  Relativistic jets propagating through an ambient medium must produce some
observational effects along their side boundaries because of interactions
across the large velocity gradient. One possible effect of such an interaction
would be a sheared magnetic field structure at the jet boundaries, leading to a
characteristic radio polarization pattern. As proposed by Ostrowski, another
effect can come from the generation of a high energy cosmic ray component at
the boundary, producing dynamic effects on the medium surrounding the jet and
forming a cocoon dominated by cosmic rays with a decreased thermal gas
emissivity. We selected this process for our first attempt to look for the
effects of this type of interaction. We analyzed the Chandra X-ray data for the
radio galaxy M87 in order to verify if the expected regions of diminished
emissivity may be present near the spectacular X-ray jet in this source. The
detailed analysis of the data, merged from 42 separate observations, shows
signatures of lower emissivity surrounding the jet. In particular we detect an
intensity dip along the part of the jet, which would be approximately 150 pc x
2 kpc in size, if situated along the jet which is inclined toward us. Due to a
highly non-uniform X-ray background in the central region we are not able to
claim the discovery of a cosmic ray cocoon around the M87 jet: we only have
demonstrated that the data show morphological structures which could be
accounted for if a cosmic ray cocoon exists.
