Magnetic cataclysmic variables are close binary systems containing a strongly magnetized white dwarf that accretes matter coming from an M-dwarf companion. High-energy radiation coming from those objects is emitted from the accretion column close to
the white dwarf photosphere at the impact region. Its properties depend on the characteristics of the white dwarf and an accurate accretion column model allows the properties of the binary system to be inferred, such as the white dwarf mass, its magnetic field, and the accretion rate. We study the temporal and spectral behaviour of the accretion region and use the tools we developed to accurately connect the simulation results to the X-ray and optical astronomical observations. The radiation hydrodynamics code Hades was adapted to simulate this specific accretion phenomena. Classical approaches were used to model the radiative losses of the two main radiative processes: bremsstrahlung and cyclotron. The oscillation frequencies and amplitudes in the X-ray and optical domains are studied to compare those numerical results to observational ones. Different dimensional formulae were developed to complete the numerical evaluations. The complete characterization of the emitting region is described for the two main radiative regimes: when only the bremsstrahlung losses and when both cyclotron and bremsstrahlung losses are considered. The effect of the non-linear cooling in- stability regime on the accretion column behaviour is analysed. Variation in luminosity on short timescales (~ 1 s quasi-periodic oscillations) is an expected consequence of this specific dynamic. The importance of secondary shock instability on the quasi-periodic oscillation phenomenon is discussed. The stabilization effect of the cyclotron process is confirmed by our numerical simulations, as well as the power distribution in the various modes of oscillation.
Quasi-periodic oscillations (QPOs) are observed in the optical flux of some polars with typical periods of 1 to 3 s but none have been observed yet in X-rays where a significant part of the accreting energy is released. QPOs are expected and predicte
d from shock oscillations. Most of the polars have been observed by the XMM-Newton satellite. We made use of the homogeneous set of observations of the polars by XMM-Newton to search for the presence of QPOs in the (0.5-10 keV) energy range and to set significant upper limits for the brightest X-ray polars. We extracted high time-resolution X-ray light curves by taking advantage of the 0.07 sec resolution of the EPIC-PN camera. Among the 65 polars observed with XMM-Newton from 1998 to 2012, a sample of 24 sources was selected on the basis of their counting rate in the PN instrument to secure significant limits. We searched for QPOs using Fast Fourier Transform (FFT) methods and defined limits of detection using statistical tools. Among the sample surveyed, none shows QPOs at a significant level. Upper limits to the fractional flux in QPOs range from 7% to 71%. These negative results are compared to the detailed theoretical predictions of numerical simulations based on a 2D hydrodynamical code presented in Paper II. Cooling instabilities in the accretion column are expected to produce shock quasi-oscillations with a maximum amplitude reaching ~ 40% in the bremsstrahlung (0.5-10 keV) X-ray emission and ~ 20% in the optical cyclotron emission. The absence of X-ray QPOs imposes an upper limit of ~ (5-10) g.cm-2.s-1 on the specific accretion rate but this condition is found inconsistent with the value required to account for the amplitudes and frequencies of the observed optical QPOs. This contradiction outlines probable shortcomings with the shock instability model.
