Large X-ray time lags from compact black hole coronae

The positive (‘hard’) and negative (‘soft’) X-ray time lags in black hole X-ray binary hard states can shed light on the innermost geometry of their emitting regions. The observed lags can be surprisingly large. Explanations for the lags which include light-travel delays (e.g. scattering in the jet, or thermal reverberation of coronal emission by the disk) or propagation through a ‘hot flow’ corona with radial temperature dependence, are difficult to reconcile with the small disk radii inferred from observed disk variability time-scales and broad Fe K profiles. Here we show that these lags can be produced by compact single-temperature coronae, by accounting for the natural delay expected between seed photon variations and coronal heating, as accretion fluctuations propagate through the disk to the corona.