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Jets

  • Chapter
Introduction to Black Hole Astrophysics

Part of the book series: Lecture Notes in Physics ((LNP,volume 876))

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Abstract

Jets are associated with accretion onto black holes in different types of astrophysical sources. This chapter discusses current ideas on the launching, collimation, structure, radiation, and termination of black hole jets.

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Notes

  1. 1.

    We can now conveniently write the electric field only in terms of the flux function as E=−(Ω/c)∇ψ.

  2. 2.

    In the general case α is the angle between the magnetic field and the wave vector. Since we are interested in waves propagating along the poloidal magnetic field, here cosα=B/B p.

  3. 3.

    Recall that the current I is not constant on magnetic surfaces, and so J can cross them.

  4. 4.

    This is the minimum angle for instability in flat and Schwarzschild space-time. It is slightly smaller for a Kerr black hole with spin a ∗=−1, and approaches 90∘ for a ∗=1; a ∗ is taken positive (negative) if the black hole and the disk rotate in the same (opposite) sense.

  5. 5.

    The critical angle is the same for a field line inclined inwards, but this case is of no interest for the launching of an outflow.

  6. 6.

    Notice that it equals dϕ/dt in Eq. (2.59) evaluated at the horizon.

  7. 7.

    Analogous considerations show that the flux of electromagnetic angular momentum \(\mathcal{L}^{\mu}= -E^{\mu}_{\phi}\) is also conserved.

  8. 8.

    This is the value of ω calculated by Blandford and Znajek (1977) to first order in a ∗ in the perturbed split monopole solution.

  9. 9.

    An example of regular coordinates in Kerr space-time are Kerr-Schild coordinates.

  10. 10.

    Also in the limit of force-free, degenerate MHD, fast waves propagate at the speed of light.

  11. 11.

    The production of magnetized, supersonic jets of plasma in laboratory experiments is nowadays possible. This could be yet another way to learn about astrophysical jets, as long as the experimental conditions in the laboratory can be correctly scaled. See the articles by Remington et al. (2006) and Ciardi (2010) for reviews on this topic.

  12. 12.

    This source hosts, of course, a neutron star and not a black hole.

  13. 13.

    Simulations in 2D by Fragile et al. (2012) showed no correlation between the disk thickness and the jet power. These simulations probe a different regime than those by Tchekhovskoy and McKinney (2012), since the authors consider disks subject to cooling with 0.04≲H/r≲0.16 and a flow not dominated by magnetic pressure. As a conclusion, they suggest that it is the corona and not the disk wind that provides confinement to the jet.

  14. 14.

    The reason is that shock waves are commonplace in a variety of astrophysical sources. Besides the first order Fermi process other acceleration mechanisms rely up to some extent in the presence of shocks, see for example Derishev et al. (2003). Of course, particles may also be accelerated without shocks by means of an electric field as expected to occur in pulsar magnetospheres.

  15. 15.

    Recall that, in general, fixing the shape of the poloidal field does not yield a consistent solution of the MHD equations since such B does not satisfy the Grad-Shafranov equation.

  16. 16.

    The results apply as well to the case of a spherical shell.

  17. 17.

    Such events are observed for instance in microquasars, see next chapter.

  18. 18.

    In a static force-free plasma, for example, the Kruskal-Shafranov criterion predicts instability when −B ϕ /B p>2πr/L, where r is the radius and L the length of the plasma column.

  19. 19.

    In the frame of the standard MHD model, then, we expect that jets become unstable beyond the Alfvén surface.

  20. 20.

    The expression in Eq. (5.105) is then valid for E γ ≫E c(E min) and E γ ≪E c(E max), i.e. far from the low-energy and the high-energy cutoffs of the synchrotron spectrum.

  21. 21.

    Inverse Compton scattering off protons and other particles much heavier than the electron is very inefficient and therefore generally neglected. Protons have other much more efficient channels of interaction with radiation as we shall see.

  22. 22.

    In this limit the energy loss rate cannot be strictly considered as a continuous function of the electron energy. A more rigorous treatment is discussed, for example, in Khangulyan and Aharonian (2005) and Moderski et al. (2005).

  23. 23.

    In certain astrophysical systems the IC scattering cannot be approximated as isotropic. An example is the interaction of electrons in the jets in X-ray binaries with the radiation field of the companion star. A full treatment taking into account the collision angle is then required, see e.g. Dermer and Schlickeiser (1993) and Khangulyan et al. (2008).

  24. 24.

    Photohadronic interactions of cosmic rays protons with the cosmic microwave background set an upper limit to the energy of cosmic rays arriving to Earth of ∼5×1019 eV. This is the famous Greisen-Zatsepin-Kuzmin (GZK) cutoff.

  25. 25.

    It is assumed that \(\widetilde{n}\) and K π depend only weakly on the energy of the proton.

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  1. Instituto Argentino de Radioastronomía, Villa Elisa, Argentina

    Gustavo E. Romero & Gabriela S. Vila

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Romero, G.E., Vila, G.S. (2014). Jets. In: Introduction to Black Hole Astrophysics. Lecture Notes in Physics, vol 876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39596-3_5

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