Abstract
Relativistic jets can be modeled as magnetohydrodynamic flows. We analyze the related equations and discuss the involved acceleration mechanisms, their relation to the collimation, to the jet confinement by its environment, and to possible rarefaction waves triggered by pressure imbalances.
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Notes
- 1.
If Ω is the same in all streamlines as is often the case in pulsar winds, this surface is a cylinder, called light cylinder.
- 2.
Note that B ϕ  < 0 so that both parts of the angular momentum are positive.
- 3.
As in the case of the angular momentum, both parts are positive since B ϕ  < 0.
- 4.
The function M f shows where the fast-magnetosonic surface is located. Besides that, M f is related to the Mach-cone of the propagation of fast magnetosonic waves in the super-fast regime. This cone has half opening angle \(\arctan (M_{f}^{2} - 1)^{-1/2}\) (the cone’s symmetry axis coincides with the poloidal field line).
- 5.
Actually the equations describing the effect in planar geometry can be found from the corresponding ones in cylindrical geometry by replacing \(\varpi \rightarrow \varpi _{0} + x\), \(z \rightarrow z_{0} + z\), \(A/\varpi _{0} \rightarrow A\), \(\varpi _{0}\varOmega /c \rightarrow \chi\), \(x_{\mathrm{A}} \rightarrow \chi _{\mathrm{A}}\), \(L/\varpi _{0} \rightarrow P =\mu c\chi _{\mathrm{A}}^{2}/\chi\), \(\varpi _{\mathrm{A}}/\varpi _{0} \rightarrow \chi _{\mathrm{A}}/\chi\), and then taking the limit \(\varpi _{0} \rightarrow \infty \).
References
Aloy, M.A., Rezzolla, L.: A powerful hydrodynamic booster for relativistic jets. ApJ 640, L115 (2006). doi:10.1086/503608
Bekenstein, J.D., Oron, E.: New conservation laws in general-relativistic magnetohydrodynamics. Phys. Rev. D 18, 1809 (1978)
Beskin, V.S.: MHD flows in compact astrophysical objects: accretion, winds and jets. Springer, Berlin/Heidelberg (2010)
Blandford, R.D., Payne, D.G.: Hydromagnetic flows from accretion discs and the production of radio jets. MNRAS 199, 883 (1982)
Blandford, R.D., Znajek, R.L.: Electromagnetic extraction of energy from Kerr black holes. MNRAS 179, 433 (1977)
Camenzind, M.: Centrifugally driven MHD-winds in active galactic nuclei. A&A 156, 137 (1986)
Contopoulos, J.: Magnetically driven relativistic jets and winds: exact solutions. ApJ 432, 508 (1994). doi:10.1086/174590
Fendt, C., Ouyed, R.: Ultrarelativistic magnetohydrodynamic jets in the context of gamma-ray bursts. ApJ 608, 378 (2004). doi:10.1086/386363
Granot, J.: Interaction of a highly magnetized impulsive relativistic flow with an external medium. MNRAS 421, 2442 (2012). doi:10.1111/j.1365-2966.2012.20473.x
Granot, J., Komissarov, S.S., Spitkovsky, A.: Impulsive acceleration of strongly magnetized relativistic flows. MNRAS 411, 1323 (2011). doi:10.1111/j.1365-2966.2010.17770.x
Komissarov, S.S., Barkov, M.V., Vlahakis, N., Königl, A.: Magnetic acceleration of relativistic active galactic nucleus jets. MNRAS 380, 51 (2007). doi:10.1111/j.1365-2966.2007.12050.x
Komissarov, S.S., Vlahakis, N., Königl, A., Barkov, M.V.: Magnetic acceleration of ultrarelativistic jets in gamma-ray burst sources. MNRAS 394, 1182 (2009). doi:10.1111/j.1365-2966.2009.14410.x
Komissarov, S.S., Vlahakis, N., Königl, A.: Rarefaction acceleration of ultrarelativistic magnetized jets in gamma-ray burst sources. MNRAS 407, 17 (2010). doi:10.1111/j.1365-2966.2010.16779.x
Li, Z.Y., Chiueh, T., Begelman, M.C.: Electromagnetically driven relativistic jets - a class of self-similar solutions. ApJ 394, 459 (1992). doi:10.1086/171597
Lovelace, R.V.E., Mehanian, C., Mobarry, C.M., Sulkanen, M.E.: Theory of axisymmetric magnetohydrodynamic flows - disks. ApJS 62, 1 (1986). doi:10.1086/191132
Lyutikov, M.: Simple waves in relativistic fluids. Phys. Rev. E 82(5), 056305 (2010). doi:10.1103/PhysRevE.82.056305
Marti, J.M., Muller, E.: Analytical solution of the Riemann problem in relativistic hydrodynamics. J. Fluid Mech. 258, 317 (1994). doi:10.1017/S0022112094003344
Matsumoto, J., Masada, Y., Shibata, K.: Effect of interacting rarefaction waves on relativistically hot jets. ApJ 751, 140 (2012). doi:10.1088/0004-637X/751/2/140
Michel, F.C.: Relativistic stellar-wind torques. ApJ 158, 727 (1969)
Millas, D., Katsoulakos, G., Lingri, D., Karampelas, K., Vlahakis, N.: Solutions of the wind equation in relativistic magnetized jets. Int. J. Mod. Phys. Conf. Ser. 28, 1460200 (2014). doi:10.1142/S2010194514602002
Mizuno, Y., Hardee, P., Hartmann, D.H., Nishikawa, K.I., Zhang, B.: A magnetohydrodynamic boost for relativistic jets. ApJ 672, 72 (2008). doi:10.1086/523625
Okamoto, I.: Relativistic centrifugal winds. MNRAS 185, 69 (1978)
Sapountzis, K., Vlahakis, N.: Rarefaction acceleration in magnetized gamma-ray burst jets. MNRAS 434, 1779 (2013). doi:10.1093/mnras/stt1142
Tchekhovskoy, A., McKinney, J.C., Narayan, R.: Simulations of ultrarelativistic magnetodynamic jets from gamma-ray burst engines. MNRAS 388, 551 (2008). doi:10.1111/j.1365-2966.2008.13425.x
Tchekhovskoy, A., McKinney, J.C., Narayan, R.: Efficiency of magnetic to kinetic energy conversion in a monopole magnetosphere. ApJ 699, 1789 (2009). doi:10.1088/0004-637X/699/2/1789
Tchekhovskoy, A., Narayan, R., McKinney, J.C.: Magnetohydrodynamic simulations of gamma-ray burst jets: beyond the progenitor star. NewA 15, 749 (2010). doi:10.1016/j.newast.2010.03.001
Tchekhovskoy, A., Narayan, R., McKinney, J.C.: Efficient generation of jets from magnetically arrested accretion on a rapidly spinning black hole. MNRAS 418, L79 (2011). doi:10.1111/j.1745-3933.2011.01147.x
Toma, K., Takahara, F.: Efficient acceleration of relativistic magnetohydrodynamic jets. Prog. Theor. Exp. Phys. 2013(8), 083E02 (2013). doi:10.1093/ptep/ptt058
Vlahakis, N.: The efficiency of the magnetic acceleration in relativistic jets. Ap&SS 293, 67 (2004a). doi:10.1023/B:ASTR.0000044653.77654.fb
Vlahakis, N.: Ideal magnetohydrodynamic solution to the σ problem in crab-like pulsar winds and general asymptotic analysis of magnetized outflows. ApJ 600, 324 (2004b). doi:10.1086/379701
Vlahakis, N., Königl, A.: Relativistic magnetohydrodynamics with application to gamma-ray burst outflows. I. theory and semianalytic trans-alfvénic solutions. ApJ 596, 1080 (2003a). doi:10.1086/378226
Vlahakis, N., Königl, A.: Relativistic magnetohydrodynamics with application to gamma-ray burst outflows. II. semianalytic super-alfvénic solutions. ApJ 596, 1104 (2003b). doi:10.1086/378227
Vlahakis, N., Königl, A.: Magnetic driving of relativistic outflows in active galactic nuclei. I. interpretation of parsec-scale accelerations. ApJ 605, 656 (2004). doi:10.1086/382670
Zenitani, S., Hesse, M., Klimas, A.: Scaling of the anomalous boost in relativistic jet boundary layer. ApJ 712, 951 (2010). doi:10.1088/0004-637X/712/2/951
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Vlahakis, N. (2015). Theory of Relativistic Jets. In: Contopoulos, I., Gabuzda, D., Kylafis, N. (eds) The Formation and Disruption of Black Hole Jets. Astrophysics and Space Science Library, vol 414. Springer, Cham. https://doi.org/10.1007/978-3-319-10356-3_7
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