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Dwarf novae (DNe) and low mass X-ray binaries (LMXBs) are compact binaries showing variability on time scales from years to less than seconds. Here, we focus on explaining part of the rapid fluctuations in DNe, following the framework of recent studies on the monthly eruptions of DNe that use a hybrid disk composed of an outer standard disk and an inner magnetized disk. We show that the ionization instability, that is responsible for the monthly eruptions of DNe, is also able to operate in the inner magnetized disk. Given the low density and the fast accretion time scale of the inner magnetized disk, the ionization instability generates small, rapid heating and cooling fronts propagating back and forth in the inner disk. This leads to quasi-periodic oscillations (QPOs) with a period of the order of $1000$ s. A strong prediction of our model is that these QPOs can only develop in quiescence or at the beginning/end of an outburst. We propose that these rapid fluctuations might explain a subclass of already observed QPOs in DNe as well as a, still to observe, subclass of QPOs in LMXBs. We also extrapolate to the possibility that the radiation pressure instability might be related to Type B QPOs in LMXBs.
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