  Fallback disks are expected to form around young neutron stars. The presence
of these disks can be revealed by their blackbody spectrum in the infrared,
optical and UV bands. We present a re-reduction of the archival optical and
infrared data of the Vela pulsar, together with the existing infrared and UV
spectrum of Vela, and model their unpulsed components with the blackbody
spectrum of a supernova debris disk. We invoke the quiescent disk solution of
Sunyaev and Shakura for the description of the disk in the propeller stage and
find the inner radius of the disk to be inside the light cylinder radius. We
perform a high resolution X-ray analysis with XMM-Newton and find a narrow
absorption feature at 0.57 keV which can be interpreted as K$_{\alpha}$ line of
He-like oxygen (OVII). The strength of the line indicates an element
over-abundance in our line of sight exceeding the amounts that would be
expected from ISM. The spectral feature may originate from the pulsar wind
nebula and may be partly caused by the reprocessed X-ray radiation by the
fallback disk. We discuss the lower-than-3 braking index of Vela as partially
due to the contribution of the propeller torques. Our results suggest that the
pulsar mechanism can work simultaneously with the propeller processes and that
the debris disks can survive the radiation pressure for at least $\sim 10^4$
years. As Vela is a relatively close object, and a prototypical pulsar, the
presence of a disk, if confirmed, may indicate the ubiquity of debris disks
around young neutron stars.
