The effects of relativistic bulk motion of X-ray flares in the corona on the iron K alpha line in Seyfert 1 galaxies

It is likely that dramatic magnetic flares in a corona above a black hole a ccretion disk dominate the X-ray emission in Seyfert 1 galaxies. Such flare s are likely to move with mildly relativistic bulk velocity. We study the e ffects of the bulk motion of X-ray flares on the shape and equivalent width of the iron K alpha line from an untruncated cold disk around a Kerr black hole using fully relativistic calculations. The flares are located above a cold accretion disk, either on or off the rotation axis. The upward/outwar d bulk motion of flares causes a reduction of the iron K alpha line width, while the downward/inward bulk motion of flares causes an increase of the i ron K alpha line width. To a distant observer with a low inclination angle theta (o) less than or similar to 30 degrees larger upward/outward bulk vel ocities decrease the extension of the red wing, with little change in the l ocation of the blue "edge" In contrast, an observer at a large inclination angle (e.g., theta (o) = 60 degrees) sees both the red wing and the blue "e dge" change with the bulk velocity. The equivalent width of the iron K alph a line decreases rapidly with increasing bulk velocity of flares. However, the "narrower" line profiles observed in some objects (e.g., IC 4329A and N GC 4593) are difficult to produce using the outflowing magnetic flare model with an appropriate equivalent width unless the X-ray emission is concentr ated in an outer region with a radius of several tens of or more. This sugg ests that other parameters, such as the "truncation radius" due to disrupti on or ionization of the inner disk, may still be needed. An important resul t is that the iron K alpha line intensity is found to be constant even thou gh the continuum flux varies significantly, which is true for outflowing ma gnetic flares with different bulk velocities but similar intrinsic luminosi ties when located close to the central black hole. This is caused by the co mbination of the effects of relativistic beaming and gravitational lensing. We find that fluctuations in the bulk velocities of outflowing low-height flares located at the inner region (r less than or similar to 15r(g)) can a ccount for a constant iron K alpha line and significant continuum variation as observed in MCG -6-30-15 and NGC 5548. This is especially interesting f or MCG -6-30-15, whose behavior is difficult to explain using the ionizatio n model.