Context. Chemically peculiar stars of the upper part of the main sequence show periodical variability in line intensities and continua, modulated by the stellar rotation, which is attributed to the existence of chemical spots on the surface of these stars. The flux variability is caused by the changing redistribution rate of the radiative flux predominantly from the short-wavelength part of the spectra to the long-wavelength part, which is a result of abundance anomalies. Many details of this process are still unknown. Aims. We study the nature of the multi-spectral variability of one of the brightest chemically peculiar stars, θ Aur. Methods. We predict the flux variability of θ Aur from the emerging intensities calculated for individual surface elements of the star taking into account horizontal variation of chemical composition. The surface chemical composition was derived from Doppler abundance maps. Results. The simulated optical variability in the Str?mgren photometric system and the ultraviolet flux variability agree well with observations. The IUE flux distribution is reproduced in great detail by our models in the near ultraviolet region. A minor disagreement remains between the observed and predicted fluxes in the far ultraviolet region. The resonance lines of magnesium and possibly also some lines of silicon are relatively weak in the ultraviolet domain, which indicates non-negligible vertical abundance gradients in the atmosphere. We also derive a new period of the star, P = 3.618 664(10)?d, from all available photometric and magnetic measurements and show that the observed rotational period is constant over decades. Conclusions. The ultraviolet and visual variability of θ?Aur is mostly caused by silicon bound-free absorption and chromium and iron line absorption. Manganese also contributes to the variability, but to a lesser extent. These elements redistribute the flux mainly from the far-ultraviolet region to the near-ultraviolet and optical regions in the surface abundance spots. The light variability is modulated by the stellar rotation. The ultraviolet domain is key for understanding the properties of chemically peculiar stars. It provides a detailed test for surface abundance models and comprises many lines that originate from states with a low excitation potential, which enable detecting vertical abundance gradients.
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