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Low frequency QPOs and possible change in the accretion geometry during the outbursts of Aquila X$-$1

We have studied the evolution of the Low Frequency Quasi-Periodic Oscillations (LFQPOs) during the rising phase of seven outbursts of the neutron star Soft X-ray Transient (SXT) Aql X$-$1 observed with the \textit{Rossi X-ray Timing Explorer (RXTE)}. The frequency correlation between the low frequency break and the LFQPO sampled on the time scale of $\sim$2 days was seen. Except for the peculiar 2001 outburst, the frequency of the LFQPOs increased with time before the hard-to-soft state transition up to a maximum $ν_{max}$ at $\sim$31 Hz, a factor of $\sim$5 higher than those seen in black hole transients such as GX 339$-$4, making the maximum QPO frequency a likely indicator of the mass of the central compact object. The characteristic frequencies increased by around ten percent per day in the early rising phase and accelerated to nearly one hundred percent per day since $\sim$2 days before the hard-to-soft state transition. We examined the dependence of the frequency $ν_{LF}$ on the source flux $f$ and found an anti-correlation between the maximum frequency of the LFQPOs and the corresponding X-ray luminosity of the hard-to-soft transition (or outburst peak luminosity) among the outbursts. We suggest that X-ray evaporation process can not be the only mechanism that drives the variation of the inner disk radius if either of the twin kHz QPO corresponds to the Keplerian frequency at the truncation radius.