Resonance condition and low-frequency quasi-periodic oscillations of the outbursting source H1743-322

It has long been proposed that low-frequency quasi-periodic oscillations (QPOs) in stellar-mass black holes or their equivalents in supermassive black holes are the result of resonances between infall and cooling timescales. We explicitly compute these two timescales in a generic situation to show that resonances are easily achieved. During an outburst of a transient black hole candidate, the accretion rate of the Keplerian disc as well as the geometry of the Comptonizing cloud change very rapidly. During some period, a resonance condition between the cooling timescale (predominantly by Comptonization) and the infall timescale of the Comptonizing cloud is roughly satisfied. This leads to low-frequency quasi-periodic oscillations (LFQPOs) of the Compton cloud and the consequent oscillation of hard X-rays. In this paper, we explicitly follow black hole candidate H1743-322 during its 2010 outburst. We compute the Compton cooling time and infall time over several days and show that QPOs take place when these two roughly agree within ~50 per cent, i.e., the resonance condition is generally satisfied. We also confirm that for the sharper LFQPOs (i.e. higher Q-factors) the ratio of the two timescales is very close to 1.