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Fig. 3.


Radius (R) – orbital period (Porb) relations for flare loops on July 22 (black), July 28 (blue), and May 27 (pink) compared to circular orbits around a black hole of 4.14 (solid lines), 3, and 5.5 (dashed grey lines) million solar masses. The solid red curve is for orbits around a spin 0 (Schwarzschild) black hole (Schwarzschild 1916; Bardeen et al. 1972). The solid green and black lines are for prograde and retrograde orbits around a maximum (spin parameter |a| = 1) Kerr black hole (Kerr 1963). Small green, red, and black circles mark the innermost stable circular orbits (ISCO) in these cases (Bardeen et al. 1972). For the three flare loops, the filled black circle, blue square, and open pink triangles mark the (R, P) estimates from the best Schwarzschild (a = 0) orbit fits with the relativistic ray tracing codes (Figs. 1, B.3, B.4, Tables 1 and 2). In principle all three flares can be accounted for by the same Schwarzschild R ≈ 6−10 Rg circular orbit with a period of ~45 min. Interestingly the data can also be fit by a retrograde orbit on ISCO for an extreme Kerr hole (a = −1). The periods Ppol for the full swings of the polarization orientation of the July 22, July 28 and May 27 flares are given as right pointing black, blue, and pink arrows (with their rms uncertainties marked as dotted vertical lines; see Fig. 2). For a polarized hot spot in a poloidal field the polarization rotation periods are equal to the spot orbital period, in agreement with our data.

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