Historical research guide · 1013 · 2001
Acceleration and collimation of relativistic plasmas ejected by fast rotators
Sergey V. Bogovalov
In one minute
A spinning magnetised star throws off plasma, and two things are meant to happen: the rotating field flings the plasma outward, and the field’s own tension wraps part of it into a narrow beam along the spin axis. Bogovalov solves that outflow numerically, following a relativistic wind from a star with a simple outward-pointing field all the way from its surface to ten thousand times the distance where the flow outruns its own fast waves. He confirms that the self-collimation really happens: a thin cylindrical core does form inside a wider radial wind, and its width matches what the theory predicts. But the core carries only about a thousandth of the mass. His explanation is the interesting part. In a wind whose energy travels as magnetic field rather than as matter, the field itself carries inertia, so squeezing harder raises the effective mass being squeezed in the same proportion, and the streamlines simply refuse to bend any further.
Connection
Chapter 9 is about plasma that organises itself into stable shapes, and this is the cleanest published statement of how far a rotating magnetic field alone can go: it forms a jet, it accelerates the flow better than the classic estimate, and then it saturates for a reason that belongs to relativity rather than to the model. Chapter 13 needs exactly that kind of honest boundary, because it says which part of the astrophysical picture still wants a further mechanism.
From the source
Self-collimation is real in relativistic winds: the steady-state solution is a radially expanding wind surrounding a cylindrically collimated core whose radius equals the initial fast-magnetosonic radius divided by the rotation parameter, and the computed transverse profile of the poloidal magnetic field matches the analytic prediction of self-collimation theory at distances of a thousand and of ten thousand fast-magnetosonic radii alike, which shows the flow near the axis has reached its asymptotic state.Section 5; Equation (26); Figures 2, 3, 5 and 6
The collimated core is thin and light: about one part in a thousand of the mass flux and of the magnetic flux of the wind travels in the jet, roughly ten times less magnetic flux than the same simulations give for a non-relativistic wind, and self-collimation weakens further as the initial Lorentz factor rises. In this cold outflow model the plasma inside the jet is not accelerated at all; the acceleration happens in the radially expanding part.Section 5; Section 6, Conclusion
Acceleration beats the classical estimate. Michel’s fixed-monopole solution predicts a terminal four-velocity ratio of 2.5 for a rotator with the parameter alpha equal to four, while the self-consistent simulation gives more than eight, and the fraction of the Poynting flux converted into kinetic energy reaches 16.7 percent for that flow. The extra acceleration happens far from the star, driven by the imbalance between the tension and the pressure gradient of the toroidal magnetic field as flux collimates towards the axis — a mechanism absent from treatments that hold the poloidal field fixed.Section 5; Figure 7
The reason relativistic winds collimate so weakly is intrinsic to the plasma, not to the model. Two relativistic effects cancel the gain: the electric force, negligible in a slow flow, grows to nearly equal the collimating Lorentz force; and in a Poynting-dominated flow the toroidal magnetic field contributes to the effective inertial mass, so the curvature of a streamline depends on the collimating force divided by a mass that rises with the same field squared. Increasing the collimating force therefore does not increase the bending, and at low latitudes the collimation scale becomes independent of the magnetic field and of the angular velocity of the source.Section 5, the discussion of curvature; Equations (37) and (38)
Two dimensionless numbers place any real object in the picture: the magnetisation, the ratio of Poynting flux to mass energy flux at the equator, and a rotation parameter that is the three-halves power of the ratio of terminal to initial four-velocity. All radio pulsars eject Poynting-dominated winds but almost all are slow rotators; the Crab pulsar, rotating at about 200 radians per second with a surface field near four times ten to the twelfth gauss and ejecting about four times ten to the thirty-eighth pairs per second, sits at a magnetisation near 1.3 times ten to the fourth and a rotation parameter of 0.57, marginally a fast rotator. Active galactic nuclei and superluminal galactic sources should have rotation parameters above one and magnetisations above the square of their jet Lorentz factors, so their winds should be Poynting dominated too.Section 4, Equations (21) to (25)
Bogovalov states the open problem himself: if only a thousandth of the wind energy reaches the jet, the model predicts a jet luminosity far below what active galactic nuclei show, where jet emission can be within a factor of ten of the total. Either this model has no observed counterpart, or self-collimation by the central rotator alone cannot gather the bulk of an outflow into a jet — and the candidate answer, already demonstrated for non-relativistic winds, is that a slower magnetised outflow from a surrounding accretion disc collimates the fast central wind indirectly.Section 6, Conclusion, closing paragraphs
The way in
https://doi.org/10.1051/0004-6361:20010201How to cite it
Sergey V. Bogovalov (2001) Acceleration and collimation of relativistic plasmas ejected by fast rotators doi:10.1051/0004-6361:20010201