Fast infrared variability from a relativistic jet in GX 339-4

We present the discovery of fast infrared/X-ray correlated variability in the black hole transient GX 339-4. The source was observed with subsecond time resolution simultaneously with Very Large Telescope/Infrared Spectrometer And Array Camera and Rossi X-ray Timing Explorer/Proportional Counter Array in 2008 August, during its persistent low-flux highly variable hard state. The data show a strong correlated variability, with the infrared emission lagging the X-ray emission by 100 ms. The short time delay and the nearly symmetric cross-correlation function, together with the measured brightness temperature of similar to 2.5 x 10(6) K, indicate that the bright and highly variable infrared emission most likely comes from a jet near the black hole. Under standard assumptions about jet physics, the measured time delay can provide us a lower limit of Gamma > 2 for the Lorentz factor of the jet. This suggests that jets from stellar-mass black holes are at least mildly relativistic near their launching region. We discuss implications for future applications of this technique.