermal precursor measure of dissipation?

**II Bubble Inflation**

- Toroidal magnetic field
- self-collimating

- Pairs combine,
- s escape

- 

- Ohio State University

- Apr 8 04

## Underlying geometry &  scalings

**I**

**I**

**B**

**B**

- B ~ 2I/cr, r = R sin
- L ~ R2B2c  (sin)-2
-  E  (sin)-2 ~ -2
-  E ~ 2E ~ const (as observations imply; Frail et al. 2001)

- Ohio State University

- Apr 8 04

## III Shell Expansion

- rGRB ~ 2cts ~ (Lts2/c)1/4 ~ 1016 cm
- V = **E**x**B**/B2;  ~ 100
- Piston thickness cts ~ 3x1012 cm
- Instability  variable -ray emission
- Facilitates escape of hardest -rays

- Shocked
- Circumstellar
- Medium

**t**

- 

**r**

- C

- ts

- 

- Ohio State University

- Apr 8 04

## Simple derivation of radial scaling

- The EM outflow travels essencially at the speed of light (i.e. EM = (1-U2)-1/2 **≫ ** = CD)
- Energy emitted at time te catches up with the CD at ti ~ R(te)/1-ti ~ te/[1-(ti)] ~ te 2(ti)
-  E(ti) ~ Lti/2(ti) ~ A(cti)3-kc22(ti) ; Rk
-  (ti) ~ (L/Ac5-kti2-k)1/4 for te < ts (ti < Rad/c)
- Rad ~ (Lts2/Ac)1/(4-k) ~ RGRB (forward shock becomes adiabatic)
- (Rad) ~ (L/Ac5-kts2-k)1/2(4-k)

- Ohio State University

- Apr 8 04

## IV Blast Wave 

- rGRB < r < rNR ~ (Lts/c2)1/3 ~ 1018 cm;  ~ 100-2
- Achromatic break when -1
- Magnetic field mixed in from CD?
- Particles accelerated at shock?
- Constant energy per decade in 
- Standard qualitative interpretation of
-   afterglow spectra
- More variation than in shock models
-  is important parameter
- Axial currents  short bursts?
- Becomes more spherical at r > rNR

- 

- Ohio State University

- Apr 8 04

## Possible Tests

- Early afterglow evolution
- Shape -VLBI
- Thermal precursors; no reverse shock
- Polarization -constant PA?
- GLAST not AMANDA; UHECR
- Orientation statistics, orphan afterglows, XRF
- Fluctuation statistics

- Ohio State University

- Apr 8 04

## Summary

- EM GRB models different from fluid models
- Circumvent hydrodynamic “middleman”
- Closer to models of other relativistic outflows
- Many interesting physical processes, poorly understood
- Simulation methods developing rapidly
- Proceed with care when drawing conclusions from observations!

- Ohio State University

- Apr 8 04