The late-B magnetic chemically peculiar star CU Vir is one of the fastest rotators among the intermediate-mass stars with strong fossil magnetic fields. It shows a prominent rotational modulation of the spectral energy distribution and absorption line profiles due to chemical spots and exhibits a unique strongly beamed variable radio emission. Little is known about the magnetic field topology of CU Vir. In this study we aim to derive, for the first time, detailed maps of the magnetic field distribution over the surface of this star. We use high-resolution spectropolarimetric observations covering the entire rotational period. These data are interpreted using a multi-line technique of least-squares deconvolution (LSD) and a new Zeeman Doppler imaging code based on detailed polarised radiative transfer modelling of the Stokes I and V LSD profiles. This new magnetic inversion approach relies on the spectrum synthesis calculations over the full wavelength range covered by observations and does not assume that the LSD profiles behave as a single spectral line with mean parameters. We present magnetic and chemical abundance maps derived from the Si and Fe lines. Mean polarisation profiles of both elements reveal a significant departure of the magnetic field topology of CU Vir from the commonly assumed axisymmetric dipolar configuration. The field of CU Vir is dipolar-like, but clearly non-axisymmetric, showing a large difference of the field strength between the regions of opposite polarity. The main relative abundance depletion features in both Si and Fe maps coincide with the weak-field region in the magnetic map. Detailed information on the distorted dipolar magnetic field topology of CU Vir provided by our study is essential for understanding chemical spot formation, radio emission, and rotational period variation of this star.
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