Rapid optical variations correlated with X-rays in the 2015 second outburst of V404 Cygni (GS 2023+338)

We present optical multicolour photometry of V404 Cyg during the outburst from 2015 December to 2016 January together with the simultaneous X-ray data. This outburst occurred less than six months after the previous outburst in 2015 June-July. 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 h) optical variations even at low luminosity (0.01-0.1L_Edd). We found correlated optical and X-ray variations in two ∼1 h 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 luminosities was L_opt ∝ L_X^{0.25-0.29} 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 the propagation of mass accretion flow to the inner optically thin region with a speed comparable to the free-fall velocity.