Introduction to Black Hole Astrophysics by Gustavo E. Romero & Gabriela S. Vila

Author:Gustavo E. Romero & Gabriela S. Vila
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(5.67)

The corresponding Lorentz factor is

(5.68)

or, equivalently,

(5.69)

The component of the velocity along the magnetic field is negligible and does not contribute significantly to γ.

From Eqs. (5.60) and (5.68) we may obtain an estimation of the value of the toroidal magnetic field in the limit r≫R L and γ≫1,

(5.70)

Thus we get that . The second term in Eq. (5.69) is related the curvature of the field lines,

(5.71)

where is a constant of the order of unity. Its exact value depends on the details of the geometry of the field lines; for a highly collimated flow with Ω=constant, for example, (Tchekhovskoy et al. 2008). We may then write Eq. (5.69) in a convenient form as

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