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 } \sim 10 ^ { 37 - 38 } ~ { } { erg } ~ { } { s } ^ { -1 } 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 } \times 10 ^ { 36 } ~ { } { erg } ~ { } { s } ^ { -1 } ( 2–10 keV ) , or L _ { X } / L _ { Eddington } = 1.8 ^ { +0.9 } _ { -0.8 } \times 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 .