  We studied the outburst properties of the hyper-luminous X-ray source ESO
243-49 HLX-1, using the full set of Swift monitoring observations. We
quantified the increase in the waiting time, recurrence time, and e-folding
rise timescale along the outburst sequence, and the corresponding decrease in
outburst duration, total radiated energy, and e-folding decay timescale, which
confirms previous findings. HLX-1 spends less and less time in outburst and
more and more time in quiescence, but its peak luminosity remains approximately
constant. We compared the HLX-1 outburst properties with those of bright
Galactic low-mass X-ray binary transients (LMXBTs). Our spectral analysis
strengthens the similarity between state transitions in HLX-1 and those in
Galactic LMXBTs. We also found that HLX-1 follows the nearly linear
correlations between the hard-to-soft state transition luminosity and the peak
luminosity, and between the rate of change of X-ray luminosity during the rise
phase and the peak luminosity, which indicates that the occurrence of the
hard-to-soft state transition of HLX-1 is similar to those of Galactic LMXBTs
during outbursts. We found that HLX-1 does not follow the correlations between
total radiated energy and peak luminosity, and between total radiated energy
and e-folding rise/decay timescales we had previously identified in Galactic
LMXBTs. HLX-1 would follow those correlations if the distance were several
hundreds of kiloparsecs. However, invoking a much closer distance for HLX-1 is
not a viable solution to this problem, as it introduces other, more serious
inconsistencies with the observations.
