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Fig. C.1.


Doppler boosting factor in the observer’s frame o relative to the hot spot’s moving frame hs, So ~ Shs × D, with D = (Γ(1 − β))−(3+α), for a moving hot spot at β = v/c, Γ = (1− β2)−1/2, and at an angle 90° −i relative to the line of sight (McCrea 1972). We show D for two radii, ISCO a = 0 (blue) and R = 10 Rg (red). Solid curves assume spectral index α = 0.6 (Sv ∝ vα, appropriate for very bright flares) and dotted curves assume = 1.5 (S / , appropriate for average bright states, Witzel et al. 2018). If one assumes that D < 2.5, the inclination has to be less than about 45°.

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