Rapid Optical Variations Correlated with X-rays in the 2015 Second Outburst of V404 Cygni (GS 2023$+$338)

We present optical multi-colour photometry of V404 Cyg during the outburst from December, 2015 to January, 2016 together with the simultaneous X-ray data. This outburst occurred less than 6 months after the previous outburst in June–July, 2015. These two outbursts in 2015 were of a slow rise and rapid decay-type and showed large-amplitude (∼2 mag) and short-term (∼10 min–3 hours) optical variations even at low luminosity (0.01–0.1LEdd). We found correlated optical and X-ray variations in two ∼1 hour time intervals and obtained a Bayesian estimate of an X-ray delay against the optical emission, which is ∼30–50 s, during those two intervals. In addition, the relationship between the optical and X-ray luminosity was Lopt ∝ L 0.25−0.29 X at that time. These features cannot be easily explained by the conventional picture of transient black-hole binaries, such as canonical disc reprocessing and synchrotron emission related to a jet. We suggest that the disc was truncated during those intervals and that the X-ray delays represent the required time for propagation of mass accretion flow to the inner optically-thin region with a speed comparable to the free-fall velocity.