Probing the hard and intermediate states of X-ray binaries using short time-scale variability

Below an accretion rate of approximately a few per cent of the Eddington accretion rate, X-ray binary systems are not usually found in the soft spectral state. However, at accretion rates a factor of a few lower still, in the hard state, there is another spectral transition which is well observed but not well understood. Below $\mathord {\sim }0.5$ –1 per cent of the Eddington accretion rate ( $\dot{m}_{\rm crit}$ ), the spectral index hardens with increasing accretion rate, but above $\dot{m}_{\rm crit}$ , although still in the hard state, the spectral index softens with increasing accretion rate. Here we use a combination of X-ray spectral fitting and a study of short time-scale spectral variability to examine the behaviour of three well-known X-ray binaries: Cygnus X-1, GX 339-4 and XTE J1118+480. In Cygnus X-1 we find separate hard and soft continuum components, and show using root mean square (rms) spectra that the soft component dominates the variability. The spectral transition at $\dot{m}_{\rm crit}$ is clearly present in the hard-state hardness–intensity diagrams of Cygnus X-1. Above $\dot{m}_{\rm crit}$ , GX 339-4 shows similar softer-when-brighter behaviour at both long and short time-scales. Similarly, XTE J1118+480, which remains well below $\dot{m}_{\rm crit}$ , has harder-when-brighter behaviour on all time-scales. We interpret these results in terms of two continuum components: a hard power law which dominates the spectra when the accretion rate is low, probably arising from Comptonization of cyclo-synchrotron photons from the corona, and a soft power law which dominates at higher accretion rates, arising from Comptonization of seed photons from the accretion disc.