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Towards Resolving the Crab Sigma-Problem: A Linear Accelerator?Using the exact solution of the axisymmetric pulsar magnetosphere derived in a previous publication and the conservation laws of the associated MHD flow, we show that the Lorentz factor of the outflowing plasma increases linearly with distance from the light cylinder. Therefore, the ratio of the Poynting to particle energy flux, generically referred to as sigma, decreases inversely proportional to distance, from a large value (typically approx. greater than 10(exp 4)) near the light cylinder to sigma approx. = 1 at a transition distance R(sub trans). Beyond this distance the inertial effects of the outflowing plasma become important and the magnetic field geometry must deviate from the almost monopolar form it attains between R(sub lc), and R(sub trans). We anticipate that this is achieved by collimation of the poloidal field lines toward the rotation axis, ensuring that the magnetic field pressure in the equatorial region will fall-off faster than 1/R(sup 2) (R being the cylindrical radius). This leads both to a value sigma = a(sub s) much less than 1 at the nebular reverse shock at distance R(sub s) (R(sub s) much greater than R(sub trans)) and to a component of the flow perpendicular to the equatorial component, as required by observation. The presence of the strong shock at R = R(sub s) allows for the efficient conversion of kinetic energy into radiation. We speculate that the Crab pulsar is unique in requiring sigma(sub s) approx. = 3 x 10(exp -3) because of its small translational velocity, which allowed for the shock distance R(sub s) to grow to values much greater than R(sub trans).
Document ID
20020048588
Acquisition Source
Goddard Space Flight Center
Document Type
Preprint (Draft being sent to journal)
Authors
Contopoulos, Ioannis (Contopoulos (Ioannis) Piraeus Greece)
Kazanas, Demosthenes (NASA Goddard Space Flight Center Greenbelt, MD United States)
White, Nicholas E.
Date Acquired
September 7, 2013
Publication Date
January 1, 2002
Subject Category
Astrophysics
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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