Figure 1: The bulk Lorentz factor of the flow as a function of radius for different values of . The black, red, blue and green curves correspond to 8, 10 and 25 respectively. The solid curves correspond to the case where Eq. (1) is used for the instability growth time scale (fast kink) and the dashed to the one where Eq. (2) is used (slow kink case). | |
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Figure 2: The bulk Lorentz factor dependence on the cooling efficiency of the flow and jet opening angles. The solid curves correspond to the fast kink case while the dashed to the slow kink one. The black, red and green curves correspond to fast cooling, slow cooling and jet opening angle of respectively. | |
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Figure 3: The dependence of the magnetization parameter on the radius for the different prescriptions of radiative cooling and the instability timescale. Notice that the flow becomes matter-dominated at distances greater than 10r_{0}. The thick lines show the ratio of the radial to the toroidal components of the magnetic field in the flow. The dominant component is clearly the toroidal one. | |
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Figure 4: The bulk Lorentz factor of the flow for different and for the fast and slow kink case. Notice that larger values for result in faster outflows. | |
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Figure 5: The bulk Lorentz factor of the flow for different jet opening angles . For smaller opening angles, the terminal Lorentz factors of the flow become larger because of more efficient dissipation of the magnetic energy. The blue curve corresponds to the non-axisymmetric case studied by Drenkhahn & Spruit (2002). | |
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Figure 6: The magnetization of the flow as a function of distance for different and jet opening angles. Keeping , the jet is still magnetically dominated at large distance from the source for . Smaller jet opening angles lead to lower values of . The blue curve corresponds to the non-axisymmetric case studied by Drenkhahn & Spruit (2002). The discontinuity at the location of the photospheric radius is a result of the subtraction of the radiation energy density from the internal energy of the flow. | |
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Figure 7: The radiative efficiency of the flow, defined as the ratio of the radiated luminosity over the luminosity of the flow for different and . The black and red stars correspond to the fast kink and slow kink cases respectively. For opening angles of (in accordance with the values deduced by achromatic breaks of the afterglows) the efficiency reaches values of 20%. The circles correspond to the non-axisymmetric case studied by Drenkhahn & Spruit (2002). | |
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