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Excitation of Supernova Remnants by Twisting of theNeutron Star Dipole Magnetic Flux

Stirling Colgate, LANLwith Hui Li, LANL & Ken Fowler, UC Berkley, LAUR-0805268Extra galactic cosmic rays, AGN jets, and Radio Lobes are all

most likely produced from the free energy of formation of SuperMassive Black Holes. In our view these are the result of the twisting ofthe magnetic field produced by the dynamo within the accretion diskforming the MBH.

Similarly I suggest that the relative winding of the magnetic fluxattached both to the neutron star and to the ejecta of the supernova willsupply the energy and similar non-thermal x-rays and gamma rays.

Winding of magnetic flux in a low density conducting medium,produces force free magnetic fields. The magnetic energy is transformedefficiently to particle energy by J. E, E(parallel to B) acceleration.

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This is the comparisonThis is the comparison

3c219 Radio LobeSynchrotron radiation.B=5x10-6 G, electrons E ~ 104 mc2 .

Radio Lobe, ~ 1061 ergs, ~ 10% M8 c2

an alpha-omega dynamo in the accretion disk; the winding of a force-free magnetic helix, ~1012

turns, reconnection, dissipation, and acceleration, finally synchrotron emission gives the radio.

This is how we think it works:Will the winding of the NS fluxdo something similar?

The Crab, ~ 1047 ergs

Optical/x-rays

Do twisted fields power the nebula?

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Magnetized Neutron Star and Supernova EjectaMagnetized Neutron Star and Supernova Ejecta

rotation axis(slow rotation)f0 = 30 Hz

explosion, radialstretching offield lines

collapse of supernova with magneticflux imbedded both in the neutronstar and in the initial stellar mass.

The radial stretching of the flux trapped in the neutron star by the explosion ejecta

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Twisting of Flux Column by the Neutron StarTwisting of Flux Column by the Neutron Star

Supernova ejectastretches the inbededdipole quadrupoleflux.

The neutron starwinds its imbeddedflux differentiallyrelative to theexpanding return fluximbedded in theejecta.

Vaccuum cavity formsby twisting a dipole in2 years, or ~2 109

turns, a robust force-free helix.explosion

expansion

Grad-Schafranovforce-free calculation, Hui Li.

Core is neutron star radius, ~106 cm; energy= 2x109 turns x (B2/8π) r3 = ~7x 1050 ergs .

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Properties of force-free helixProperties of force-free helixFlux conservation: compression of dynamo flux, 104G in main-sequence star to neutron star. Collapse from 3 x 1010 cm to 106 cm.

Then B0 = 3 x1012 gauss (issues with crust strength for dipoleB>~1013G. (Ruderman and Flowers, ~ 1963))

No differential rotation or winding during collapse because ofconvection in nuclear burning.

Magnetic core of helix is radius of NS, r0 = 106 cm.

Diffusion: Bohm diffusion = maximum diffusion = 1.4 x 104 cm2/s= resistivity = η; at maximum temperature; (Te,i ~ gev)

Then the life time of helix, thelix = r2/D = 2 years, or >>?.

Axial velocity of helix, progression, = ω r0 /(ln(r1/r0)) = 107 cm/s.

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Properties of force-free helix, cont.Properties of force-free helix, cont.Length, Lhelix = thelex ω r0 /(ln(r1/r0)) = 6 x 1014 cm

Number of turns = f x thelex = 1.8 x109

= amplification of Flux generated by helical winding:

The dissipation of this flux is then the luminosity of theCrab nebula.

Power = ω (Β02 /8π) (πr0

2 ) = 2 x 1038 ergs/s.

Electric field, volts = ωr0 B0 x 10-8 = 5 x 1012 volts/cm.

Particles are accelerated and lost by diffusion : a betterway to make cosmic rays, electrons and x-ray sources.

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Geometry of Force-free Neutron Star Driven HelixGeometry of Force-free Neutron Star Driven Helix

Winding of radial flux, atthe “nose”; end of helix,produces azimuthal fluxand a current, I0 .

Pressure equilibrium inthe core, r0 , Bz

2 + Βφ2 = B0

2.

Pressure equilibrium atthe outer boundary, r1 ,P1 = Βφ1

2 = Bz12 = B1

2 .

P1 = expanding nebulapressure.

Bz

Bz1

Bφ = B0/(R/R0) I0 = 5 B0R0 =

1.5 x 1019 amps

P1RR0 R1

R1 /R0 ~ 1015

I0

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TokamakTokamak, Tangled field Drift waves, Tangled field Drift waves

A new twist. Gyro-kinetic simulation of plasma density fluctuations in a shapedtokamak. Image shows a cut-away view of the density fluctuations (red/bluecolors indicate positive/negative fluctuations). The blue halo is the last closedmagnetic flux surface in the simulated tokamak. Krulsnick & Cowley, 2005,Science 309, 1502

Weakly tangled field allows run-aways to random-walk out of field. Drift waves too weak for β ~ 10-11 ; plasma = current carriers only, ne ~ 1015/ccc

1010

The Current-Carrier Starved HelixThe Current-Carrier Starved HelixA high temperature, 100 Mev, can support a plasma above a NS.

Matter will fall back until an electric field supports it against g=1014

cm/s2 (Starvation). Ee = 1014 x 1.6 x10-24 ; E= 100 volts/cm, or 100Mev, produced by a trivial charge separation.

The inductive electric field due to a diffusion time of 2 yearsbecomes: E = L (dI/dt) ; L = ~ 3x10-8 henries/cm, I = B 5 rg =1.5 x 1019 amperes, / t = 6 x 107 s, = 7 x 103 volts/cm.

A voltage of E L = 4.5 x 1018 volts, enough for galactic cosmic rays.

Starvation of current carriers leads to drift velocity c.ne,i = (I x 6x1018 )/(π r2 c) = 1015 /cc.

How to find such a diffusion coefficient.?

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Q: Is this sheet-pinch configuration stable? noQ: If so, how does it convert B2 into particleenergy?

An idealized Problem, helical shearAn idealized Problem, helical shear

0)(

sin)(

cos)(

0

0

=

=

=

zB

zBzB

zBzB

z

y

x

!

!

Sheet Pinch:

Sheet-pinch is force-free, with a constant, continuous shear.

Li, H.; Nishimura, K.; Barnes, D. C.; Gary, S. P.; Colgate, S. A. 2003, Phys of Plamas, 7, 2763

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Current Filaments on the scale of Current Filaments on the scale of ddii the ionthe ioncollisonless collisonless skin depth =skin depth = c/c/ωωpipi

t ωpi = 8

Li et al. 03

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Current filament diffusion; at the collisionless skin depthCurrent filament diffusion; at the collisionless skin depth

The currrent, J, supporting the sheared field is unstable to filamentation at a sizedi = c/ωpi , the ion collisionless skin depth, (distance of separation of electronsfrom ions in a magnetized plasma).

In the current carrier starved helix, di = c/ωpi = c/(3x1011 Hz) = 0.1 cm.

Run-away current carriers at velocity c follow tangled field lines of force out of,(into) the core, or plasma ~R0.

The random step size <x> = di (ΔB/B) .

ΔB = J (π di2) / di = J (π di) ; and B = I /5R0 = J (π R0

2)/5R0;

Hence (ΔB/B) = 5 di / R0 = 5x10-7 ;And so the random step size <x> = 5x10-8 cm.

The Diffusion coefficient η = c <x>/3 = 500 cm2/s.The diffusion time or energy conversion time becomes R0

2 /η =2x108 s= 6 years.

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ConclusionConclusionMagnetic flux is trapped during the stellar evolution leading to imbedded, compressed flux in the pre supernova star.

During the explosion hydrodynamic forces exceed magneticforces by many orders of magnitude and stretch this flux radially within the SN ejecta.

We consider the result of differential winding, twisting of this trapped flux external to the NS.

We find that the total magnetic flux is increased by ~ x109 before resistive dissipation limits twist.

The dissipation of this helical flux leads to acceleration through E parallel to J, of electron, ion, run-aways, non-thermal spectra, x-rays, gamma rays, and cosmic rays.