Some polars show quasi-periodic oscillations (QPO) in their optical light curves which have been interpreted as the result of shock oscillations driven by the cooling instability. Although numerical simulations can recover this physics, they wrongly predict QPOs in the X-ray luminosity and have also failed to reproduce the observed frequencies, at least for the limited range of parameters explored so far. Given the uncertainties on the observed polar parameters, it is still unclear whether simulations can reproduce the observations. The aim of this work is to study QPOs covering all relevant polars showing QPOs. We perform numerical simulations including gravity, cyclotron and bremsstrahlung radiative losses, for a wide range of polar parameters, and compare our results with the astronomical data using synthetic X-ray and optical luminosities. We show that shock oscillations are the result of complex shock dynamics triggered by the interplay of two radiative instabilities. The secondary shock forms at the acoustic horizon in the post-shock region in agreement with our estimates from steady-state solutions. We also demonstrate that the secondary shock is essential to sustain the accretion shock oscillations at the average height predicted by our steady-state accretion model. Finally, in spite of the large explored parameter space, matching the observed QPO parameters requires a combination of parameters inconsistent with the observed ones. This difficulty highlights the limits of one-dimensional simulations, suggesting that multi-dimensional effects are needed to understand the non-linear dynamics of accretion columns in polars and the origins of QPOs.

Quasi-periodic oscillations (QPOs) of a few seconds have been detected in some polars, the synchronised subclass of cataclysmic systems containing a strongly magnetised white dwarf which accretes matter from a red dwarf companion. The QPOs are thought to be related to instabilities of a shock formed in the accretion column, close to the white dwarf photosphere above the impact region. We present optical observations of the polar V834 Centauri performed with the fast ULTRACAM camera mounted on the ESO-VLT simultaneously in three filters (u , He ii λ4686, r ) to study these oscillations and characterise their properties along the orbit when the column is seen at different viewing angles. Fast Fourier transforms and wavelet analysis have been performed and the mean frequency, rms amplitude, and coherence of the QPOs are derived; a detailed inspection of individual pulses has also been performed. The observations confirm the probable ubiquity of the QPOs for this source at all epochs when the source is in a high state, with observed mean amplitude of 2.1% (r ), 1.5% (He ii), and 0.6% (u ). The QPOs are present in the r filter at all phases of the orbital cycle, with a higher relative amplitude around the maximum of the light curve. They are also detected in the He ii and u filters but at a lower level. Trains of oscillations are clearly observed in the r light curve and can be mimicked by a superposition of damped sinusoids with various parameters. The QPO energy distribution is comparable to that of the cyclotron flux, consistent for the r and He ii filters but requiring a significant dilution in the u filter. New 1D hydrodynamical simulations of shock instabilities, adapted to the physical parameters of V834 Cen, can account for the optical QPO amplitude and X-ray upper limit assuming a cross section of the accretion column in the range ∼(4−5) × 10 14 cm 2 . However, the predicted frequency is larger than the observed one by an order of magnitude. This shortcoming indicates that the QPO generation is more complex than that produced in a homogeneous column and calls for a more realistic 3D treatment of the accretion flow in future modelling.