Broad Fe K-alpha emission lines have recently been reported in a number of Galactic black holes. Such lines are useful accretion flow diagnostics because they may be produced at the inner accretion disk and shaped by relativistic effects, but in general they have only been observed at luminosities of L_X ~ 10^(37-38) erg/s in soft X-rays. The Galactic microquasar V4641 Sgr -- widely known for its 12.2 Crab (1.5-12 keV) outburst in 1999 September -- displayed low-level activity in 1999 March. BeppoSAX observed the source in this state and Fe K-alpha line emission was found (in t Zand et al. 2000). In re-analyzing these data, we find strong evidence that the Fe K-alpha line profile is broadened. For the most likely values of the source distance and black hole mass measured by Orosz et al. (2001), our fits to the total spectrum indicate that the source was observed at a luminosity of L_X = 1.9 (+1.0, -0.8) * 10^(36) erg/s (2-10 keV), or L_X/L_Edd. = 1.8 (+0.9, -0.8) * 10^(-3). Advection-dominated accretion flow (ADAF) models predict a radially-recessed disk in this regime. In contrast, fits to the observed Fe K-alpha emission line profile with a relativistic line model constrain the inner disk to be consistent with the marginally stable circular orbit of a Schwarzschild black hole.
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