On the Optical -- X-ray correlation from outburst to quiescence in Low Mass X-ray Binaries: the representative cases of V404 Cyg and Cen X-4

Low mass X-ray binaries (LMXBs) show evidence of a global correlation of debated origin between X-ray and optical luminosity. We study for the first time this correlation in two transient LMXBs, the black hole V404 Cyg and the neutron star Cen X-4, over 6 orders of magnitude in X-ray luminosity, from outburst to quiescence. After subtracting the contribution from the companion star, the Cen X-4 data can be described by a single power law correlation of the form $L_{opt}\propto\,L_{X}^{0.44}$, consistent with disk reprocessing. We find a similar correlation slope for V404 Cyg in quiescence (0.46) and a steeper one (0.56) in the outburst hard state of 1989. However, V404 Cyg is about $160-280$ times optically brighter, at a given $3-9$ keV X-ray luminosity, compared to Cen X-4. This ratio is a factor of 10 smaller in quiescence, where the normalization of the V404 Cyg correlation also changes. We show that once the bolometric X-ray emission is considered and the known main differences between V404 Cyg and Cen X-4 are taken into account (a larger compact object mass, accretion disk size, and the presence of a strong jet contribution in the hard state for the black hole system) the two systems lie on the same correlation. In V404 Cyg, the jet dominates spectrally at optical-infrared frequencies during the hard state, but makes a negligible contribution in quiescence, which may account for the change in its correlation slope and normalization. These results provide a benchmark to compare with data from the 2015 outburst of V404 Cyg and, potentially, other transient LMXBs as well.