  Simultaneous X-ray and optical observations of black hole X-ray binaries have
shown that the light curves contain multiple correlated and anti-correlated
variation components when the objects are in the hard state. In the case of the
black hole X-ray binary, GX 339-4, the cross correlation function (CCF) of the
light curves suggests a positive correlation with an optical lag of 0.15 s and
anti-correlations with an optical lag of 1 s and X-ray lag of 4 s. This
indicates the two light curves have some common signal components with
different delays. In this study, we extracted and reconstructed those signal
components from the data for GX 339-4. The results confirmed that correlation
and anti-correlation with the optical lag are two common components. However,
we found that the reconstructed light curve for the anti-correlated component
indicates a positively correlated variation with an X-ray lag of ~ +1 s. In
addition, the CCF for this signal component shows anti-correlations not only
with the optical lag, but also with the X-ray lag, which is consistent with the
CCF for the data. Therefore, our results suggest that the combination of the
two positively correlated components, that is, the X-ray preceding signal with
the 0.15-s optical lag and the optical preceding signal with the 1-s X-ray lag,
can make the observed CCF without anti-correlated signals. The optical
preceding signal may be caused by synchrotron emission in a magnetically
dominated accretion flow or in a jet, while further study is required to
understand the mechanism of the X-ray time lag.
