We investigate the effects of ram pressure on the ordered magnetic field of a galaxy hosting a radio halo and strong nuclear outflows .
New radio images in total and polarized intensity of the edge-on Virgo galaxy NGC 4388 were obtained within the CHANG-ES EVLA project .
The unprecedented noise level reached allows us to detect striking new features of the ordered magnetic field .
The nuclear outflow extends far into the halo to about 5 kpc from the center and is spatially correlated with the { H \alpha } and X-ray emission .
For the first time , the southern outflow is detected .
Above and below both spiral arms we find extended blobs of polarized emission with an ordered field oriented perpendicular to the disk .
The synchrotron lifetime of the cosmic ray electrons ( CREs ) in these regions yields a mean outflow velocity of ( 270 \pm 70 ) { km s ^ { -1 } } , in agreement with a galactic wind scenario .
The observed symmetry of the polarized halo features in NGC 4388 excludes a compression of the halo gas by the ram pressure of the intra-cluster medium ( ICM ) .
The assumption of equilibrium between the halo pressure and the ICM ram pressure yields an estimate of the ICM density that is consistent with both the ICM density derived from X-ray observations and the recent Planck Sunyaev-Zel ’ dovich measurements .
The detection of a faint radio halo around cluster galaxies could thus be used for an estimate of ICM ram pressure .