Cosmic rays play a pivotal role in launching galactic winds, particularly in quiescently star-forming galaxies where the hot gas alone is not sufficient to drive a wind. Except for the Milky Way, not much is known about the transport of cosmic rays in galaxies. In this Letter, we present low-frequency observations of the nearby edge-on spiral galaxy NGC 4565 using the LOw-Frequency ARray (LOFAR). With our deep 144-MHz observations, we obtain a clean estimate of the emission originating from old cosmic-ray electrons (CRe), which is almost free from contamination by thermal emission. We measured vertical profiles of the non-thermal radio continuum emission that we fitted with Gaussian and exponential functions. The different profile shapes correspond to 1D cosmic-ray transport models of pure diffusion and advection, respectively. We detect a warp in the radio continuum that is reminiscent of the previously known HI warp. Because the warp is not seen at GHz-frequencies in the radio continuum, its minimum age must be about 100 Myr. The warp also explains the slight flaring of the thick radio disc that can otherwise be well described by a Gaussian profile with an FWHM of 65 arcsec (3.7 kpc). The diffusive radio halo together with the extra-planar X-ray emission may be remnants of enhanced star-forming activity in the past where the galaxy had a galactic wind, as GHz-observations indicate only a weak outflow in the last 40 Myr. NGC 4565 could be in transition from an outflow- to an inflow-dominated phase.
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