Electromagnetic Models of Gamma Ray Bursts: A Tutorial

1. Electromagnetic Models of Gamma Ray Bursts:A Tutorial Roger Blandford KIPAC Stanford With thanks to Jonathan Granot

2. Outline • Some Reasons to Consider EM Models • Variations on a Theme • General Principles • Formal Approaches • Sketch EM Model for Long GRBs Physics not phenomenology Santorini

3. Some reasons to consider EM models • Fireball model presents some difficulties • Hard to create large entropy outflows • Like the early universe S(GRB)~106k; S(COS) ~1010k • Hard to make high Mach number flows • M ~ G~300 • 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 Santorini

4. 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 Santorini

5. 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

6. Pictor A Magnetic Pinch?

7. 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

8. 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 Santorini

9. 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 Santorini

10. 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 ~ B2c • Center of momentum frame moves relativistically • Need equipartition particle pressure along axis to oppose hoop stress of toroidal field in comoving frame. Santorini

11. 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 Santorini

12. General Principles • Generation • Collimation • Propagation • Dissipation Santorini

13. 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 ~ W B, which drives a current • The relevant impedance is generally that of free space under relativistic, electromagnetic conditions - ~ 100W. • 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 Santorini

14. Generation B  M Unipolar Induction • Rules of thumb: • F ~ B R2 ; V ~W F • I~ V / Z0 ; P ~ V I PWN AGN GRB B1012 G 104 G 1016 G n10 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 W1043 W (W =107 erg/s)

15. Simulations are transforming our understanding • MHD • 3D • GR • Plot of magnetic energy density Villiers et al Santorini

16. 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!

17. 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. Santorini

18. Asymmetric Outflows/Jets B I X Even Field Odd Current Odd Field Even Current Hybrid Mixed Parity Can you measure the toroidal field pattern? Santorini

19. 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 Santorini

20. Simple Model of Cylindrical Jet I I Pext r • 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=(2pPext)-1/2I • Pjet is mixture of particles and tangled field Pjet R Santorini

21. 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. Santorini

22. Magnetic field Nonthermal emission is ohmic dissipation of current flow? 1018 not 1017 A DC not AC Electromagnetic models of extragalactic radio sources and pulsar wind nebulae

23. 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 Santorini

24. 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 Santorini

25. Cylindrical Jet (again) • Jets are likely to have a relativistic velocity gradient G(r) and there has to be internal pressure to balance magnetic hoop stress • Force balance: • Electromagnetic and fluid jet powers • Rough equipartition of energy Santorini

26. 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! Santorini

27. 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

28. Let there be Light • Faraday • Maxwell • Definition • Initial Condition  Maxwell Tensor, Poynting Flux Santorini

29. Electromagnetic Velocity U U I • 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 - 1022 Volts • QED effects E < B • Cosmic sources have inductance. • Velocity of frame in which E = 0 ExB U Santorini +Q -Q U

30. Force-Free Limit of Relativistic MHD • Ignore inertia of matter s =UM/UP>>G2, 1 • Electromagnetic stress acts on electromagnetic energy density • Fast and intermediate wave characteristics • Simpler than RMHD Santorini

31. Electromagnetic GRB Model • Gravitational binding energy  EM energy flux • Organized, anisotropic, axisymmetric current flow/Poynting flux • VEM=E/B ~ c • Electromagnetic acceleration G ~100, M ~ 1 • Pairs combine, gs 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

32. Sketch EM Model of Long Bursts • I Energy Release • II Bubble Inflation • III Shell Expansion • IV Blast Wave

33. I Energy Release • Long bursts • Spinning Black Hole + Torus • Millisecond Magnetar • LEM ~ R2B2c • B ~ 1014 G,n~ 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

34. II Bubble Inflation • Collapsar/hypernova within stripped star, R ~ 1011 cm • Surface return current, surface stress ~ (I/Rsinq)2 • Anisotropric expansion in absence of rotation • Dissipation inevitable if V < c/ln(qmax/qmin) ~ 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? Toroidal magnetic field self-collimating G ~104 Pairs combine, gs escape

35. Underlying geometry &  scalings • B ~ 2I/cr, r = Rsin • L ~ R2B2c  (sin)-2 •  E(sin)-2 ~ -2 •  E ~ 2E~ const (as observations imply; Frail et al. 2001) I B B I Santorini

36. r III Shell Expansion Shocked Circumstellar Medium • rGRB ~ G2cts ~ (Lts2/rc)1/4 ~ 1016 cm • V = ExB/B2;G ~ 100 • Piston thickness cts ~ 3x1012 cm • Instability  variable g-ray emission • Facilitates escape of hardest g-rays t  C ts q r

37. 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Rk • (ti) ~ (L/Ac5-kti2-k)1/4for 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) Santorini

38. IV Blast Wave • rGRB < r < rNR ~ (Lts/rc2)1/3 ~ 1018 cm;G ~ 100-2 • Achromatic break when G ~ q-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 q

39. 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

40. 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! Santorini