  Here we study the potential observational signatures of supermassive black
hole binaries (SMBHBs) in the Fe K$\alpha$ line profiles emitted from the
accretion disks around their components. We simulated the Fe K$\alpha$ line
emission from the relativistic accretion disks using ray tracing method in Kerr
metric. The obtained profiles from the SMBHBs are then compared with those in
the case of the single supermassive black holes (SMBHs). We considered two
models of the SMBHBs: a model when the secondary SMBH is embedded in the
accretion disk around the primary, causing an empty gap in the disk, and a
model with clearly separated components, where the accretion disks around both
primary and secondary give a significant contribution to the composite Fe
K$\alpha$ line emission of a such SMBHB. The obtained results showed that both
models of SMBHBs can leave imprints in the form of ripples in the cores of the
emitted Fe K$\alpha$ line profiles, which may look like an absorption component
in the line profile. However, in the case of the composite line profiles
emitted from two accretion disks, these ripples could have much higher
amplitudes and strongly depend on orbital phase of the system, while for those
emitted from a disk with an empty gap, the corresponding ripples mostly have
lower amplitudes and do not vary significantly with orbital phase. The present
day X-ray telescopes are not able to detect such signatures in the observed
X-ray spectra of SMBHBs. However this will be possible with the next generation
of X-ray observatories, which will also enable application of such effects as a
tool for studying the properties of these objects.
