The X-ray transient IGR J18245-2452 in the globular cluster M28 contains the first neutron star (NS) seen to switch between rotation-powered and accretion-powered pulsations. We analyse its 2013 March-April 25d-long outburst as observed by Swift, which had a peak bolometric luminosity of ~6% of the Eddington limit (L$_{E}$), and give detailed properties of the thermonuclear burst observed on 2013 April 7. We also present a detailed analysis of new and archival Chandra data, which we use to study quiescent emission from IGR J18245-2452 between 2002 and 2013. Together, these observations cover almost five orders of magnitude in X-ray luminosity (L$_X$, 0.5-10 keV). The Swift spectrum softens during the outburst decay (photon index $Gamma$ from 1.3 above L$_X$/L$_{E}$=10$^{-2}$ to ~2.5 at L$_X$/L$_{E}$=10$^{-4}$), similar to other NS and black hole (BH) transients. At even lower luminosities, deep Chandra observations reveal hard ($Gamma$=1-1.5), purely non-thermal and highly variable X-ray emission in quiescence. We therefore find evidence for a spectral transition at L$_X$/L$_{E}$~10$^{-4}$, where the X-ray spectral softening observed during the outburst decline turns into hardening as the source goes to quiescence. Furthermore, we find a striking variability pattern in the 2008 Chandra light curves: rapid switches between a high-L$_X$ active state (L$_Xsimeq$3.9x10$^{33}$ erg/s) and a low-L$_X$ passive state (L$_Xsimeq$5.6x10$^{32}$ erg/s), with no detectable spectral change. We put our results in the context of low luminosity accretion flows around compact objects and X-ray emission from millisecond radio pulsars. Finally, we discuss possible origins for the observed mode switches in quiescence, and explore a scenario where they are caused by fast transitions between the magnetospheric accretion and pulsar wind shock emission regimes.
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