We present new ATCA multi-wavelength radio measurements (range 2.1-21.2 GHz) of the early-type magnetic star rho Oph A, performed in March 2019 during 3 different observing sessions. These new ATCA observations evidence a clear rotational modulation of the stellar radio emission and the detection of coherent auroral radio emission from rho Oph A at 2.1 GHz. We collected high-resolution optical spectra of rho Oph A acquired by several instruments over a time span of about ten years. We also report new magnetic field measurements of rho Oph A that, together with the radio light curves and the temporal variation of the equivalent width of the HeI line (lambda=5015 Angstrom), were used to constrain the rotation period and the stellar magnetic field geometry. The above results have been used to model the stellar radio emission, modelling that allowed us to constrain the physical condition of rho Oph As magnetosphere. Past XMM measurements showed periodic X-ray pulses from rho Oph A. We correlate the X-ray light curve with the magnetic field geometry of rho Oph A. The already published XMM data have been re-analyzed showing that the X-ray spectra of rho Oph A are compatible with the presence of a non-thermal X-ray component. We discuss a scenario where the emission phenomena occurring at the extremes of the electromagnetic spectrum, radio and X-ray, are directly induced by the same plasma process. We interpret the observed X-ray and radio features of rho Oph A as having an auroral origin.
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